CN102685501B - Fixed-point wavelet transform method for joint photographic experts group 2000 (JPEG2000) image compression - Google Patents
Fixed-point wavelet transform method for joint photographic experts group 2000 (JPEG2000) image compression Download PDFInfo
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Abstract
The invention discloses a fixed-point wavelet transform method for joint photographic experts group 2000 (JPEG2000) image compression. The method comprises the steps of: (1) inputting an image; (2) performing direct current (DC) level shifting; (3) judging whether 9/7 wavelet transform is to be adopted or not; (4) performing bounded input bounded output (BIBO) gain-controlled 9/7 lifting wavelet transform; (5) quantifying a coefficient after the BIBO gain-controlled 9/7 lifting wavelet transform; (6) performing BIBO gain-controlled 5/3 lifting wavelet transform; (7) outputting a wavelet transform coefficient; (8) performing arithmetic coding; (9) performing rate distortion optimization interception; and (10) performing code stream organization to obtain a JPEG2000 compressed code stream. A BIBO gain control method is introduced, the storage bit depth of a wavelet transform intermediate value is determined by using a 9/7 wavelet transform BIOB gain, and a selection mode and a quantification mode of a 9/7 lifting wavelet transform quantification parameter are determined by using a 5/3 wavelet transform BIBO gain, so that JPEG2000 system storage resources and running time are greatly saved.
Description
Technical Field
The invention relates to the technical field of image processing, in particular to a high-efficiency hardware fixed-point implementation method compatible with 5/3 wavelet transform and 9/7 wavelet transform in a JPEG2000 image compression system. The invention uses 9/7 BIBO (bound Input bound output) gain of lifting wavelet transform to determine the storage bit depth of the wavelet transform intermediate value, uses 5/3 BIBO gain of lifting wavelet transform to determine the selection mode of quantization parameter and the realization mode of quantization in 9/7 lifting wavelet transform, and finally uses the same storage space to store fixed point 5/3 lifting wavelet transform and fixed point 9/7 lifting wavelet transform. The invention can be used for image compression coding of various digital devices.
Background
With the development and application of multimedia and network technologies, the conventional image compression algorithm has not been able to meet the requirements of current market and practical application, and a new standard JPEG2000 for still image compression was established in 11 months of 2000 by the international standards organization. The new standard adopts a rate distortion optimized intercepting embedded code block coding algorithm (EBCOT) based on wavelet transform technology to obtain better image compression effect, and comprises a wavelet transform module, a bit plane arithmetic coding module based on context, a rate distortion optimized intercepting module and a code stream organization module. The wavelet transform module adopts two implementation modes, namely reversible integer 5/3 wavelet transform and irreversible floating point 9/7 wavelet transform. Since the second generation lifting wavelet transform requires less working memory and less algorithm calculation, a lifting structure is adopted in JPEG2000 to realize the two wavelet transforms, but two systems of fixed point and floating point are still required to realize 5/3 and 9/7 wavelet transforms.The 9/7 wavelet transform used in the standard uses the standard fourAnd (5) step lifting.“Standard four-step promotion Reference is made to the formula F.11 on page 132 of the JPEG2000 International Standard document ISO/IEC 15444-1. "first step The lifting is to use the formula STEP1]And processing the data. The second STEP of lifting is to use the formula STEP2] And processing the data. The third STEP of lifting is to use the formula STEP3]And processing the data. ' the fourth step is carried Liter "is simply the formula [ STEP4]And processing the data.
The university of sienna electronics technology in its patent application "VLSI architecture based on wavelet transform of lines" (patent application No. 200510042864.0, publication No. CN1717049) discloses a VLSI architecture based on wavelet transform of lines. The structure utilizes the characteristics of the wavelet transform filter, so that the line transform and the column transform of each level of wavelet decomposition are processed in parallel, and the requirement on a data storage space is reduced by effectively managing the buffer space of intermediate data. However, the method still has the disadvantages that different storage spaces are required to be respectively adopted due to the difference between the 5/3 wavelet transform and the 9/7 wavelet transform, and the coefficients of all lifting steps of the 9/7 wavelet transform adopt a very large fixed storage bit depth. This configuration thus wastes significant memory space in systems requiring both the 5/3 wavelet transform and the 9/7 wavelet transform.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a fixed point implementation method of wavelet transformation based on BIBO gain control in a JPEG2000 image compression system. The invention uses as few hardware resources as possible and the same storage space to store two types of wavelet transformation coefficients. According to the invention, 9/7 wavelet transform each-step lifting algorithm is finely divided, BIBO gain of each-step lifting algorithm is analyzed according to different characteristics of each lifting step in each-step wavelet transform, and the minimum value of storage bit depth of wavelet coefficient after each-step lifting is designed. Under the limit of 5/3 wavelet transform lossless compression, the BIBO gain of 5/3 wavelet transform is used to design the selection mode of quantization parameter and the implementation mode of quantization in 9/7 wavelet transform, and finally all wavelet coefficients are stored in 19 bits. The invention not only greatly saves the hardware storage resource and the running time in the wavelet transform module, but also saves the storage resource and the running time of a subsequent context-based bit plane arithmetic coding module and a rate distortion optimization module in JPEG 2000.
