CN112218085A - Image compression method based on singular vector sparse reconstruction - Google Patents
Image compression method based on singular vector sparse reconstruction Download PDFInfo
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- CN112218085A CN112218085A CN202011018569.2A CN202011018569A CN112218085A CN 112218085 A CN112218085 A CN 112218085A CN 202011018569 A CN202011018569 A CN 202011018569A CN 112218085 A CN112218085 A CN 112218085A
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Abstract
The invention discloses an image compression method based on singular vector sparse representation in the technical field of image compression, which comprises the following steps: s1: singular value decomposition is carried out on an original image matrix to obtain a left singular vector matrix, a right singular vector matrix and a singular value matrix of the image; s2: selecting a proper singular value according to the calculated contribution of the singular value to the image signal, and discarding the singular value with smaller contribution to the image signal; s3: for a singular vector matrix generated by singular value decomposition of an image matrix, carrying out sparse sampling on the singular vector matrix to construct further compression of a sparse singular matrix experiment on the basis of singular value decomposition; s4: the method achieves further compression of the image by extracting key points of image signals through a least square method, the quality of the image reconstructed by the method is better than that of the image reconstructed by other image compression methods under the same compression ratio, and the image reconstruction result of the method is closer to the original image than that of the original singular value decomposition method.
Description
Technical Field
The invention relates to the technical field of image compression, in particular to an image compression method based on singular vector sparse reconstruction.
Background
The Discrete Cosine Transform (DCT) can effectively remove the correlation among image pixels, and the image improves the information concentration capability of the transform coefficient after DCT transform, but the DCT transform can generate a fast effect in the compression process, and the compression ratio is limited to a certain extent. The highest compression ratio can only reach the range of 33-55: 1. Wavelet transform, which is used to expand a signal into a weighted sum of a series of basis functions, performs multi-resolution decomposition on image data, decomposes the image data into sub-images with different spatial frequencies, and then performs coding and quantization processing on the decomposed sub-images, is not flexible in application because the conventional wavelet basis is determined when performing wavelet decomposition. The structural characteristics of the image cannot be well acquired for some linear singular objects. Fractal coding is to realize compression of image data by using a self-similarity principle in fractal, and mainly depends on the similarity degree of a specific image and a part of the same image with other parts. Fractal compression takes a long time because of the large number of matching and geometric operations required to search for the similarity of the images themselves. Because the image data is stored in the computer in a matrix form, the singular value decomposition theory has good application in the aspect of image compression. The image compression coding method based on singular value decomposition can encounter the problems of difficult calculation of singular values of a large image matrix, poor coding efficiency and the like in the calculation process, which also causes that the singular value decomposition theory is not applied to other image compression methods in image compression.
Although many algorithms are applied to the field of image compression, there is still further room for improvement. For example, most of the existing algorithms (1) are computationally complex and require a certain cost in implementation. (2) The existing compression technology can only reach a certain compression ratio due to the limitation of the algorithm. (3) In different image compression standards (such as JPEG and JPEG2000), when a compression multiple is larger than 64 of a gray image or the bit rate is smaller than 0.125bpp, a block effect is usually generated, the image compression and reconstruction effect is not obvious, and the image quality is poor.
Disclosure of Invention
In order to achieve the purpose, the invention provides the following technical scheme: an image compression method based on singular vector sparse reconstruction comprises the following steps:
s1: singular value decomposition is carried out on an original image matrix to obtain a left singular vector matrix, a right singular vector matrix and a singular value matrix of the image;
s2: selecting proper singular values according to the calculated contribution of the singular values to the image signals to realize first-order compression of the image;
the compression ratio calculation formula of the algorithm is as follows:
r represents r singular values selected after singular value decomposition, p is the ratio of singular matrix key points after sparse representation, and the lower bound of the image compression ratio of the algorithm can be seen as the compression ratio of the image compression method based on singular value decomposition;
s3: sparse singular matrixes are constructed by fitting an image signal curve and carrying out sparse sampling on the left singular matrix and the right singular vector matrix to realize further compression on the basis of singular value decomposition, and the sampling efficiency close to 4:1 can be realized after sparse sampling to be superior to the traditional Nyquist sampling theorem;
s4: in the decompression stage, the left singular vector matrix and the right singular vector matrix of the image are subjected to linear interpolation to realize the reconstruction of the compressed image.
Preferably, in S3, the sparse representation of the singular vectors can further increase the compression ratio of the image while effectively retaining the detail information.
