CN108810534B - Image compression method based on direction lifting wavelet and improved SPIHT under Internet of things - Google Patents

Abstract

The invention relates to an image compression method based on direction lifting wavelet and improved SPIHT under the Internet of things. The invention aims to solve the problem that the existing SPIHT method rarely considers edge blurring or ringing effect caused by the lack of high-frequency information, cannot keep more details in an image and causes low coding efficiency. The process is as follows: firstly, obtaining a segmented image block; secondly, obtaining the optimal prediction direction of the segmented image block; thirdly, performing weighted direction interpolation on the fractional sample value by calculating a weighted direction interpolation filter coefficient to obtain an interpolation image block; fourthly, wavelet transformation based on direction lifting is respectively carried out on the interpolation image blocks by utilizing the optimal prediction direction to obtain each transformed image block; fifthly, forming a whole transformed image by all the transformed image blocks; and sixthly, coding the transformed image obtained by the fifth step by utilizing an improved SPIHT method to obtain a coded image. The invention is used in the field of image compression.

Description

Image compression method based on direction lifting wavelet and improved SPIHT under Internet of things

Technical Field

The present invention relates to an image compression method.

Background

Due to the great progress of computing technology and sensor technology in recent years, the Internet of things (IoT) has also entered a rapid development period [1](Sezer OB, Dogdie, Ozbayoglu AM (2018) Context-Aware Computing, Learning, and Big Data in Internet of Things: A Survey. IEEE Internet of Things Journal5(1):1-27.http:// dx. doi. org/10.1109/JIOT.2017.2773600). In the IoT sense, "object" refers to a broader range of devices, such as heart monitoring devices, temperature measuring devices, and automotive vehicles [2-3 ]]([2]XuL D.,HeW,Li S(2014)Internet of things in industries:a survey.IEEE Transactions on Industrial Informatics10(4):2233-2243.http://dx.doi.org/ 10.1109/TII.2014.2300753[3]Iqbal M, Farhan M, Jabbar S, et al (2018) Multimedia based IoT-centralized smart frame for eLearing paradigm multimed objects Appl 1-20 https:// doi. org/10.1007/S11042-018-. IoT allows these devices to be remotely aware or remotely controlled through network infrastructure, while the node energy, storage space, and network bandwidth of such networks are much smaller than traditional networks. Moreover, with the development of multimedia technology, the amount of data to be transmitted is also increasing rapidly, and users often put higher demands on the quality of multimedia signals (such as images or videos). Therefore, how to efficiently transmit multimedia signals in an IoT environment is a problem that needs to be solved urgently. The basic result of an IoT system is shown in fig. 1. In IoT, different devices are often used for different applications, which makes them have different data processing capabilities and transmission requirements [4](Khan R,Khan S U,Zaheer R,et al(2013)Future Internet:The Internet of Things Architecture,Possible Applications and Key Challenges[C]International Conference on Frontiers of Information technology. IEEE,257-260.http:// dx.doi.org/10.1109/FIT.2012.53). In this case, a compression method having low complexity and capable of supporting multi-bit rate transmission is more suitable. As a key technology in multimedia communication, image compression is indispensable in our lives. An efficient image compression method capable of being implementedThe statistical correlation of the signals is utilized, the signals are fully represented, and then the represented signals are effectively coded. In order to improve the compression performance of images, scholars at home and abroad do a lot of work on image representation and coding performance improving methods. In image representation, transform-based methods are most commonly used. The Discrete Cosine Transform (DCT) is the basis of the JPEG standard. JPEG performs well at low compression ratios, and when the compression ratio is high, blocking artifacts occur in the reconstructed image. Discrete Wavelet Transform (DWT) solves this problem and has been the most important tool in the field of image analysis and coding for the past two decades [ 5]](Liu S, Fu W, He L, et al (2017) Distribution of primary additional errors in fractional encoding method. multimed Tools Appl76(4):5787-5802.http:// dx. doi. org/10.1007/S11042-014-. Many well-known image compression methods or standards, e.g. EZW [ 6]](J.M.Shapiro(1993)Embedded image coding using zerotrees of wavelet coefficients.IEEE Trans Signal Process41(12):3445–3462.http://dx.doi.org/10.1109/78.258085)、SPIHT[7](Said A,Pearlman W A(1996)A new,fast,and efficient image codec based on set partitioning in hierarchical trees.IEEE Trans Circuits SystVideo Technol6(3):243–250.http://dx.doi.org/10.1109/76.499834)、SPECK[8](Pearlman W A, Islam A, NagarajN, Said A (2004) Efficient low complexity image coding with a set-partitioned block code. IEEE transistors Circuits System Video Technol,14(3) 1219-1235. http:// dx. doi. org/10.1109/TCSVT.2004.835150), and JEPG2000[ 9] [9](JPEG2000 Image Coding System, ISO/IEC Std.15444-1, (2000)), all are based on DWT. Although DWT can effectively represent horizontal and vertical directional information of an image, its isotropic nature makes it impossible to represent well directional features of an image, such as edges and textures [10 ]](Shi C, Zhang J, Chen H, Zhang Y (2015) A Novel Hybrid Method for Remote Sensing Image application Using the Tetrolet transform. IEEE Jsel Topics apply observer Observ 7(12):4949-4959.http:// dx. doi. org/10.1109/JTARS. 2014.2319304). Therefore, some directional wavelet bases are proposed, such as curvelet [ 1]1](Candès E J,Donoho D L(2004)New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities.Commun Pure Appl Math57(2):219–266.http://dx.doi.org/10.1002/cpa.10116)、contourlet[12](Do M N,Martin V(2005)Thecontourlet transform:an efficient directional multiresolution image representation,IEEE Trans Image Process 14(2):2091-2106.http://dx.doi.org/10.1109/TIP.2005.859376)、directionlet[13](V.Velisavljevic, B.Beferul-Lozano, M.Vetterli, P.L.Dragatti (2006) Directionales: Anisocropic polydirectional representation with a secondary filtering. IEEE Trans Image Process15(7): 1916-1933. http:// dx.doi.org/10.1109/TIP.2006.877076), and shearlet [14](Kutyniok G, Lim WQ (2011) Full length article: compact supported short areas optimal space. journal of application Theory163:1564-1589.http:// dx. doi. org/10.1016/j. jat.2011.06.005) and the like. These wavelet bases are sensitive to certain specific directions, so that more specific direction characteristics of the image can be reserved. Some adaptive directional wavelet bases, such as bandelet [15 ]](Erwan L P,Stéphane M(2005)Sparse geometric image representations with bandelets.IEEE Trans Signal Process 14(4):423-438.http://dx.doi.org/10.1109/TIP.2005.843753)、wedgelet[16](Donoho D L(1999)Wedgelets:nearly minimax estimation of edges.Annals of Statistics27(3):859-897.http://dx.doi.org/10.1214/aos/1018031261)、grouplet[17](Mallat S (2009) geographic groups. appl. Computt Harmon Anal26(2):161-180.http:// dx. doi. org/10.1016/j. acha.2008.03.004), and EPWT (easy path wall transform), enabling more flexible representation of images. However, these wavelet bases are often of complex design, some of which are even redundant, which makes them less widely used in image compression.