The invention starts from the research of the requirement of realizing fixed point of numerical values, and reserves enough protection bits for the expansion of the dynamic range of data in each lifting step in order to ensure that the lifting result of each step of the wavelet transformation system does not overflow. The number of guard bits is controlled by the BIBO gain, which is the ratio of the maximum absolute value of the output samples to the maximum absolute value of the input samples.
To achieve the above object, the method of the present invention comprises the steps of:
(1) image data to be compressed is input in the JPEG2000 image compression system.
(2) And performing DC level shift on the input image data to obtain 0 symmetrically distributed image data.
(3) Judging whether the wavelet transform is 9/7
The user decides to adopt 9/7 lifting or 5/3 lifting wavelet transform according to whether lossy compression is carried out; if the compression is lossy, 9/7 lifting wavelet transform is adopted, and the step (4) is carried out; otherwise, go to step (6).
(4) 9/7 lifting wavelet transform with BIBO gain control
4a) Shifting all data after the DC level shift to the left by upshift bits, wherein the upshift value is an integer which is arbitrarily larger than 0;
4b) sequentially carrying out standard 9/7 lifting wavelet transformation first-step lifting, second-step lifting, third-step lifting and fourth-step lifting on each line of data subjected to left shifting by adopting a floating point-to-fixed point method, and respectively controlling the storage bit depth of the lifted data in each step according to a lifting gain table of each step of two-dimensional 9/7 lifting wavelet transformation;
4c) dividing the image after the fourth step of lifting into a left part and a right part, wherein the left part is used as a low-frequency part after horizontal transformation, then performing standard four-step lifting in the vertical direction, and respectively controlling the storage bit depth of data after each step of lifting according to a two-dimensional 9/7 lifting wavelet transformation lifting gain table in each step; taking the right half part as a high-frequency part after horizontal transformation, performing standard four-step lifting in the vertical direction, and respectively controlling the storage bit depth of data after each step of lifting according to a two-dimensional 9/7 lifting wavelet transformation step-by-step lifting gain table;
4d) and performing second-level wavelet transformation on the low-frequency sub-band of the data subjected to the first-level wavelet transformation, controlling the storage bit depth of the data subjected to the lifting in each step according to a two-dimensional 9/7 lifting wavelet transformation step-by-step lifting gain table of the lifted data, and performing third-level wavelet transformation and fourth-level wavelet transformation in sequence until four-level wavelet transformation is completed.
(5) 9/7 lifting wavelet transformed coefficient quantization for BIBO gain control
5a) Obtaining a minimum quantization step initial value of each sub-band by searching a minimum quantization step initial value table of each sub-band, and quantizing the 9/7 wavelet transformed coefficients of each sub-band by using the quantization step initial value;
5b) right shifting the 9/7 wavelet coefficient in step 5a) by Y bit to realize quantization of larger quantization step size, wherein the quantization step size is the Y power of 2 of the initial value of the quantization step size, and the value of Y is an integer which is arbitrarily more than or equal to 0;
5c) shifting all 9/7 wavelet coefficients in step 5b) to the right by upshift bits;
5d) the 9/7 wavelet transform coefficients quantized in step 5c) are stored with 19 bits.
(6) 5/3 lifting wavelet transform with BIBO gain control
6a) Carrying out standard 5/3 wavelet first-step lifting and second-step lifting on data in each line, storing all lifted data and 9/7 wavelet-transformed data of the same type in the same space, and respectively controlling the storage bit depth of the lifted data in each step according to a two-dimensional 9/7 lifting wavelet transform lifting gain table in each step;
6b) dividing the image after the second step of lifting into a left part and a right part, taking the left part as low-frequency data after horizontal transformation, performing two-step standard 5/3 wavelet lifting in the vertical direction, and storing all the data after lifting and data of the same type after 9/7 wavelet transformation in the same space; taking the right half part as high-frequency data after horizontal transformation, performing two-step standard 5/3 wavelet lifting in the vertical direction, storing all the lifted data and 9/7 wavelet-transformed data of the same type in the same space, and completing the first-level wavelet transformation;
6c) and performing second-level wavelet transformation on the low-frequency sub-band of the data subjected to the first-level wavelet transformation, storing all the data subjected to lifting and 9/7 wavelet transformation in the same space, and sequentially performing third-level wavelet transformation and fourth-level wavelet transformation until four-level wavelet transformation is completed.