Preferably, in S4, after obtaining the value of the key point, for the point to be interpolated, calculating a quotient between a difference between the point and the key point and a distance between the point and the key point as a prediction basis, that is, according to information of a point on the interpolation point, predicting and restoring each interpolation point, where point information reconstructed by the key value is substantially matched with original image information, and the image information is effectively expressed.
Preferably, two-stage compression of the image is realized on the basis of singular value decompression, the compression ratio of the image is improved on the premise of ensuring the image quality, and the image reconstruction quality of the method is better under the condition of the same compression ratio.
Compared with the prior art, the invention has the beneficial effects that: the image is further compressed, and the quality of the reconstructed image is better than that of other image compression methods under the same compression ratio; an effective interpolation method is designed according to the information of the original image and the characteristics of the left and right singular matrixes to realize the restoration of the left and right singular matrixes, and the image reconstruction result of the method is closer to the original image than the original singular value decomposition method.
Of course, it is not necessary for any product in which the invention is practiced to achieve all of the above-described advantages at the same time.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a visual line graph of singular matrix column information according to the present invention;
FIG. 2 is a left image of the present invention, which is an original image, and a middle image and a right image are comparative views of compression conditions of SVD under different compression ratios;
FIG. 3 is a diagram of the signal reconstruction results of downsampling and random sampling according to the present invention;
FIG. 4 is a graph of a selected distribution of singular vector keypoints according to the present invention;
FIG. 5 is a graph of the image interpolation result distribution according to the present invention;
FIG. 6 is a comparison graph of compression effects of different image compression methods under the condition of the compression ratio of 20: 1.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1 to 6, the present invention provides a technical solution of an image compression method based on singular vector sparse reconstruction: a image compression method based on singular vector sparse reconstruction comprises the steps of carrying out singular value decomposition on an original image matrix to obtain a left singular vector matrix, a right singular vector matrix and a singular value matrix of an image; firstly, according to the contribution of the calculated singular value to an image signal, selecting a proper singular value, discarding the singular value with smaller contribution to the image signal, and realizing first-order compression of the image; for a singular vector matrix generated by singular value decomposition of an image matrix, carrying out sparse sampling on the singular vector matrix to construct further compression of a sparse singular matrix experiment on the basis of singular value decomposition; the proposed sampling method is that for the singular vector matrix of each column value, the singular matrix of the key point characteristic vector is selected by matching the least square method of the corresponding function curve column, and the peak value and the valley value of the function are searched, so that the sparse representation matrix of the singular vector is realized; the selection of singular vector key points is shown in fig. 4; the sparse representation of the singular vector can further improve the compression ratio of the image on the premise of effectively retaining detail information, and the method has the advantages that key points are selected for high-frequency and low-frequency information of the image, the main characteristics of the image are saved, and the details of the image are not directly discarded like original singular value decomposition; the method for selecting the singular vector key points can realize the selection of key points close to 4:1, so that the sampling method has advantages over the traditional Nyquist sampling theorem; in a decompression stage, performing sparse representation on a left singular vector matrix and a right singular vector matrix of the image, and performing linear interpolation recovery to reconstruct the image; after the value of the key point is obtained, calculating the quotient of the difference value of the point and the key point and the distance between the point and the key point as a prediction basis for the point to be interpolated; in short, each interpolation point is predicted and restored according to the information of one point on the interpolation point; the image interpolation results are shown in fig. 5; it can be seen that the point information reconstructed by the key value is basically matched with the original image information, and the image information is effectively expressed; the image compression method provided by the patent has good performance in the aspects of signal recovery and image reconstruction;
the compression ratio calculation formula of the algorithm is as follows:
wherein r represents r singular values selected after singular value decomposition, and p is the ratio of singular matrix critical point operation after sparse representation. The lower bound of the image compression ratio of the algorithm can be seen as the compression ratio of the image compression method based on singular value decomposition.
On the basis of SVD compression, two-stage compression of the image is realized, and the compression ratio of the image is improved on the premise of ensuring the image quality. Algorithm 1 summarizes a complete image compression algorithm based on singular vector sparse reconstruction.