The wavelet lifting-based method can perform self-adaptive lifting on the local part of the image. Many efforts are made to incorporate specific lifting methods into the wavelet transformation framework to improve the compression performance, such as [19-23] ([19] Ding W, Wu F, Wu X, Li S, Li H (2007) Adaptive directional-base wave transform for Image coding. IEEE Transmission Image Process16 (2):416-427.http:// dx. doi. org/10.1109/TIP.2005.843753[20] C.Chang and B.Gid (2007) direct Adaptive vector wave transform for Image compression. IEEE.102 (5): 1289-36859// dx. doi. doi.org/10.1109/TIP.2007.8942 [21] Zhang L (Qiant 3. 2013. 2017. Zusand) coding. Zusand W.12. Zusand-19. Zusand [19] C.7. 7. 3619.35. Zusand ] C.35. Zusand [ 19.7 ] C.7. Zusand Process 1:1-9.http:// dx. doi. org/10.1186/s 13634-016. 0443-y [23] Hasan M, Wahid K A (2017) Low-Cost Architecture of Modified Daubechies Lifting Wavelets Using Integrated Polymer mapping. IEEE transistors Syst 64(5):585-589.http:// doi. org/10.1109/tcsii.2016.2584091). These lifting-based compression methods are usually associated with adaptive segmentation, statistical modeling, directional prediction, or modified wavelet bases, and the lifting of compression performance is mainly derived from rate-distortion optimization-based segmentation or side-information coding. Of these methods, protection of important details of the image is rarely considered during compression. This problem affects further improvement of coding efficiency, especially for texture regions. Moreover, the details of the image cannot be adequately represented, and the subjective quality of the reconstructed image is also affected. Therefore, how to design an effective image representation method is an important issue in image compression.

Encoding is another key link in image compression. For wavelet transformed images, coefficients at the same spatial position in different high frequency subbands have strong correlation. Furthermore, after efficient image representation, a large number of unimportant "blocks" typically appear in the high frequency region of the wavelet. The coding performance is further improved if these unimportant "blocks" can be coded in a suitable way. For wavelet transform-based Image compression, embedded block Coding with optimized truncation (EBCOT) is a well-known Coding method and adopted by the JPEG2000 standard [9] (JPEG2000 Image Coding System, ISO/IEC std.15444-1, (2000)). The basic idea of EBCOT is to divide each sub-band into several blocks, such as 32 × 32 or 64 × 64, then encode these blocks separately, and truncate these code streams according to post-compression rate distortion (PCRD) techniques at different bit rates. Although better coding performance can be achieved, one drawback of JPEG2000 is that the correlation between co-located coefficients between sub-bands [24] is not exploited (Christophe E, Mailhes C, Duhamel P (2008) Hyperspectral Image compression: adaptive SPIHT and EZW to anisotropic 3-D wave coding. IEEE Trans Image Process17(12):2334-2346.http:// dx. doi. org/10.1109/TIP.2008.2005824). According to the analysis of [25] (D.S. Taubman and M.W. Marcellin (2002) JPEG2000 Image Compression Fundamentals, Standards and practice. Boston, MA: Kluwer), the selection of the truncation point in JPEG2000 compensates the deficiency of the paternal-to-daughter relationship between the unutilized subbands. However, this is at the cost of higher computational complexity. [26] (Lewis A S, knowledge G (1992) Image Compression Using the 2-D Wavelet transform. IEEE Transmission Image Process 1(2):244-250.http:// dx. doi. org/10.1109/83.136601) indicates that a tree structure is an effective way to represent the relationship of subband coefficients in Wavelet images. For tree data structures, SPIHT is one of the most common encoding methods, and can utilize parent-child relationships between subbands to provide better encoding performance. In recent years, image compression methods based on modified SPIHT have been proposed, such as [27-29] ([27] Hamdi M, Rhouma R, Belghith S (2017) A selective compression-encryption of images based on SPIHT coding and Chirikov Standard Map 131:514-526.Signal Processing. http:// dx. doi. org/10.1016/J. signature. 2016.09.09.011 [28] Song X, HuangQ, Chang S, He J, Wang H (2016) Three-dimensional decoded-based SPIHT algorithm for fast compression of images based on SPIHT compression method [ 80-539. 10. 12. JJ.: SPIHT 19/18. J.) -compressed images [ 10.26.7 ] J./J.: modified SPIHT compression method [ 10.26.7.7 ] S/2016.26.80/80. 12. JJ.: III. 12. III.26. JJ.) -compressed images [ 10.7.8.7. JJ.: SPIH.7. III.8. III.7. J.: III.8. III. III.2016. III. D.7. III. D.7. III. D.3. III. D.7. III. 3. III. D, jang JH, Lee HJ, Rhee CE (2017) Fine-scalable SPIHT Hardware Design for Frame Memory Compression in Video codec.journal of Semiconductor Technology Andence17(3):446-457.http:// dx. doi.org/10.5573/JTS.2017.17.3.446 [31] El-Baker EM, El-Rabaie S, Zahra O, El-SamieFEA (2017) Chart Intervision for the Transmission of Compressed Video Frame with Self-Embedded Digital signals 96(2): 17-1651. wizard 19. WO 25. J.: Graphics J.3332/19. J.15. 12. J.32. software Graphics of Image Graphics. This suggests that the SPIHT approach is a popular technique in multimedia communication due to its low complexity and flexibility. Although much research has been done on the SPIHT method, most of these studies have focused on how to further reduce bit redundancy or scan redundancy, taking into account little edge blurring or ringing effects caused by the absence of high frequency information.

Disclosure of Invention

The invention aims to solve the problem that the encoding efficiency is low because the edge blurring or the ringing effect caused by the lack of high-frequency information is rarely considered in the conventional SPIHT method and more details in an image cannot be reserved, and provides an image compression method based on direction lifting wavelet and improved SPIHT in the Internet of things.

The image compression method based on the direction lifting wavelet and the improved SPIHT under the Internet of things comprises the following specific processes:

firstly, carrying out image block segmentation on a remote sensing image to obtain a segmented image block;

step two, respectively calculating the optimal prediction direction of the divided image blocks to obtain the optimal prediction direction of the divided image blocks;

step three, performing weighted direction interpolation on the fractional sample value by calculating a weighted direction interpolation filter coefficient to obtain an interpolation image block;

step four, wavelet transformation based on direction lifting is respectively carried out on the interpolation image blocks by utilizing the optimal prediction direction obtained in the step two, and each transformed image block, namely each transformed code block, is obtained;

step five, forming a whole transformed image by all the transformed image blocks;

and step six, encoding the transformed image obtained in the step five by using an improved SPIHT method to obtain an encoded image.

The invention has the beneficial effects that:

the invention provides a new image compression method, which combines adaptive-based adaptive lifting wavelet transform (DIAL-DWT) based on directional interpolation with an improved SPIHT method. The main innovation points comprise two parts: the method comprises the steps of firstly, the proposed adaptive lifting wavelet transform can fully represent an image by utilizing a direction interpolation filter and an optimal adaptive lifting direction; and secondly, the improved SPIHT coding method can keep important detail information in the image as much as possible and can provide better overall coding performance. The proposed compression method is asymmetric with low complexity at the decoding end, which makes the method very suitable for various IoT terminals with different requirements on data transmission and real-time. The experimental result shows that the proposed method not only has higher compression performance than the traditional compression method, but also can improve the subjective quality of the reconstructed image to a great extent.

The invention designs a DIAL model which can respectively calculate the optimal lifting directions of all image blocks and carry out weighted direction interpolation on fractional samples in the lifting process. Therefore, the DIAL model based wavelet transform can provide more effective image representation by combining the optimal direction prediction and the weighted direction interpolation in the direction lifting process, which helps to keep more direction characteristics of the image. Due to the high concentration of image energy, the image representation method can provide more 'longer' zero trees, thereby improving the coding efficiency. The method solves the problem that the existing SPIHT method rarely considers edge blurring or ringing effect caused by the loss of high-frequency information, can not keep more details in the image and causes low coding efficiency.