(7) The coefficients of the wavelet transform are output 5/3 or 9/7 according to the user's request.
(8) And processing the wavelet transformed coefficients by using a standard context-based bit plane arithmetic coding module in a JPEG2000 image compression system to obtain an arithmetic coding code stream.
(9) And performing rate distortion optimization interception on the code stream of the arithmetic coding by using a standard rate distortion optimization interception module in the JPEG2000 image compression system, and recording interception point information.
(10) The standard code stream organization module in the JPEG2000 image compression system uses the interception point information to organize the code stream of the arithmetic coding to obtain the compressed code stream of the JPEG 2000.
Compared with the prior art, the invention has the following advantages:
firstly, because the data after 5/3 lifting wavelet transform and the data of the same type after 9/7 lifting wavelet transform in the JPEG2000 image compression system are stored in the same space, the invention overcomes the defect that the 5/3 wavelet transform and the 9/7 wavelet transform in the prior art have two sets of storage spaces respectively, so that the invention adopts the same storage space to store two types of wavelet transform coefficients, and saves storage resources.
Secondly, because the invention finely divides the lifting algorithms of all levels of 9/7 lifting wavelet transformation, the BIBO gain of the lifting algorithms of all levels is analyzed according to different characteristics of all lifting steps in all levels of wavelet transformation, the minimum value of the storage bit depth of the wavelet coefficient after all levels of lifting is designed, and the minimum storage bit depth is used for storing intermediate variables. The defect caused by the fact that the storage bit depth of 9/7 lifting wavelet transformation intermediate variables in the prior art uses a large enough uniform value is overcome, and the method adopts less storage resources to store 9/7 lifting wavelet transformation intermediate coefficients.
Thirdly, because the invention adopts the minimum storage bit depth to store 9/7 the lifting wavelet transform intermediate coefficients, the invention can adopt shorter multipliers to process the intermediate data, and the speed of wavelet transform is accelerated.
Fourthly, because the invention designs a quantization step selection mode and a quantization mode of 9/7 wavelet transform under the limit of 5/3 wavelet transform lossless compression, the defect that the storage space of the coefficient after the wavelet transform quantization is infinite in the prior art 9/7 is overcome, and the invention adopts fixed storage resources to store the coefficient after the 9/7 wavelet transform quantization.
Fifth, because the invention stores the quantized wavelet coefficient by 19 bits, it not only realizes lossless wavelet transform, lossy wavelet transform, but also fully utilizes the storage resource, thus making the subsequent context-based bit plane arithmetic coding module and rate-distortion optimization intercepting module have less storage resource and faster speed.
Sixth, the method of the present invention can be applied to wavelet transform in both control software systems and control hardware systems, resulting in savings of storage resources and runtime when used in both systems.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The implementation steps of the present invention are described in detail below with reference to fig. 1.
Step1, inputting image data to be compressed in a JPEG2000 image compression system, wherein the image data is stored by adopting X bits, and the value range of X is 1-16 bits.
And 2, carrying out DC level shift on the input image data to obtain 0 symmetrically distributed image data.
Step3, the user determines to adopt 9/7 lifting or 5/3 lifting wavelet transformation according to whether lossy compression is carried out; if the compression is lossy, 9/7 lifting wavelet transform is adopted, and the step4 is switched to; otherwise, go to step 6.
Step 4. 9/7 lifting wavelet transform of BIBO gain control
4a) And shifting all the data subjected to DC level shifting to the left by upshift bits, wherein the upshift value is an integer which is arbitrarily larger than 0.
4b) And (3) sequentially carrying out standard 9/7 lifting wavelet transform first-step lifting, second-step lifting, third-step lifting and fourth-step lifting on each line of data after left shift by adopting a floating point-to-fixed point method, and respectively controlling the storage bit depth of the lifted data of each step according to a two-dimensional 9/7 lifting wavelet transform step lifting gain table, wherein the two-dimensional 9/7 lifting wavelet transform step lifting gain table is used for deducing the data change range caused by filtering according to the characteristic of a filter coefficient of each lifting step in the 9/7 lifting wavelet transform to obtain a maximum bit depth expansion table reflecting the lifted data of each step. The storage bit depth of the boosted data is the sum of X, upshift values and values corresponding to the transform level and the boosting step in the boosting gain table of each step of the two-dimensional 9/7 boosted wavelet transform.
