Image compressed sensing method based on bilateral sparse representation

Abstract

The invention relates to a bilateral sparse representation-based image compressed sensing method, which comprises the following steps of: obtaining an original image, and segmenting the original image to obtain a plurality of image blocks; performing bidirectional Haar wavelet transform on the image blocks to obtain a sparse matrix, vectorizing the sparse matrix, and obtaining a one-dimensional sparse vector; and carrying out compression and image reconstruction on the one-dimensional sparse vector to obtain a final reconstructed image. According to the method, the precision of the compressed sensing algorithm in the image reconstruction process can be greatly improved, and meanwhile, the calculation processing efficiency is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical fields of image processing and compressive sensing, and particularly to an image compressive sensing method based on bilateral sparse representation. Background Art

[0002] In order to save the costs of signal storage and transmission, the Compressed Sensing (CS) algorithm can compress a one-dimensional sparse signal (most elements in the signal are 0, or elements with very small absolute values close to zero) into an observation signal with a shorter length, and then reconstruct the original signal from the observation signal when necessary. If the original signal is not sparse, it can be converted into a sparse signal under a certain sparse basis representation, and this conversion is usually reversible. Therefore, after compressing the signal using the compressive sensing algorithm, the original non-sparse signal can still be recovered from the sparse signal. The compressive sensing theory breaks through the limitations of the traditional Nyquist sampling theorem and realizes the high-precision recovery of the original signal from a small amount of observation data through the three elements of sparse representation, linear measurement, and optimization reconstruction. The core formula of its compression process can be expressed as: y = Φx = ΦΨα, where, x ∈ R ,

[0006] ,

[0005] is the original signal with length N, y ∈ R M is the observation signal with length M (M << N), Φ ∈ R M*N is the measurement matrix, Ψ ∈ R N*N is the sparse basis, α ∈ R N×1 is the sparse signal, x = Ψα represents the process of converting the non-sparse original signal into a sparse signal, which is called sparse representation. Since the length of the signal y is much smaller than the original signal x, using y to replace x during storage and transmission can save a lot of memory. The signal y has no logical information, so when needed, the compressive sensing algorithm can reconstruct the sparse signal α from the observation signal y, and then, according to the reversibility of the sparse representation, reconstruct the original signal x = Ψα to the greatest extent.

[0003] Since an image is a two-dimensional signal, during the process of image processing, it is necessary to convert the two-dimensional signal form of the image, that is, the matrix, into a vector, and then use the compressive sensing algorithm for compression and reconstruction. Then, when needed, the original image can be reconstructed from the vector in the reverse order of the matrix splitting at that time. If the image pixels are too large, the image also needs to be cut into several image blocks, and then the compressive sensing algorithm is used for compression and reconstruction.

[0004] In the prior art, the main methods for image sparse representation are as follows:

[0005] (1) Global transformation method:

[0006] Discrete Cosine Transform (DCT): Converts the image to the frequency domain and uses the energy concentration characteristic to achieve sparseness. Wavelet Transform:

[0007] Image edge and texture features are captured through multi-scale decomposition. Common bases include Haar and Daubechies.

[0008] (2) Local dictionary learning method:

[0009] Use K-SVD and other algorithms to train overcomplete dictionaries to improve adaptability to specific image features.

[0010] There are three core problems with existing technologies:

[0011] 1. Problems of two-dimensional structure destruction and information loss:

[0012] Traditional sparse representation methods (such as DCT, single-level wavelet transform) need to transform the two-dimensional image matrix X∈R in the preprocessing stage. M×N Force expansion to a one-dimensional vector x∈R M·N×1 When performing thinning, such as Figure 1 This approach of first vectorizing a two-dimensional image and then performing sparse representation and compression reconstruction has the following key flaws:

[0013] Spatial correlation is destroyed: During image processing, the inherent spatial correlation between rows and columns of an image is forcibly decoupled. This decoupling operation directly leads to a significant decrease in the ability to co-encode high-frequency details in the image (such as key information such as edges and textures) during compression. This decrease in ability means that after compression, the details of the image may be distorted, affecting the overall image quality.

[0014] Boundary artifact generation: During block processing, independent vectorization between adjacent blocks can easily cause discontinuities at the boundaries. This discontinuity can further lead to visible blocking artifacts during image reconstruction. According to actual measurement data, this blocking artifact can cause a loss of 1.5 to 2.0 dB in peak signal-to-noise ratio (PSNR), which is highly detrimental to maintaining image quality.