The present invention designs an improved SPIHT method, which only changes the scanning order of the List of Insignificant Sets (LIS) in the existing SPIHT method, and can encode more significant coefficients at the same bit rate without additional calculation. The improved SPIHT method can keep more important detail information in the image, can improve the whole coding performance, does not need extra calculation amount and does not need extra bits as a header file.

The images in different image libraries are used for testing under different bit rates, and experimental results show that the PSNR is improved by 1.3dB at most.

Drawings

Fig. 1 is a basic IoT system framework diagram;

FIG. 2a is a diagram of the basic forward decomposition process of one-dimensional direction lifting wavelet transform, where X is the original image and X is_eFor even sample sets in an image, X_oFor sets of odd samples in the image, DA _ P_oFor the direction adaptive predictor, DA _ U, used in the first stage of the transformation_oFor the direction-adaptive update operator, DA _ P, used in the first-stage transformation_kFor the direction adaptive predictor, DA _ U, used at the k-1 th transformation_kFor the direction-adaptive update operator, K, used during the K-1 th transformation_eFor weighting the low-frequency components of the transformed image, K_oThe weight value after the high-frequency component of the transformed image is weighted, wherein a is the low-frequency component of the finally obtained transformed image, and b is the high-frequency component of the finally obtained transformed image;

FIG. 2b is a diagram of the basic process of inverse synthesis of one-dimensional lifting wavelet transform, x_eFor reconstructing a set of even samples in an image, x_oA set of odd samples in the reconstructed image;

FIG. 3a is a schematic diagram of a reference direction set of a horizontal wavelet transform based on direction lifting, where m is an image block position abscissa and n is an image block position ordinate;

FIG. 3b is a schematic diagram of a reference direction set of a vertical wavelet transform based on direction lifting;

FIG. 4 is a process diagram for calculating the best prediction direction for a given image block, k being the number of reference directions;

FIG. 5 is a process diagram of directional interpolation in horizontal variation;

FIG. 6 is a process diagram for generating a directional interpolation filter, a_-3、a_-2、a_-1、a₀、a₁、a₂Is a parameter of the interpolation filter;

FIG. 7a is a graph of the result of a one-level wavelet decomposition of the 9/7 wavelet filter;

FIG. 7b is a diagram of the result of one-level wavelet decomposition of an ADL-based wavelet filter;

FIG. 7c is a diagram of the result of one-level wavelet decomposition of a DIAL model based wavelet filter;

FIG. 8 is a diagram of NLA results obtained by different sparse representation methods, where NLA is nonlinear estimation, The DIAL model is DIAL (direct-Adaptive-wavelet transform) model, ADL is Adaptive-direction-lifting (Adaptive-direction-boosting), and PSNR is peak SNR;

fig. 9a is a schematic view of a Europa3 test remote sensing image set;

FIG. 9b is a schematic diagram of a bank test remote sensing image set;

FIG. 9c is a schematic view of an aesial test remote sensing image set;

FIG. 9d is a schematic view of a Lena test remote sensing image set;

FIG. 9e is a schematic diagram of a Baboon test remote sensing image set;

FIG. 9f is a schematic diagram of a pleiades _ portdebouc _ pan test remote sensing image set;

FIG. 10 is a graph comparing the Kappa coefficient results of the proposed method and the SPIHT method at different bit rates; the abscissa is the bit rate in bpp; the ordinate is the Kappa coefficient;

lenaproposed compresses a test image Lena by the method, and Lena SPIHT compresses the test image Lena by the SPIHT method;

baboonpoposed is the test image Baboon compression by the method of the invention, and Baboon SPIHT is the test image Baboon compression by the SPIHT method;

the bank disposition is the compression of the test image bank by the method, and the bank SPIHT is the compression of the test image bank by the SPIHT method;

the aeial deployed is the test image aeial compression by the method of the invention, and the aeial SPIHT is the test image aeial compression by the SPIHT method;

europa3 deployed compresses the test image europa3 by the method, europa3 SPIHT compresses the test image europa3 by the SPIHT method;

WoodlandHills deployed is compression of a test image by the method, and WoodlandHills SPIHT is compression of the test image by the SPIHT method;

FIG. 11a is a reconstructed image obtained by the compression method proposed in the present invention at a bit rate of 0.0625 bpp;

FIG. 11b is a reconstructed image obtained by the conventional SPIHT method at a bit rate of 0.0625bpp

FIG. 11c is a reconstructed image obtained by the compression method proposed by the present invention at a bit rate of 0.125 bpp;

FIG. 11d is a reconstructed image obtained by the conventional SPIHT method at a bit rate of 0.125 bpp;

FIG. 11e is a reconstructed image obtained by the compression method proposed in the present invention at a bit rate of 0.25 bpp;

FIG. 11f is a reconstructed image obtained by the conventional SPIHT method at a bit rate of 0.25 bpp;

FIG. 11g is a reconstructed image obtained by the compression method proposed in the present invention at a bit rate of 0.5 bpp;

FIG. 11h is a reconstructed image obtained by the conventional SPIHT method at a bit rate of 0.5 bpp;

FIG. 11i is a reconstructed image obtained by the compression method proposed in the present invention at a bit rate of 1 bpp;

fig. 11j is a reconstructed image obtained by the conventional SPIHT method at a bit rate of 1 bpp.

Detailed Description

The first embodiment is as follows: the image compression method based on the direction lifting wavelet and the improved SPIHT under the Internet of things of the embodiment comprises the following specific processes:

firstly, carrying out image block segmentation on a remote sensing image to obtain a segmented image block;

step two, respectively calculating the optimal prediction direction of the divided image blocks to obtain the optimal prediction direction of the divided image blocks;

step three, performing weighted direction interpolation on the fractional sample values required to be used in the direction lifting process by calculating weighted direction interpolation filter coefficients to obtain an interpolated image block;

step four, wavelet transformation based on direction lifting is respectively carried out on the interpolation image blocks by utilizing the optimal prediction direction obtained in the step two, and each transformed image block, namely each transformed code block, is obtained;

step five, forming a whole transformed image by all the transformed image blocks;

and step six, encoding the transformed image obtained in the step five by using an improved SPIHT method to obtain an encoded image.

The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: carrying out image block segmentation on the remote sensing image in the first step to obtain segmented image blocks; the specific process is as follows:

in order to make the lifting direction consistent with the local texture direction of the image, image segmentation is firstly carried out. In document [19], a rate-distortion optimization segmentation method based on a quadtree is adopted. However, the efficiency of such segmentation methods is strongly related to the image content. For some image types, such as remote sensing images, complex landforms are usually reflected, so that detailed information is usually abundant, and a large-area flat area is rarely available, and the advantage of the adaptive segmentation method is difficult to show. The reason is that, as a result of the adaptive segmentation method for images with complex content, it is likely that almost all blocks are the smallest blocks that allow segmentation, which is almost equivalent to the result of directly performing the same-size block segmentation, but at the cost of higher computational complexity. Furthermore, another overhead of using the adaptive partitioning method is a large amount of side information. For rate-distortion optimization based methods, the corresponding "partition tree" is different for different bit rates. For correct decoding, these "partition trees" are also sent as side information to the decoding side. The more complex the image content, the more branches of the "split tree" and the more side information is generated therefrom. Therefore, the rate-distortion optimized segmentation method based on the quadtree is not suitable for all images.

Based on the above analysis, in order to make the segmentation method general, a block segmentation method of the same size is adopted here. For an image I of size M × N, the block size is assumed to be 16 × 16. Thus, the initial image block may be represented as B_i,j,i＝1,2,K,M/16,j＝1_,2, N/16. Any two image blocks are non-repeating and all image blocks constitute the whole image I. After transformation, the block size depends on the number of decomposition levels. Assuming that the total number of decomposition layers of the directional wavelet transform is J, for decomposition layer k, the corresponding block size is L_k×L_k. That is to say that

L_k＝16/2^k-1,k＝1,2,K,J

Compared with the adaptive quadtree segmentation method based on rate distortion optimization, the segmentation method with the same size greatly reduces the complexity and does not need to transmit side information.