The two-dimensional 9/7 lifting wavelet transformation each step lifting gain table is obtained according to the following steps:
first, a detailed analysis is made without considering a regularized multiplication operation9/7 lifting BIBO gains in each lifting step of wavelet transform. Is provided withRepresents the analysis vector of the first step in the lifting at a decomposition level d of the one-dimensional discrete wavelet transform, and n represents the dimension of the analysis vector. The corresponding BIBO gain is related to the analysis vector as follows:
wherein,indicating the BIBO gain at the first step in the lifting, at a decomposition level d of the wavelet transform,represents the analysis vector of the first step in the lifting at d, n represents the dimension of the analysis vector, and Σ is the consecutive sign in the mathematics.
For 9/7 lifting wavelet transform, the BIBO gain values corresponding to four-step lifting of one-dimensional wavelet transform in 1-4 levels are shown in the following table "gain tables for each lifting step in four-level one-dimensional 9/7 lifting wavelet transform". The BIBO gains for the four steps are different in each decomposition level due to the different analysis vectors for the four steps. The analysis vectors of the same step in different decomposition levels are different, so the BIBO gains of different decomposition levels are also different.
Because the two-dimensional wavelet transform is a separable two-dimensional linear operator, horizontal lifting is firstly carried out and then vertical lifting is carried out, low-pass sub-bands and high-pass sub-bands are generated after horizontal four-step lifting, and the two sub-bands are respectively subjected to four-step vertical lifting. Since the analysis vectors of the horizontal four-step lifting and the vertical four-step lifting are the same in the same decomposition level, the BIBO gain of the individual horizontal lifting and the BIBO gain of the individual vertical lifting are the same. From the above characteristics, the BIBO gains for each lifting step of the four-level two-dimensional 9/7 wavelet transform are shown in the following table, "two-dimensional 9/7 lifting wavelet transform each step lifting gain table". Each coefficient in the table is the maximum bit depth extension of the sample after each step of lifting. The invention designs an efficient 9/7 wavelet transform fixed-point algorithm based on the following table and the characteristics of two-dimensional wavelet transform.
9/7 wavelet transform uses four-step lifting, whereas 5/3 wavelet transform uses only two-step lifting. The BIBO gains for each sub-band at each level of the wavelet transform are analyzed 5/3 below, and the detailed values are given in the following table, "two-dimensional 5/3 lifting wavelet transform each sub-band gain table at each level".
From the above table, it can be seen that, after the four-level 5/3 wavelet transform is performed, the maximum expansion bit depth of the coefficient of each wavelet sub-band is 3, that is, if the original image is stored by using X bits, after the four-level 5/3 wavelet transform, the wavelet coefficient can be stored by using (X +3) bits, and some sub-bands can even be stored by using (X +2) bits.
When designing hardware wavelet implementation, it is hoped that wavelet transform coefficients of different sub-bands at different levels can be stored in the same physical space in two different transform modes. As can be seen by comparing the table "two-dimensional 9/7 lifting wavelet transform step-by-step lifting gain table" with the table "two-dimensional 5/3 lifting wavelet transform sub-band gain tables at each level", the 9/7 lifting wavelet transform requires more memory space than the 5/3 lifting wavelet transform for the wavelet coefficients of different sub-bands at different levels. Therefore, 9/7 is used to raise the BIBO gain of wavelet transform when designing the storage space of wavelet transform coefficients.
4c) Dividing the image after the fourth step of lifting into a left part and a right part, wherein the left part is used as a low-frequency part after horizontal transformation, then performing standard four-step lifting in the vertical direction, and respectively controlling the storage bit depth of data after each step of lifting according to a two-dimensional 9/7 lifting wavelet transformation lifting gain table in each step; and taking the right half part as a high-frequency part after horizontal transformation to perform standard four-step lifting in the vertical direction, and respectively controlling the storage bit depth of data after each step of lifting according to a two-dimensional 9/7 lifting wavelet transformation step-by-step lifting gain table.
4d) And performing second-level wavelet transformation on the low-frequency sub-band of the data subjected to the first-level wavelet transformation, controlling the storage bit depth of the data subjected to the lifting in each step according to a two-dimensional 9/7 lifting wavelet transformation step-by-step lifting gain table of the lifted data, and performing third-level wavelet transformation and fourth-level wavelet transformation in sequence until four-level wavelet transformation is completed.
Step 5, 9/7 lifting coefficient quantization after wavelet transformation under BIBO gain control
5a) Obtaining a minimum quantization step initial value of each sub-band by searching a minimum quantization step initial value table of each sub-band, and quantizing the 9/7 wavelet transformed coefficients of each sub-band by using the quantization step initial value; the minimum quantization step initial value table of each sub-band is obtained by the following steps:
the original 9/7 wavelet transform adopts floating point operation, and integer representation is adopted when hardware is realized, so that the original data is firstly shifted to the left by a certain position for expansion before transformation, and after all operations are finished, the result is shifted to the right by corresponding positions, and the initial position of a decimal point is recovered.