Inputting color or gray-scale images
Converting the original image into a two-dimensional matrix A:
selecting proper singular values for image compression:
sparse representation of left and right singular matrices:
U→U'sprase
V→V'sprase
image reconstruction based on singular vector sparse reconstruction:
outputting the compressed image, compression ratio and peak signal-to-noise ratio;
experiments are carried out on different data sets, and the peak signal-to-noise ratio and the structural similarity of the compressed images are calculated as shown in tables 1 and 2, so that the performance of the method provided by the patent is superior to that of other image compression methods. The image reconstruction effects of different compression methods are shown in fig. 6, and under the same compression ratio, the proposed algorithm has better subjective visual effect after image reconstruction;
TABLE 1 Peak SNR for images at 10:1 compression ratio
TABLE 2 image Structure similarity at a compression ratio of 10:1
In order to overcome the information loss and improve the compression ratio of the traditional image compression method based on singular value decomposition, a singular vector sparse reconstruction strategy is provided;
the image is further compressed, and the quality of the reconstructed image is better than that of other image compression methods under the same compression ratio; an effective interpolation method is designed according to the information of an original image and the characteristics of left and right singular matrixes to realize the restoration of the left and right singular matrixes, and the image reconstruction result of the method is closer to an original image than that of the original singular value decomposition method;
the experimental results clearly demonstrate the advantages of the proposed strategy in compression ratio and reconstruction quality.
1. An effective singular vector sparse reconstruction image compression strategy based on singular value decomposition is provided.
2. According to the information of the original image and the characteristics of the left and right singular matrixes, an effective image interpolation method is designed to reconstruct the left and right singular matrixes.
3. Experiments are carried out on data sets such as natural images, low-light-level images, remote sensing images and underwater images, and the effectiveness and the generalization of the algorithm are verified.
In the description herein, references to the description of "one embodiment," "an example," "a specific example" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise embodiments disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.
Claims (4)
1. An image compression method based on singular vector sparse reconstruction is characterized by comprising the following steps:
s1: singular value decomposition is carried out on an original image matrix to obtain a left singular vector matrix, a right singular vector matrix and a singular value matrix of the image;
s2: selecting proper singular values according to the calculated contribution of the singular values to the image signals to realize first-order compression of the image;
the compression ratio calculation formula of the algorithm is as follows:
r represents r singular values selected after singular value decomposition, p is the ratio of singular matrix key points after sparse representation, and the lower bound of the image compression ratio of the algorithm can be seen as the compression ratio of the image compression method based on singular value decomposition;
s3: sparse singular matrixes are constructed by fitting an image signal curve and carrying out sparse sampling on the left singular matrix and the right singular vector matrix to realize further compression on the basis of singular value decomposition, and the sampling efficiency close to 4:1 can be realized after sparse sampling to be superior to the traditional Nyquist sampling theorem;
s4: in the decompression stage, the left singular vector matrix and the right singular vector matrix of the image are subjected to linear interpolation to realize the reconstruction of the compressed image.
2. The image compression method based on singular vector sparse reconstruction as claimed in claim 1, wherein: in S3, the sparse representation of the singular vectors can further increase the compression ratio of the image while effectively retaining the detail information.
3. The image compression method based on singular vector sparse reconstruction as claimed in claim 1, wherein: in S4, after the value of the key point is obtained, for the point to be interpolated, a quotient between a difference between the point and the key point and a distance between the point and the key point is calculated as a prediction basis, that is, each interpolation point is predicted and restored according to information of a point on the interpolation point, point information reconstructed by the key value is substantially matched with original image information, and the image information is effectively expressed.
4. The image compression method based on singular vector sparse reconstruction as claimed in claim 1, wherein: and realizing two-stage compression of the image on the basis of singular value decompression.
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| CN107170018A (en) * | 2017-05-25 | 2017-09-15 | 中国科学院光电技术研究所 | Constitution optimization method based on compressed sensing calculation matrix in image reconstruction |
| CN108832934A (en) * | 2018-05-31 | 2018-11-16 | 安徽大学 | A kind of two-dimensional quadrature match tracing optimization algorithm based on singular value decomposition |
| US10671697B1 (en) * | 2017-02-24 | 2020-06-02 | Cyber Atomics, Inc. | Iterative and efficient technique for singular value decomposition |
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|---|---|---|---|---|
| US10671697B1 (en) * | 2017-02-24 | 2020-06-02 | Cyber Atomics, Inc. | Iterative and efficient technique for singular value decomposition |
| CN107170018A (en) * | 2017-05-25 | 2017-09-15 | 中国科学院光电技术研究所 | Constitution optimization method based on compressed sensing calculation matrix in image reconstruction |
| CN108832934A (en) * | 2018-05-31 | 2018-11-16 | 安徽大学 | A kind of two-dimensional quadrature match tracing optimization algorithm based on singular value decomposition |
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Application publication date: 20210112 |