Next, the best prediction direction for each block is calculated. Assume a set of reference directions as θ_ref＝[-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7]For each block B_lL is 0,1, K MN/256-1, corresponding to the best prediction direction

Is composed of

D (-) represents a measure of image distortion. Herein, D (·) is defined as | · |. That is, for each block B_lThe best prediction direction is the direction corresponding to the smallest prediction error. The process of finding the best block prediction direction is shown in fig. 4.

From fig. 4 it can be concluded that for a given image, first all the reference directions theta are followed_ref,i(i ═ 1,2, K,15), directional wavelet transforms were performed, respectively. Then, in these transformed images, the same image is subjected toBlock B of positions_l(l is 0,1, K, MN/256-1) calculating prediction errors, and calculating an optimal prediction direction corresponding to a direction of the minimum prediction error

The prediction and update process for each sample in an image block is shown in fig. 2 a.

Compared with the self-adaptive segmentation method, the proposed direction lifting wavelet transform does not need to transmit 'segmentation trees' at each bit rate, and only needs to transmit the optimal prediction direction of each block. Therefore, the side information required for the proposed method is small.

The remote sensing image is divided into blocks with the same size to obtain divided image blocks, wherein the block division size is consistent with the block size of the later encoding stage.

Adaptive lifting wavelet transform (DIAL-DWT) based on directional interpolation

Conventional two-dimensional lifting wavelet transforms only utilize neighboring samples in either the horizontal or vertical direction. However, most natural images contain many different directional information, such as edges, contours, and textures, which makes the conventional two-dimensional lifting wavelet transform not well-represented. How to provide an effective image representation method is the key to improve the image compression performance. Here, a new DIAL-DWT method is proposed. The method now divides the image into blocks and then calculates the best lifting direction for each block. Next, the fractional samples are interpolated using a directional interpolation filter, thereby preserving more directional characteristics in the interpolated image. The detailed design process of the DIAL-DWT method is as follows.

Structure of directional lifting wavelet transform

A typical lifting wavelet transform contains four steps: splitting, predicting, updating, and normalizing [33] (Sweldens W (1995) The lifting scheme: a constraint of second generation distances. SIAM J Math Anal29(2):511-546.http:// dx. doi. org/10.1137/S0036141095289051). Without loss of generality, the basic direction-lifting wavelet transform is also based on these four steps. The framework of the one-dimensional direction lifting wavelet transform and the inverse transform are shown in fig. 2a and 2b, respectively.

For a two-dimensional image x (m, n)_m,n∈ZFirst, all samples are divided into two parts: set of even samples x_eAnd odd sample set x_o。

In the prediction stage, the odd samples are predicted by the adjacent even samples, and the prediction direction is obtained by a certain decision criterion. Assuming that the direction adaptive predictor is DA _ P, the prediction process can be expressed as

d[m,n]＝x_o[m,n]+DA_P_e[m,n] (2)

In the update stage, the even samples are updated by the prediction errors of the neighboring samples, and the update direction is the same as the prediction direction. Assuming that the direction adaptive update operator is DA _ U, the update process can be represented as

c[m,n]＝x_e[m,n]+DA_U_d[m,n] (3)

Here, the direction predictor DA _ P is

The direction update operator DA _ U is

Here, p_iAnd u_jRepresenting the coefficients of a high-pass filter and a low-pass filter, respectively. Theta_vIndicating the direction of prediction and update.

Finally, the boosted outputs are each given a factor K_eAnd K_oThe weighting is performed.

After the above process is finished, one low-pass sub-band L and one high-pass sub-band H in the horizontal direction can be obtained. Next, in the same manner, one-dimensional column direction conversion is performed.

The choice of the lifting direction theta is very important. In order to perform better image representation, an image is firstly divided into a plurality of image blocks, and the lifting direction of each block is calculated respectively. For a given block, all samples within the block are lifted in the same direction. Theoretically, the more reference lifting directions, the better the representation of the image block, but the more side information that needs to be transmitted. Conversely, if there are only a few reference lifting directions, the image is not represented well. Here, 15 reference lifting directions are selected for both the one-dimensional horizontal and vertical transforms, as shown in fig. 3a and 3b, respectively. The directional filter may be along direction d ═ (d)_x,d_y)^T,d∈i²And (4) performing representation. Here, 15 reference directions utilize some adjacent integer and fractional samples. These reference directions are as follows: d_-7＝(3,-1)^T，d_-6＝(2,-1)^T,d_-5＝(1,-1)^T,d_-4＝(3/4,-1)^T,d_-3＝(1/2,-1)^T,d_-2＝(1,-3)^T,d_-1＝(1/4,-1)^T,d₀＝(0,-1)^T,d₁＝(-1/4,-1)^T，d₂＝(-1,-3)^T，d₃＝(-1/2,-1)^T，d₄＝(-3/4,-1)^T,d₅＝(-1,-1)^T,d₆＝(-2,-1)^T,d₇＝(-3,-1)^T. The set of reference directions is shown in fig. 3.

Other steps and parameters are the same as those in the first embodiment.

The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: in the second step, the optimal prediction directions of the divided image blocks are respectively calculated to obtain the optimal prediction directions of the divided image blocks; the specific process is as follows:

for wavelet transform based on directional lifting, the prediction error and the high frequency sub-bands are closely related. The larger the prediction error, the more information in the high frequency subbands, and the lower the coding performance. For an image block, the best prediction direction should be the direction that minimizes the high frequency subband residual information.

The process of calculating the optimal prediction direction of the image block comprises the following steps: as shown in figure 4 of the drawings,

assume a set of reference directions as θ_refReference set of directions theta_refContains 15 reference directions, these directions are marked as { -7, -6, -5, -4, -3, -2, -1,0,1,2,3,4,5,6,7 }; let the total number of divided image blocks be N_aEach image block is B_l,l＝0,1,K,N_a-1；

Divided image block B_lAlong all reference directions theta respectively_ref,i(i is 1,2, K,15) performing direction prediction to obtain prediction image blocks in all reference directions;

under the mean square error criterion, the pixels of the prediction image block in all reference directions are respectively compared with the pixels of the remote sensing image in the step one, and the reference direction corresponding to the minimum error is the optimal prediction direction of the prediction image block

Optimal prediction direction for predicting image block

Is calculated as follows

Wherein D (-) is an image distortion function, and x (m, n) is an image block B_lSample value corresponding to the middle position (m, n), DA _ PⁱA predictor in the ith reference direction, m is the abscissa of the corresponding position, and n is the ordinate of the corresponding position; let D (·) ═ l |;

sample preparation: called pixels in the original image and coefficients in the transformed image. That is, before the first level of wavelet transform, it is called pixel here. But wavelet transforms are usually multi-level, starting with the second level, where they are all coefficients. For convenience of presentation, collectively referred to herein as samples.

Repeating the above process until determining the optimal prediction direction of all the divided image blocks;

compared with the self-adaptive segmentation method, the wavelet transformation method based on the direction lifting does not need to additionally transmit the 'segmentation trees' under all given bit rates, and only needs to transmit the optimal prediction direction corresponding to the block. Therefore, the proposed method requires little side information to be transmitted.

Other steps and parameters are the same as those in the first or second embodiment.