9/7 after left shift, the input data of wavelet transform needs higher bit depth to store the wavelet coefficients of each sub-band, and it is sufficient to use these hardware storage resources to store 5/3 lossless coefficients after wavelet transform. 5/3 the coefficients after wavelet transform are directly EBCOT coded, whereas the coefficients after 9/7 wavelet transform need to be quantized first and then EBCOT coded on the quantized coefficients. The quantization step can be selected to be a very small value, that is, the number of bit planes to be encoded is very large, so that the bit plane encoding will take a lot of time and storage space, and meanwhile, a lot of truncation points will be generated by too many bit planes, thereby greatly increasing the burden of the rate-distortion optimization truncation algorithm. But with a proper number of bit planes, more information can be reserved at a lower compression multiple, and better compression performance can be obtained. The technology provided by the invention considers the storage bit depth requirement of 5/3 wavelet transform lossless compression and the bit plane number of the quantized coefficients of 9/7 wavelet transform which is reserved by less hardware resources.
Since both the reversible 5/3 wavelet transform and the irreversible 9/7 wavelet transform need to provide the same range of integers to be encoded for the block encoder, the setting of the quantization step size after the 9/7 wavelet transform needs to be based on the results of the 5/3 wavelet transform.
First, the maximum value of the quantized absolute value of the wavelet transform coefficients is analyzed 9/7. GsAn 9/7 wavelet transform representing a sub-band s synthesizes the squared norm of the basis vector. This variable represents the energy of an image reconstructed from a unit amplitude sample in the subband s, which becomes an energy gain factor. Order toIs L of wavelet basis function in the sub-band frame2Norm, detailed value is shown inThe following table2Norm table ".
Then the quantization step size delta for sub-band ssCan be calculated by the following equation:
where Δ is the basic quantization step, GsThe square norm of the 9/7 wavelet transform complex basis vectors, L2_ G, representing sub-band ssIs L of wavelet basis function in the sub-band frame2And (4) norm. In order to ensure the consistency of the whole restored image, the delta values of all sub-bands are required to be the same in the JPEG2000 encoding process. The required whole compression code rate or distortion level is realized by adjusting the value of delta in the coding process. The designed delta value not only ensures 5/3 wavelet transform lossless compression, but also ensures that 9/7 wavelet transform occupies less storage resources under the condition of hardly influencing the performance.
From the above analysis of 9/7 wavelet transform BIBO gain, it can be seen that the maximum value of the absolute value of the wavelet coefficient of the subband s after the original unsigned integer represented by X bits is subjected to multiple DC level shift, four-step lifting and two-step regularization multiplication operations can be expressed as follows:
wherein X represents the storage bit depth of the input image, BIBOsBIBO gain, K, representing the s-th sub-bandsThe specific values of the normalized multiplication gains of the s-th subband are shown in the following table, "normalized multiplication gain table of each subband in each stage", and k is 1.23017.
Therefore 9/7 the maximum value of the absolute value of the quantized coefficient of each sub-band of the wavelet transform is the following formula:
wherein X represents the storage bit depth of the input image, BIBOsRepresenting the BIBO gain of the s-th sub-band, Δ being the basic quantization step, KsIs the s th subband normalized multiplication gain, L2_ GsIs L of wavelet basis function in the sub-band frame2And (4) norm. From the BIBO gain analysis of 5/3 wavelet transform in the table "two-dimensional 5/3 lifting each level of sub-band gain table of wavelet transform", it can be seen that the maximum value of the absolute value of the wavelet coefficient of sub-band s can be expressed as 2 after DC level shift and 5/3 wavelet lifting of the unsigned integer represented by the original X bits(X-1)+3. Under the condition of ensuring 5/3 lossless compression of wavelet transform, the maximum value of the coefficient after 9/7 wavelet transform should be less than or equal to 2(X-1)+3. Therefore 9/7 quantization step size delta of wavelet transform sub-band ssSatisfies the following formula:
where Δ is the basic quantization step size, BIBOsBIBO gain, L2_ G, for the s-th sub-bandsIs L of wavelet basis function in the sub-band frame2Norm from the table "per subband L2Norm table ", KsThe normalized multiplication gain of the s-th sub-band is from the table "normalized multiplication gain table of each sub-band at each level", BIBOsThe values of (a) are from the table "two-dimensional 9/7 lifting wavelet transform step-by-step lifting gain table". From the above equation, it can be seen that under the 5/3 wavelet constraint condition, the 9/7 wavelet transform has a minimum value of one basic quantization step per sub-band, and the detailed values are shown in the following table "minimum value table of basic quantization step for each sub-band".