[0015] Entropy redundancy: After vectorizing an image, the resulting signal's entropy increases significantly compared to the original image matrix. Shannon entropy measurements show this increase ranges from 15% to 30%. This increase in entropy means the encoder must allocate more bits to process this redundant information during encoding, increasing encoding complexity and resource consumption while reducing efficiency.

[0016] 2. Imbalance between sparsity and attenuation characteristics:

[0017] In current sparse transform methods, there is a significant trade-off between sparsity (the number of non-zero elements) and decay rate (the proportion of large coefficients in the total number). This imbalance has brought many inconveniences and limitations to practical applications.

[0018] Limitations of the DCT: First, the slow decay characteristic of the DCT (Discrete Cosine Transform) is a significant problem. Specifically, the energy of the DCT coefficients decays according to the 1 / f law, meaning that among the transformed coefficients, significant non-zero elements with an absolute value greater than 10 account for a staggering 14.92% (this data is based on actual measurements of a 100×100 pixel block). This slow decay characteristic makes it difficult for the DCT to effectively reduce the amount of data during the compression process.

[0019] Secondly, DCT's directional insensitivity is a significant drawback. Because DCT cannot effectively distinguish between horizontal and vertical features in an image, high-frequency noise and significant image details are mixed together during encoding. This mixed encoding not only degrades image quality but also increases the complexity of subsequent processing.

[0020] Disadvantages of wavelet transforms: Traditional wavelet transforms, especially the single-level Haar wavelet transform, also have significant shortcomings. The drawback of single-level decomposition is that it only achieves a decay rate of O(1 / √N), which is far from sufficient to meet the requirements of high compression ratios. In high-compression applications, this low decay rate prevents the effective removal of a large amount of redundant information.

[0021] Another shortcoming of the wavelet transform is the basis function mismatch problem. A fixed wavelet basis cannot flexibly adapt to a variety of image features, such as smooth areas and highly textured regions. This mismatch makes it difficult for the wavelet transform to achieve ideal results when processing complex images.

[0022] High computational complexity and real-time bottlenecks: Existing sparse transformation methods face severe computational efficiency challenges due to the limitations of the algorithm architecture, which seriously restricts their performance and real-time performance in practical applications.

[0023] First, the computational complexity of the global DCT is very high. Specifically, the complexity of the two-dimensional DCT reaches O(N 3 ), which means that when processing high-resolution 4K images (resolution of 3840×2160), the number of operations required will exceed 10^11 times. Such a large amount of calculation is not only time-consuming, but also places extremely high demands on hardware resources.

[0024] Secondly, the computational complexity of dictionary learning methods is also daunting. Taking the K-SVD algorithm as an example, its training complexity is as high as O(KN 3 ), which makes it difficult to implement online updates in dictionary learning in practical applications. The lack of online update capabilities limits the application scope and effectiveness of dictionary learning in dynamic environments.

[0025] 3. Analysis of defects in existing technologies:

[0026] Structural destruction problem: Traditional methods require forced vectorization of two-dimensional images, destroying their row and column spatial correlation, resulting in block effects and blurred details in the reconstructed image.

[0027] Insufficient sparsity: The DCT coefficient decays slowly. Measured data show that in a 100×100 image block, the number of elements with an absolute value greater than 10 reaches 1,492 (accounting for 14.92% of the total elements).

[0028] High computational complexity: The computational complexity of non-separable transformation is O(N 2 ), which makes it difficult to meet real-time processing requirements (such as 4K video streaming).

[0029] Analysis of relevant technical solutions: By searching domestic and foreign patent databases, existing representative technical solutions include:

[0030] Existing technology solutions disclose image compression methods based on adaptive dictionary learning. While these methods improve sparsity, dictionary training is time-consuming and generalization is poor. Existing technology solutions also disclose sparse representation systems using a hybrid DCT-wavelet basis, but these fail to address the structural loss caused by vectorization. Existing technology solutions also disclose multidimensional signal processing based on tensor decomposition, which is extremely complex and difficult to implement in hardware. Summary of the Invention

[0031] In order to solve the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide an image compression sensing method based on bilateral sparse representation, which can not only greatly improve the accuracy of the compression sensing algorithm in the image reconstruction process, but also significantly improve the efficiency of computational processing.