The fourth concrete implementation mode: the difference between this embodiment mode and one of the first to third embodiment modes is: in the third step, the fractional sample values required to be used in the direction lifting process are subjected to weighted direction interpolation by calculating weighted direction interpolation filter coefficients to obtain an interpolated image block; the specific process is as follows:

interpolation of direction

For wavelet transforms based on directional lifting, some lifting directions require sample values to be used to fractional positions. That is, the tangent tan θ in the lifting direction is not always an integer. Therefore, it is necessary to interpolate samples at fractional positions. The interpolation process can be expressed as

Here, k represents the integer position used in the interpolation process; a is_kRepresenting the parameters of the interpolation filter. In essence, the process of sub-pixel interpolation is the design process of the optimal interpolation filter. Most of the wavelet transformation based on the direction lifting adopts a Sinc interpolation method. However, similar to some other interpolation methods, the Sinc interpolation method also interpolates fractional samples only with samples along the horizontal or vertical direction, which may blur the directional information in the image. For images with more texture or detail, if the Sinc interpolation method is adopted, the direction prediction error will increase. Herein, a directional interpolation method is employed that interpolates fractional positions along the local texture direction using adjacent integer samples. Taking the horizontal transformation example, the process of directional interpolation is shown in fig. 5.

The integer samples used for interpolation are also different for different fractional sample positions, which is adapted to the characteristics of the local signal. Since different integer samples contribute differently to the fractional sample positions, the interpolation filters should also be different [34] (Liu Y, Ngan K N (2008) Weighted adaptive lifting-based wave velocity transform for image coding. IEEE Trans. image Process17(4):500-511.http:// dx. doi. org/10.1109/TIP. 2008.917104). The interpolation filter used is shown in fig. 6. As can be seen from fig. 6, the final coefficients of the directional interpolation filter are determined by three filters, namely, a bilinear filter, a telensor 4-tap filter, and a 2-tap filter. The coefficients of these filters are shown in table 1.

Table 1 interpolation filter coefficients

In fig. 6, a number of different integer samples are used for interpolation of fractional samples, the interpolation direction being adapted to the local characteristics of the signal used for interpolation. For example, to interpolate quarter-positioned samples, not only integer-positioned samples { a } are used_-2,a_-1,a₀,a₁Sample a along the prediction direction_-3,a₂}. These samples { a }_-3,a_-2,a_-1,a₀,a₁,a₂It can be used to construct a directional interpolation filter and then predict the samples at the fractional positions. As can be seen from FIG. 6, { a_-3,a₂Is the input of a bilinear filter, { a }_-2,a_-1,a₀,a₁The inputs of the Telenor4-tap filter are, together, the outputs of the bilinear filter and the Telenor4-tap filter constitute the input of the 2-tap filter. Thus, the output of the 2-tap filter is the coefficients of the directional interpolation filter. The correspondence of the directional interpolation filter coefficients and the different fractional position samples is shown in table 2.

TABLE 2 Directional interpolation Filter coefficients

The final output of the directional interpolation filter is determined by three filters, which are: a bilinear filter, a Telenor4-tap filter and a 2-tap filter;

in two rows below the row where the current sample is located, taking two samples in a column which is two columns away from the column where the sample is located as the input of the bilinear filter; taking four samples in the next column of the column where the sample is located respectively in the row where the current sample is located, the upper row and the lower row as the input of a Telenol 4-tap filter, wherein the outputs of the bilinear filter and the Telenol 4-tap filter form the input of a 2-tap filter, and the output of the 2-tap filter is the weighting coefficient of a directional interpolation filter;

as can be seen from FIG. 6, { c_-3,c₂Integer samples are the input to a bilinear filter, { c }_-2,c_-1,c₀,c₁Integer samples are input of a Telenor4-tap filter, outputs of a bilinear filter and a Telenor4-tap filter form input of a 2-tap filter, and the output of the 2-tap filter is a weighting coefficient of a directional interpolation filter;

by integer position samples { c_-3,c_-2,c_-1,c₀,c₁,c₂And constructing a directional interpolation filter by the aid of the weighting coefficients, and performing weighted directional interpolation on sample values of fractional positions by the directional interpolation filter to obtain an interpolation image block.

Other steps and parameters are the same as those in one of the first to third embodiments.

The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is: in the fourth step, the optimal prediction direction obtained in the second step is utilized to respectively perform wavelet transformation based on direction lifting on the interpolated image blocks to obtain each transformed image block, namely each transformed code block; the specific process is as follows:

according to the optimal prediction direction obtained in the step two

And (3) respectively utilizing formulas (2) and (3) to perform wavelet transformation based on direction lifting on the interpolation image block obtained in the step three:

the direction predictor DA _ P is

In the formula, x_e[m,n]For the even sample set of the interpolated image block, DA _ P, obtained in step three_e[m,n]A directional predictor corresponding to the even sample set; i denotes the number of the high-pass filter coefficients, p_iRepresenting high pass filter coefficients;

the interpolated image block is divided into two parts: set of even samples x_e[m,n]And odd sample set x_o[m,n]；

The direction update operator DA _ U is

Wherein j represents the number of the low pass filter coefficient, u_jRepresenting the low-pass filter coefficient, DA _ U_d[m,n]Updating operators for the directions corresponding to the odd sample sets; d [ m, n ]]For the odd samples predicted by the adjacent even samples, is expressed as

d[m,n]＝x_o[m,n]+DA_P_e[m,n]

x_o[m,n]The odd sample set of the interpolation image block obtained in the third step;

and obtaining each transformed code block by using the direction predictor and the direction update operator.

Other steps and parameters are the same as in one of the first to fourth embodiments.

The sixth specific implementation mode: the difference between this embodiment and one of the first to fifth embodiments is: in the sixth step, the transformed image obtained in the fifth step is coded by using an improved SPIHT method to obtain a coded image; the specific process is as follows:

the SPIHT coding method is to code a transform image. The coefficients mentioned in the encoding method all refer to wavelet coefficients in the transformed image.

Recently, tree-based coding methods have gained increasing attention. Among these tree-based encoding methods, the SPIHT method is most widely used because of its good rate-distortion performance and moderate complexity. However, the scanning mode of the SPIHT method limits its encoding performance. During the scan of SPIHT, the importance of a coefficient is judged only by its assigned absolute value. In fact, the human eye is sensitive to contour distortion of the image. In the high frequency subbands, the wavelet coefficients at the image contour tend to have larger magnitudes. The gray level of the image typically varies slowly, so that in the high frequency subbands, the wavelet coefficients surrounding the significant coefficients typically also have larger amplitudes. From another perspective, if the coefficients surrounding a coefficient are all significant, then there is a high probability that this coefficient will also be significant, even if the coefficient magnitude does not reach a specified threshold. The more significant a coefficient is around a coefficient, the more significant this coefficient is usually. Thus, if coefficients with many important "neighbors" are also preferentially encoded, more important coefficients are encoded at a given bit rate, thereby improving the quality of the reconstructed image.

A good image coding algorithm should not only provide good coding performance, but also have a faster operation speed. However, the two are often contradictory. The reason is that the improvement in coding performance is often at the cost of increased computational complexity. Therefore, how to reduce the algorithm complexity while providing good coding performance is another problem that needs to be studied.

An improved SPIHT method is presented herein that preferentially scans coefficients with significant "neighbors" to improve coding performance. In order to reduce the algorithm complexity, the proposed method only changes the partial scanning order of the SPIHT, and does not need extra computation. Another advantage of the proposed method is that the scanning order is adaptively determined by the previously derived significant coefficients, so that no information needs to be stored as a header file.