From the above equation, it can be seen that under the 5/3 wavelet constraint condition for each different sub-band s, the 9/7 wavelet transform has a minimum value of one basic quantization step size for each sub-band, and since the basic quantization step sizes of all sub-bands adopt the same value, Δ should be the maximum value of the minimum values of the basic quantization step sizes of each sub-band to satisfy the 5/3 wavelet constraint requirement. I.e., the minimum value of the basic quantization step size of the final 9/7 wavelet transform must be ≧ 3.593.
The minimum value of the basic quantization step is obtained when only an image with one bit depth is supported, the wavelet transform system realized by the invention supports unsigned images with 1-16 bits, and the storage bit depth of the wavelet coefficient which meets 5/3 wavelet transform lossless compression is 19 bits. Therefore, 9/7 wavelet transform wavelet coefficients of each sub-band are under 19-bit constraint, and the basic quantization step Δ of each sub-band is updated as follows:
wherein BIBOsBIBO gain, L2_ G, for the s-th sub-bandsIs L of wavelet basis function in the sub-band frame2Norm, KsIs the s-th subband normalized multiplication gain, the minimum quantization step size of each subband becomes smaller when X < 16, and is the negative integer power of 2 of the minimum quantization step size when X is 16. So for an image of input X (X ≦ 16) bit depth, the final selected basic quantization step size is 3.593 × 2X-16。
In an actual JPEG2000 image coding system, the minimum basic quantization step size delta can be 3.593 and the L of the wavelet base function in the sub-band frame2Norm L2_ GsThe quotient of (A) is made into a lookup table of the minimum quantization step initial value of each sub-band of each level as shown in the following table, and the lookup table is directly used during quantization.
5b) And (3) right shifting the 9/7 wavelet coefficients in the first step by Y bits to realize quantization of a larger quantization step size, wherein the quantization step size is the Y power of 2 of the initial value of the quantization step size, and the value of Y is an arbitrary integer greater than or equal to 0.
5c) All 9/7 wavelet coefficients after the second step of processing are right shifted by the upshift bit.
5d) The 9/7 wavelet transform coefficients processed in the third step are stored in 19 bits.
Step 6, 5/3 lifting wavelet transform of BIBO gain control
6a) And performing standard 5/3 wavelet first-step lifting and second-step lifting on the data of each row, storing all the lifted data and 9/7 wavelet-transformed data of the same type in the same space, and respectively controlling the storage bit depth of the lifted data of each step according to a two-dimensional 9/7 lifting wavelet transform lifting gain table of each step.
6b) Dividing the image after the second step of lifting into a left part and a right part, taking the left part as low-frequency data after horizontal transformation, performing two-step standard 5/3 wavelet lifting in the vertical direction, and storing all the data after lifting and data of the same type after 9/7 wavelet transformation in the same space; and taking the right half part as high-frequency data after horizontal transformation, performing two-step standard 5/3 wavelet lifting in the vertical direction, storing all the lifted data and 9/7 wavelet-transformed data of the same type in the same space, and completing the first-level wavelet transformation.
6c) And performing second-level wavelet transformation on the low-frequency sub-band of the data subjected to the first-level wavelet transformation, storing all the data subjected to lifting and 9/7 wavelet transformation in the same space, and sequentially performing third-level wavelet transformation and fourth-level wavelet transformation until four-level wavelet transformation is completed.
And 7, outputting 5/3 wavelet transform coefficients if lossless compression is adopted or outputting 9/7 wavelet transform and quantized coefficients if lossy compression is adopted according to whether lossless compression is adopted by a user.
And 8, processing the wavelet transformed coefficients by using a standard context-based bit plane arithmetic coding module in the JPEG2000 image compression system to obtain an arithmetic coding code stream.
And 9, performing rate distortion optimization interception on the code stream of the arithmetic coding by using a standard rate distortion optimization interception module in the JPEG2000 image compression system, and recording interception point information.
And 10, using the interception point information by a standard code stream organization module in the JPEG2000 image compression system to organize the code stream of the arithmetic coding to obtain the JPEG2000 compressed code stream.
The effect of the present invention is verified by an embodiment of the change of hardware storage resources due to the improvement of wavelet transform module in JPEG2000 hardware simulation system.
The JPEG2000 hardware simulation system is realized by using Verilog HDL language in Xilinx ISE9.1 integrated development software environment. Compared with the VLSI structure of wavelet transform based on lines in the prior art, the invention adopts similar wavelet transform structure, and has the difference that the method of the invention is adopted to control 9/7 lifting wavelet transform, 5/3 lifting storage bit depth of wavelet transform intermediate value, and 9/7 lifting quantization step size selection mode and quantization mode of wavelet transform.
In the prior art, "VLSI structure based on line wavelet transform", the estimated line buffer occupancy is shown in the following table "four-level two-dimensional 9/7 lifting wavelet transform hardware resource analysis table", in which each level of wavelet transform stores 5 lines of data, and the width supports 4096 pixels of wavelet transform, according to the data bit width of 32 bits.
After the method is adopted to improve the storage precision in the VLSI structure based on line wavelet transform in the prior art, the data bit width of 5 FIFOs of the first-level line cache is respectively 26bit, 27bit, 26bit and 26bit, the storage capacity is 4096 x (26+26+27+26+26) ═ 524Kbit, 116Kbit is reduced compared with the original structure, namely 18.125% of storage space is saved compared with the VLSI structure based on line wavelet transform in the prior art.
From the above table, it can be seen that after the wavelet transform is promoted by the four levels 9/7, the total storage capacity in the VLSI structure of the line-based wavelet transform in the prior art is 1200Kbit, and the data bit width and capacity of the line transform FIFO of each level in the method of the present invention are as shown in the following table "four levels 9/7 promotion wavelet transform hardware resource analysis table after precision modification".
It can be seen from the above table that after the data storage bit depth is improved, the storage capacity is estimated to be 988Kbit, which is 212Kbit less than 1200Kbit in the prior art "VLSI structure based on line wavelet transform", i.e. 17.67% of storage space is saved.
The improvement of the wavelet transform module in the invention leads to the change of the storage resources of the subsequent context-based bit plane arithmetic coding module and the rate distortion optimization interception hardware module in the JPEG2000 image coding system, and the detailed change is shown in the following table, namely a resource-saving analysis table of each module of JPEG2000 after wavelet modification.
It can be seen from the above table that the same storage space is used to store two types of wavelet transform coefficients, 9/7 is used to raise the BIBO gain in wavelet transform to determine the storage bit depth of the intermediate value of wavelet transform, 5/3 is used to determine the selection mode and quantization mode of quantization parameter in 9/7 lifting wavelet transform, which not only greatly saves the storage resource of wavelet transform module, but also greatly saves the storage resource and running time of context-based bit plane arithmetic coding because the wavelet coefficients adopt less storage bit depth and the number of bit planes to be processed in bit plane coding is reduced. Meanwhile, the number of bit planes to be processed is reduced, the number of coding channels is reduced, namely the number of interception points is reduced, and storage resources and running time of rate distortion optimization interception are greatly saved. The saving of storage resources and running time of each module finally saves hardware implementation resources of the JPEG2000 algorithm and saves the running time of the whole algorithm.
Claims (4)
1. The fixed point wavelet transform method for realizing JPEG2000 image compression comprises the following steps:
(1) inputting image data to be compressed in a JPEG2000 image compression system;
(2) performing DC level shift on input image data to obtain 0 symmetrically distributed image data;
(3) judging whether the wavelet transform is 9/7
The user decides to adopt 9/7 lifting or 5/3 lifting wavelet transform according to whether lossy compression is carried out; if the compression is lossy, 9/7 lifting wavelet transform is adopted, and the step (4) is carried out; otherwise, go to step (6);
(4) 9/7 lifting wavelet transform with BIBO gain control
4a) Shifting all data after the DC level shift to the left by upshift bits, wherein the upshift value is an integer which is arbitrarily larger than 0;
4b) sequentially carrying out standard 9/7 lifting wavelet transformation first-step lifting, second-step lifting, third-step lifting and fourth-step lifting on each line of data subjected to left shifting by adopting a floating point-to-fixed point method, and respectively controlling the storage bit depth of the lifted data in each step according to a lifting gain table of each step of two-dimensional 9/7 lifting wavelet transformation;
4c) dividing the image after the fourth step of lifting into a left part and a right part, wherein the left part is used as a low-frequency part after horizontal transformation, then performing standard four-step lifting in the vertical direction, and respectively controlling the storage bit depth of data after each step of lifting according to a two-dimensional 9/7 lifting wavelet transformation lifting gain table in each step; taking the right half part as a high-frequency part after horizontal transformation, performing standard four-step lifting in the vertical direction, and respectively controlling the storage bit depth of data after each step of lifting according to a two-dimensional 9/7 lifting wavelet transformation step-by-step lifting gain table;
4d) performing second-level wavelet transformation on the low-frequency sub-band of the data subjected to the first-level wavelet transformation, controlling the storage bit depth of the data subjected to the lifting in each step according to a two-dimensional 9/7 lifting wavelet transformation step-by-step lifting gain table of the lifted data, and performing third-level wavelet transformation and fourth-level wavelet transformation in sequence until four-level wavelet transformation is completed;