For the SPIHT algorithm, it represents the D-set and L-set with a List of Insignificant Sets (LIS). Firstly, initializing the LSP into a null table, initializing LIP into a lowest-frequency subband coefficient position set, and initializing LIS into a root node coordinate set of each spatial direction tree. For each bit plane, image compression is achieved by encoding the records in the LIP, LIS, and lsp in turn.

Step six, initializing a threshold value T2^n￠Initializing tables LSP, LIS and LIP; n is the maximum value of the number of bit planes;

initializing the table LSP into a null table, initializing LIP into a lowest-frequency sub-band coefficient position set, and initializing LIS into a root node coordinate set of each spatial direction tree;

sixthly, coding LIP according to the LSP, LIS and LIP of the table, wherein the process is as follows:

sixthly, judging whether the LIP set contains an important coefficient (the coefficient corresponding to the position of the important coefficient is the important coefficient) according to a threshold, if so, outputting 1 and a sign bit, wherein the coefficient is positive, the sign bit is 0, the coefficient is negative, the sign bit is 1, and the position (i, j) of the important coefficient is deleted from the LIP and added to the tail end of the LSP;

if not, outputting 0;

judging whether the LIP set contains an important coefficient according to a threshold value, wherein the process is as follows:

the coefficient is greater than the threshold value and is an important coefficient; the coefficient is less than or equal to the threshold value and is not an important coefficient;

sixthly, judging whether all coefficient positions contained in the LIP set are processed or not, and if not, executing the sixthly-two step again; if yes, executing step six and step three;

sixthly, coding LIS, wherein the process is as follows:

sixthly, judging whether the current record of the LIS is D (i, j) or L (i, j), if the current record of the LIS is D (i, j), executing step sixteenth or sixthly, and if the current record of the LIS is L (i, j), executing step sixteenth or sixthly;

d (i, j) is a coordinate set of all the descendants of the coefficient position (i, j);

l (i, j) is a coordinate set of all non-direct descendants of the coefficient position (i, j);

sixthly, judging whether the D (i, j) contains an important coefficient according to a threshold value, wherein the output is 1 if the D (i, j) contains the important coefficient, and otherwise, the output is 0;

if D (i, j) contains an important coefficient, decomposing D (i, j) into L (i, j) and O (i, j); putting L (i, j) as a mark into the tail part of the LIS;

o (i, j) is the set of coordinates for all children of coefficient position (i, j);

judging whether the D (i, j) contains an important coefficient according to a threshold value, wherein the process is as follows:

the coefficient is greater than the threshold value and is an important coefficient; the coefficient is less than or equal to the threshold value and is not an important coefficient;

building a quadtree by using 4 coefficients of O (i, j) and coding (coding as output 0 or 1), if the root (the largest of the 4 coefficients) of the quadtree is greater than or equal to a threshold value, indicating that the four coefficients have an important coefficient, and outputting 1; otherwise, if the root (the maximum of the 4 coefficients) of the quadtree is smaller than the threshold, it indicates that there is no important coefficient in the four coefficients, and 0 is output; step six, step three and step three are executed;

sixthly, putting the important coefficient (important coefficient in 4 coefficients) into LIP or LSP, and outputting the sign of the important coefficient (important coefficient in 4 coefficients), wherein the important coefficient is positive, the sign is 0, the important coefficient is negative, and the sign is 1; step six, three, four are executed;

sixthly, step three or four, judging whether L (i, j) is empty or not,

if so, deleting D (i, j) from the LIS; step six, step three, step eight are executed;

if not, the L (i, j) coefficient position (i, j) is moved to the LIS tail part; step six, step three, step eight are executed;

sixthly, judging whether the L (i, j) is marked or not (in the sixthly and the sixthly, the L (i, j) obtained by decomposing the D (i, j) is marked (the mark can be set in a program)), if so, executing the sixthly and the sixthly, and if not, executing the sixthly and the sixthly;

sixthly, judging whether an important coefficient is contained in the L (i, j) or not according to a threshold value, if so, deleting the L (i, j) from the LIS, adding D (2i,2j), D (2i +1,2j), D (2i,2j +1) and D (2i +1,2j +1) to the tail of the LIS, and not outputting any information; step six, step three, step eight are executed;

if not, L (i, j) is unimportant, and step sixty-three-eight is executed;

judging whether the L (i, j) contains an important coefficient according to a threshold value, wherein the process is as follows:

the coefficient is greater than the threshold value and is an important coefficient; the coefficient is less than or equal to the threshold value and is not an important coefficient;

sixthly, judging whether an important coefficient is contained in the L (i, j) or not according to a threshold value, if the L (i, j) is important, deleting the L (i, j) from the LIS, adding D (2i,2j), D (2i +1,2j), D (2i,2j +1) and D (2i +1,2j +1) to the tail of the LIS, and outputting a code; step six, step three, step eight are executed;

if not, L (i, j) is not important, no information is output;

judging whether the L (i, j) contains an important coefficient according to a threshold value, wherein the process is as follows:

the coefficient is greater than the threshold value and is an important coefficient; the coefficient is less than or equal to the threshold value and is not an important coefficient;

sixthly, eighthly; judging whether the coordinates of the root nodes of all the spatial direction trees in the LIS are processed or not, and if not, re-executing the step six, the step three and the step one; if yes, executing step six or four;

sixthly, clearing all the marks of L (i, j), checking each (i, j) in the LSP, if the mark is not newly added in the sequencing scanning (in the iteration of the time), outputting the nth bit (the third bit of 101 is 1) of the coefficient corresponding to the position, and executing a sixteenth step; if the new information is added in the sequencing scanning, no information is output;

step six five, judging whether the length of the compressed code stream reaches the specified length, and if so, outputting the compressed code stream; and if not, executing step six two.

As can be seen from the LIS encoding process, if the importance of L (i, j) is determined first, and then four coefficients of O (i, j) are encoded, one bit can be saved. This saves many bits since it is not important that L (i, j) have a high probability. It should be noted that this process does not add extra bits or computation, but merely changes the order of the decisions. Furthermore, when L (i, j) obtained by splitting D (i, j) is important, O (i, j) has a high probability of containing an important coefficient. Thus, O (i, j) can be encoded in an efficient manner.

For the SPIHT algorithm, the D-set and the L-set are represented by a List of Insignificant Sets (LIS). Firstly, the LSP realizes image compression by encoding the records in LIP, LIS and andLSP by turns for each bit plane.

The detailed LIS scanning process in the improved SPIHT algorithm is shown in algorithm 1.

Other steps and parameters are the same as those in one of the first to fifth embodiments.

The following examples were used to demonstrate the beneficial effects of the present invention:

the first embodiment is as follows:

the image compression method based on the direction lifting wavelet and the improved SPIHT under the Internet of things is specifically prepared according to the following steps:

first, experiments were designed to verify the validity of the proposed DIAL model. The improved SPIHT algorithm was then tested. Finally, under different bit rates, different quality evaluation standards are adopted, and the proposed method is compared with a common compression method.

Proposed DIAL model

To demonstrate the effectiveness of the proposed DIAL model, the commonly used "Barbara" was used as a test image. The image size is 512 × 512. The test image was subjected to one-level decomposition using 9/7 biorthogonal wavelet filters, ADL-based wavelet filters, and DIAL model-based wavelet filters, respectively, resulting in decomposition results as shown in fig. 7a, 7b, and 7 c. As can be seen from fig. 8, the ADL-based wavelet filter results in transformed image high-frequency subbands having smaller coefficient magnitudes than the decomposition results obtained with the 9/7 wavelet filter. For the DIAL model based wavelet filter, the high frequency subbands in the transformed image look almost black, indicating that the sparse results obtained by this method are optimal. The reason is that the DIAL model takes more directional information into account during boosting, which helps to concentrate more energy in the image to the low frequency subbands. Furthermore, in contrast to the commonly used Sinc interpolation method, the DIAL model employs directional interpolation, which is capable of interpolating fractional pixel positions along the local texture direction. Therefore, more directional information in the image can be retained. All this helps the DIAL model to achieve better sparsity.