(5) 9/7 lifting wavelet transformed coefficient quantization for BIBO gain control
5a) Obtaining a minimum quantization step initial value of each sub-band by searching a minimum quantization step initial value table of each sub-band, and quantizing the 9/7 wavelet transformed coefficients of each sub-band by using the quantization step initial value;
5b) right shifting the 9/7 wavelet coefficient in step 5a) by Y bit to realize quantization of larger quantization step size, wherein the quantization step size is the Y power of 2 of the initial value of the quantization step size, and the value of Y is an integer which is arbitrarily more than or equal to 0;
5c) shifting all 9/7 wavelet coefficients in step 5b) to the right by upshift bits;
5d) storing the 9/7 wavelet transform coefficients quantized in step 5c) with 19 bits;
(6) 5/3 lifting wavelet transform with BIBO gain control
6a) Carrying out standard 5/3 wavelet first-step lifting and second-step lifting on data in each line, storing all lifted data and 9/7 wavelet-transformed data of the same type in the same space, and respectively controlling the storage bit depth of the lifted data in each step according to a two-dimensional 9/7 lifting wavelet transform lifting gain table in each step;
6b) dividing the image after the second step of lifting into a left part and a right part, taking the left part as low-frequency data after horizontal transformation, performing two-step standard 5/3 wavelet lifting in the vertical direction, and storing all the data after lifting and data of the same type after 9/7 wavelet transformation in the same space; taking the right half part as high-frequency data after horizontal transformation, performing two-step standard 5/3 wavelet lifting in the vertical direction, storing all the lifted data and 9/7 wavelet-transformed data of the same type in the same space, and completing the first-level wavelet transformation;
6c) performing second-level wavelet transformation on the low-frequency sub-band of the data subjected to the first-level wavelet transformation, storing all the data subjected to lifting and the same type of data subjected to 9/7 wavelet transformation in the same space, and sequentially performing third-level wavelet transformation and fourth-level wavelet transformation until four-level wavelet transformation is completed;
(7) outputting 5/3 the coefficients of the wavelet transform or 9/7 the coefficients of the wavelet transform according to the user's request;
(8) processing the wavelet transformed coefficient by using a standard context-based bit plane arithmetic coding module in a JPEG2000 image compression system to obtain an arithmetic coding code stream;
(9) performing rate distortion optimization interception on the code stream of the arithmetic coding by using a standard rate distortion optimization interception module in a JPEG2000 image compression system, and recording interception point information;
(10) the standard code stream organization module in the JPEG2000 image compression system uses the interception point information to organize the code stream of the arithmetic coding to obtain the compressed code stream of the JPEG 2000.
2. The fixed-point wavelet transform method for JPEG2000 image compression according to claim 1, characterized in that: and (2) storing the image data in the step (1) by adopting X bits, wherein the value range of X is 1-16 bits.
3. The fixed-point wavelet transform method for JPEG2000 image compression according to claim 1, characterized in that: the storage bit depth of the boosted data in the steps 4b), 4c), 4d) and 6a) is the sum of X, upshift and the values corresponding to the transformation level and the boosting step in each step of the two-dimensional 9/7 boosting wavelet transformation.
4. The fixed-point wavelet transform method for JPEG2000 image compression according to claim 1, characterized in that: the initial value table of the minimum quantization step size of each sub-band in the step 5a) is obtained by the following steps:
firstly, improving BIBO gain of wavelet transform by using 5/3 to obtain the maximum value of the wavelet coefficient absolute value of each sub-band after 5/3 wavelet transform;
secondly, improving the BIBO gain of wavelet transform by using 9/7 to obtain the maximum value of the wavelet coefficient absolute value of each sub-band after 9/7 wavelet transform;
thirdly, utilizing 9/7 to promote normalized multiplication operation in the wavelet transformation standard promotion step to obtain 9/7 normalized multiplication operation gain of each sub-band wavelet coefficient after wavelet is promoted;
fourthly, the square norm of the comprehensive base vector of 9/7 wavelet transform is subjected to evolution to obtain 9/7L of the wavelet base function in each sub-band frame after wavelet transform2A norm;
fifthly, 9/7 is used for lifting the maximum value of the absolute value of each sub-band wavelet coefficient of the wavelet, regularized multiplication gain and L of the sub-band intra-frame wavelet basis function2Multiplying the norm by the three, and dividing the product of the multiplication by 5/3 to obtain the minimum value of the quantization step size of each sub-band;
sixthly, selecting the maximum value in the minimum values of the quantization step sizes of all the sub-bands, and enabling the maximum value to be matched with the L of the wavelet basis function in each sub-band frame2And multiplying the norms to obtain the minimum quantization step initial value of each sub-band, and forming an initial value table of the minimum quantization step of each sub-band by the initial values.
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