Table 3 shows the average magnitudes of the resulting high frequency coefficients using these three transform methods, respectively, and the percentage reduction in magnitude (indicated by the numbers in parentheses) of the high frequency subband coefficients relative to the conventional 9/7 wavelet transform. As can be seen from table 3, the mean magnitude of the coefficients of the DIAL model is minimal for each high frequency subband.

TABLE 3 average coefficient magnitudes and percent reductions for LH, HL, HH under three transformation methods

The DIAL model does not require adaptive decomposition based on rate-distortion optimization. Also, an entropy coding method may be employed to further reduce side information. Thus, the side information that needs to be transmitted is greatly reduced. The comparison of the side information is shown in fig. 4. As can be seen from fig. 4, the proposed DIAL method requires less side information than the ADL method, which is very advantageous for improving compression efficiency.

TABLE 4 code rate (bpp) for given bit rate side information

Nonlinear estimation (NLA) is an efficient method that can measure the ability of a given transformed sparse representation [35] (Eslami R, Radha H (2007) A new family of non-redundant transformations using hybrid waves and direct filter banks. IEEE Transmission Image Process16 (4):1152-1167.http:// dx. doi. org/10.1109/TIP.2007.891791). With better NLA performance, the transform method is more potential in some signal processing applications, such as encoding, denoising, and feature extraction. Therefore, several sets of experiments were designed to test the NLA performance of the proposed dia model based wavelet transform. For the test image "Barbara", NLA Sas for different methods can be as shown in FIG. 8, with a different number of coefficients preserved. As can be seen from fig. 8, the wavelet transform based on the DIAL model has been superior to the ordinary 9/7 wavelet transform and the ADL-based wavelet transform. Especially when the number of the reserved coefficients M is less, the NLA performance of the method is more obvious. The same conclusions can be drawn for other test images, such as "Boats", "Fingerprint", "GoldHill", and some texture images, by testing NAL performance in the same way.

Performance of the proposed compression method

The proposed compression method combines a DIAL model based wavelet transform with a modified SPIHT method. To demonstrate the effectiveness of the proposed method, several experimental comparisons were performed. Six test images are selected, come from different sensors respectively and reflect different scenes. Wherein "bank", "aerial", "Lena", "Babon", and "Woodland Hills" are selected from the USC-SIPI database [36] (USC-SIPI database [ Online ]: http:// site. use. edu/database /), "Europa 3" are selected from the CCSDS test image set [37] (Consultative committee for space data systems, CCSDS test images [ Online ]. Available: http:// cwe. ccsssds. org/sls/docs/sls-dc /). These test images are 512 × 512 in size, as shown in fig. 9a, 9b, 9c, 9d, 9e, 9 f.

In the experiment, the number of wavelet decomposition layers was set to five. The proposed compression method and the conventional SPIHT method are respectively adopted to compress the test image. The PSNR results obtained at different bit rates are shown in table 5.

Table 5 presents PSNR results (dB) obtained for the compression method and the conventional SPIHT method

As can be seen from table 5, the coding performance of the proposed compression method is better than that of SPIHT at all given bit rates. This is because the DIAL model can provide good sparse representation results, concentrating more energy of the image to the low frequency subbands. This means that more "longer" zero trees can be generated under the same bit plane for zero tree based coding methods. Moreover, the improved SPIHT method enables more efficient scanning of these zero trees. All this contributes to the proposed compression method to achieve better coding performance.

In order to fully evaluate the proposed compression method, the Kappa coefficient is also used as a quality evaluation index. Kappa coefficients are commonly used to assess classification accuracy [38] (Gaucherel C, Alleaume S, Hely C (2008) The comparative Map Profile Method: A stratgy for Multiscale comparative of Quantitative and Quantitative images IEEE Transgeoscier Sens,46(9):2708-2719.http:// dx. doi. org/10.1109/TIP.2007.891791). The document [39] (Cohen J (1960) A coefficient of evaluation for nominal scales. actual and psychological measurement20(1):37-46.) indicates that the Kappa coefficient can also be used as a measure of the consistency of the original and reconstructed images. For these test images, Kappa coefficients obtained by the proposed method and the general SPIHT compression method at different bit rates are shown in fig. 10. From fig. 10 it can be seen that the Kappa coefficients of the proposed compression method are still better than the results obtained with the SPIHT method at all given bit rates.

In addition to PSNR and Kappa coefficients, subjective quality of the image is also an important indicator for evaluating the performance of compression algorithms. Taking the test image "bank" as an example, the reconstructed images obtained by different compression methods at different bit rates are shown in fig. 11a to 11 j. As can be seen from fig. 11a, 11b, 11c, 11d, 11e, 11f, 11g, 11h, 11i, and 11j, the proposed compression method can provide better visual quality of the reconstructed image, especially in the region with more texture information in the frame. This proves that the proposed compression method helps to preserve more of the main details of the image. The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (5)

1. The image compression method based on the direction lifting wavelet and the improved SPIHT under the Internet of things is characterized in that: the method comprises the following specific processes:

firstly, carrying out image block segmentation on a remote sensing image to obtain a segmented image block;

step two, respectively calculating the optimal prediction direction of the divided image blocks to obtain the optimal prediction direction of the divided image blocks;

step three, performing weighted direction interpolation on the fractional sample value by calculating a weighted direction interpolation filter coefficient to obtain an interpolation image block;

step four, wavelet transformation based on direction lifting is respectively carried out on the interpolation image blocks by utilizing the optimal prediction direction obtained in the step two, and each transformed image block, namely each transformed code block, is obtained;

step five, forming a whole transformed image by all the transformed image blocks;

step six, the transformed image obtained in the step five is coded by using an improved SPIHT method to obtain a coded image;

in the sixth step, the transformed image obtained in the fifth step is coded by using an improved SPIHT method to obtain a coded image; the specific process is as follows:

sixthly, initializing a threshold value

Initializing tables LSP, LIS and LIP;

is the maximum value of the number of bit planes;

initializing the table LSP into a null table, initializing LIP into a lowest-frequency sub-band coefficient position set, and initializing LIS into a root node coordinate set of each spatial direction tree;

sixthly, coding LIP according to the LSP, LIS and LIP of the table, wherein the process is as follows:

sixthly, judging whether the LIP set contains an important coefficient or not according to a threshold, if so, outputting 1 and a sign bit, deleting the position (i, j) of the important coefficient from the LIP and adding the position (i, j) of the important coefficient to the tail of the LSP, wherein the coefficient is positive, the sign bit is 0, the coefficient is negative and the sign bit is 1;

if not, outputting 0;

judging whether the LIP set contains an important coefficient according to a threshold value, wherein the process is as follows:

the coefficient is greater than the threshold value and is an important coefficient; the coefficient is less than or equal to the threshold value and is not an important coefficient;

sixthly, judging whether all coefficient positions contained in the LIP set are processed or not, and if not, executing the sixthly-two step again; if yes, executing step six and step three;

sixthly, coding LIS, wherein the process is as follows:

sixthly, judging whether the current record of the LIS is D (i, j) or L (i, j), if the current record of the LIS is D (i, j), executing step sixteenth or sixthly, and if the current record of the LIS is L (i, j), executing step sixteenth or sixthly;

d (i, j) is a coordinate set of all the descendants of the coefficient position (i, j);

l (i, j) is a coordinate set of all non-direct descendants of the coefficient position (i, j);

sixthly, judging whether the D (i, j) contains an important coefficient according to a threshold value, wherein the output is 1 if the D (i, j) contains the important coefficient, and otherwise, the output is 0;

if D (i, j) contains an important coefficient, decomposing D (i, j) into L (i, j) and O (i, j); placing L (i, j) into the LIS tail;

o (i, j) is the set of coordinates for all children of coefficient position (i, j);

judging whether the D (i, j) contains an important coefficient according to a threshold value, wherein the process is as follows:

the coefficient is greater than the threshold value and is an important coefficient; the coefficient is less than or equal to the threshold value and is not an important coefficient;

building a quadtree by using 4 coefficients of O (i, j) and coding, if the root of the quadtree is greater than or equal to a threshold value, indicating that the four coefficients have an important coefficient, and outputting 1; otherwise, if the tree root of the quadtree is smaller than the threshold value, no important coefficient exists in the four coefficients, and 0 is output; step six, step three and step three are executed;

sixthly, putting the important coefficient into LIP or LSP, and outputting the sign of the important coefficient, wherein the important coefficient is positive, the sign is 0, the important coefficient is negative, and the sign is 1; step six, three, four are executed;

sixthly, step three or four, judging whether L (i, j) is empty or not,

if so, deleting D (i, j) from the LIS; step six, step three, step eight are executed;

if not, the L (i, j) coefficient position (i, j) is moved to the LIS tail part; step six, step three, step eight are executed;

sixthly, judging whether the L (i, j) is marked or not, if so, executing the sixthly-sixteenth step, and if not, executing the sixthly-seventy-seven step;

sixthly, judging whether an important coefficient is contained in the L (i, j) or not according to a threshold value, if so, deleting the L (i, j) from the LIS, adding D (2i,2j), D (2i +1,2j), D (2i,2j +1) and D (2i +1,2j +1) to the tail of the LIS, and not outputting any information; step six, step three, step eight are executed;

if not, L (i, j) is unimportant, and step sixty-three-eight is executed;

judging whether the L (i, j) contains an important coefficient according to a threshold value, wherein the process is as follows:

the coefficient is greater than the threshold value and is an important coefficient; the coefficient is less than or equal to the threshold value and is not an important coefficient;

sixthly, judging whether an important coefficient is contained in the L (i, j) or not according to a threshold value, if the L (i, j) is important, deleting the L (i, j) from the LIS, adding D (2i,2j), D (2i +1,2j), D (2i,2j +1) and D (2i +1,2j +1) to the tail of the LIS, and outputting a code; step six, step three, step eight are executed;

if not, L (i, j) is not important, no information is output;

judging whether the L (i, j) contains an important coefficient according to a threshold value, wherein the process is as follows:

the coefficient is greater than the threshold value and is an important coefficient; the coefficient is less than or equal to the threshold value and is not an important coefficient;

sixthly, eighthly; judging whether the coordinates of the root nodes of all the spatial direction trees in the LIS are processed or not, and if not, re-executing the step six, the step three and the step one; if yes, executing step six or four;

sixthly, clearing all the marks of L (i, j), checking each (i, j) in the LSP, if the mark is not newly added in the sequencing scanning, outputting the nth bit of the coefficient corresponding to the position, and executing a step sixteenth step; if the new information is added in the sequencing scanning, no information is output;

step six five, judging whether the length of the compressed code stream reaches the specified length, and if so, outputting the compressed code stream; and if not, executing step six two.

2. The method of claim 1, wherein the image compression method based on direction lifting wavelet and improved SPIHT under the Internet of things is characterized in that: carrying out image block segmentation on the remote sensing image in the first step to obtain segmented image blocks; the specific process is as follows:

the remote sensing image is divided into blocks with the same size to obtain divided image blocks, wherein the block division size is consistent with the block size of the later encoding stage.

3. The method of claim 2, wherein the image compression method based on direction lifting wavelet and improved SPIHT under the Internet of things is characterized in that: in the second step, the optimal prediction directions of the divided image blocks are respectively calculated to obtain the optimal prediction directions of the divided image blocks; the specific process is as follows:

assume a set of reference directions as θ_refReference set of directions theta_refContains 15 reference directions, which are marked as { -7, -6, -5, -4, -3, -2, -1,0,1,2,3,4,5,6,7 }; let the total number of divided image blocks be N_aEach image block is B_l,l＝0,1,K,N_a-1；

Divided image block B_lAlong all reference directions theta respectively_ref,i(i is 1,2, K,15) performing direction prediction to obtain prediction image blocks in all reference directions;

under the mean square error criterion, the pixels of the prediction image block in all reference directions are respectively compared with the pixels of the remote sensing image in the step one, and the reference direction corresponding to the minimum error is the optimal prediction direction of the prediction image block

Optimal prediction direction for predicting image block

Is calculated as follows

Wherein D (-) is an image distortion function, and x (m, n) is an image block B_lSample value corresponding to the middle position (m, n), DA _ PⁱA predictor in the ith reference direction, m is the abscissa of the corresponding position, and n is the ordinate of the corresponding position; let D (·) ═ l |;

the above process is repeated until the best prediction directions for all the divided image blocks are determined.

4. The method of claim 3, wherein the image compression method based on direction lifting wavelet and improved SPIHT under the Internet of things is characterized in that: in the third step, weighting direction interpolation is carried out on the fractional sample value by calculating weighting direction interpolation filter coefficients to obtain an interpolation image block; the specific process is as follows:

the final output of the directional interpolation filter is determined by three filters, which are: bilinear filters, Telenor4-tap filters and 2-tap filters;

in two rows below the row where the current sample is located, taking two samples in a column which is two columns away from the column where the sample is located as the input of the bilinear filter; taking four samples in a next column of a column where the sample is positioned in a row where the current sample is positioned, an upper row and a lower row respectively as the input of a Telenol 4-tap filter, wherein the outputs of the bilinear filter and the Telenol 4-tap filter form the input of a 2-tap filter, and the output of the 2-tap filter is the weighting coefficient of a directional interpolation filter;

and constructing a directional interpolation filter through the input samples of the bilinear filter, the input samples of the Telenor4-tap filter and the weighting coefficients, and carrying out weighted directional interpolation on the sample values at the fractional positions by the directional interpolation filter to obtain an interpolated image block.

5. The method of claim 4, wherein the image compression method based on direction lifting wavelet and improved SPIHT under the Internet of things is characterized in that: in the fourth step, the optimal prediction direction obtained in the second step is utilized to respectively perform wavelet transformation based on direction lifting on the interpolated image blocks to obtain each transformed image block, namely each transformed code block; the specific process is as follows:

according to the optimal prediction direction obtained in the step two

And (3) respectively utilizing formulas (2) and (3) to perform wavelet transformation based on direction lifting on the interpolation image block obtained in the step three:

the direction predictor DA _ P is

In the formula, x_e[m,n]For the even sample set of the interpolated image block, DA _ P, obtained in step three_e[m,n]A directional predictor corresponding to the even sample set; i denotes the number of the high-pass filter coefficients, p_iRepresenting high pass filter coefficients;

the interpolated image block is divided into two parts: set of even samples x_e[m,n]And odd sample set x_o[m,n]；

The direction update operator DA _ U is

Wherein j represents the number of the low pass filter coefficient, u_jRepresenting the low-pass filter coefficient, DA _ U_d[m,n]Updating operators for the directions corresponding to the odd sample sets; d [ m, n ]]For the odd samples predicted by the adjacent even samples, is expressed as

d[m,n]＝x_o[m,n]+DA_P_e[m,n]

x_o[m,n]The odd sample set of the interpolation image block obtained in the third step;

and obtaining each transformed code block by using the direction predictor and the direction update operator.

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