[0032] To achieve the above object, the present invention provides the following solutions:

[0033] An image compression sensing method based on bilateral sparse representation, comprising:

[0034] Acquire an original image, segment the original image, and obtain a plurality of image blocks;

[0035] Performing a bidirectional Haar wavelet transform on the image block to obtain a sparse matrix, and vectorizing the sparse matrix to obtain a one-dimensional sparse vector;

[0036] The one-dimensional sparse vector is compressed and an image is reconstructed to obtain a final reconstructed image.

[0037] Optionally, obtaining the sparse matrix includes:

[0038] Performing Haar wavelet transform on the image block in horizontal and vertical directions to obtain the sparse matrix.

[0039] Optionally, when performing Haar wavelet transform on the image block in the horizontal and vertical directions, the power of 2 of the Haar wavelet matrix is used as a sparse basis.

[0040] Optionally, using the power of 2 of the Haar wavelet matrix as a sparse basis, performing Haar wavelet transform on the image block in the horizontal and vertical directions includes:

[0041] Y=D·X·D -1

[0042] Among them, Y is the sparse matrix, D is the sparse basis, X is the image block, D -1 is the inverse matrix of the sparse basis.

[0043] Optionally, obtaining the one-dimensional sparse vector includes:

[0044]

[0045] in, is a one-dimensional sparse vector, vec(·) represents the vectorization process of the matrix, Y N×N is an N×N image block matrix.

[0046] Optionally, obtaining the final reconstructed image includes:

[0047] The one-dimensional sparse vector is compressed to obtain a plurality of observation signals. When the original image needs to be restored, each observation signal is reconstructed to obtain a corresponding sparse signal. The corresponding sparse signals are used to gradually restore each image block, and the image blocks are recombined according to the original order when they were segmented to obtain the final reconstructed image.

[0048] Optionally, compressing the one-dimensional sparse vector includes:

[0049]

[0050] Among them, a M×1 is the observation signal, a one-dimensional sparse vector, is the measurement matrix, M is the sparse vector a M×1 The length of N is the image block matrix Y N×N Length and height, N 2 is a sparse vector length.

[0051] The beneficial effects of the present invention are:

[0052] The present invention adopts a more efficient strategy. Specifically, first, the Haar wavelet transform matrix is applied to perform detailed decomposition processing in the horizontal and vertical directions of the image. Through this two-way decomposition, the characteristic information of the image in different directions can be captured more comprehensively. Next, the matrix data obtained after the decomposition processing is converted into a one-dimensional vector form. This conversion process not only retains the original information of the image, but also significantly improves the overall effectiveness of the sparse representation by optimizing the sparsity and attenuation characteristics of the obtained one-dimensional signal. The use of this sparse representation method not only greatly improves the accuracy of the compressed sensing algorithm in the image reconstruction process, but also significantly improves the efficiency of the computational processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0054] Figure 1 A schematic diagram of the background technology of forcibly expanding a two-dimensional image matrix into a one-dimensional vector for sparsification;

[0055] Figure 2 Schematic diagram of image segmentation according to an embodiment of the present invention;

[0056] Figure 3 This is a flowchart of image block processing according to an embodiment of the present invention;

[0057] Figure 4 Schematic diagram of the reconstruction process of an embodiment of the present invention;

[0058] Figure 5 This is a flow chart of an image compression sensing method based on bilateral sparse representation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0059] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0060] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0061] This embodiment discloses an image compression sensing method based on bilateral sparse representation, including: obtaining an original image, segmenting the original image to obtain a plurality of image blocks; performing a bidirectional Haar wavelet transform on the image blocks to obtain a sparse matrix, vectorizing the sparse matrix to obtain a one-dimensional sparse vector; compressing the one-dimensional sparse vector and reconstructing the image to obtain a final reconstructed image.

[0062] Furthermore, image segmentation includes: in order to significantly improve the overall efficiency of the image during compression and reconstruction, the present invention performs a detailed and systematic segmentation of the original image into multiple smaller image blocks, such as Figure 2 shown.

[0063] This segmentation method evenly and orderly divides the original image into several independent blocks. Each block accurately carries a portion of the original image information. This refined segmentation method not only ensures information integrity but also greatly facilitates subsequent compression processing and efficient reconstruction operations. This segmentation strategy makes the image compression and reconstruction process more efficient and accurate, significantly improving overall processing efficiency.

[0064] Furthermore, obtaining the sparse matrix includes performing Haar wavelet transform on the image block in the horizontal and vertical directions to obtain the sparse matrix. When performing Haar wavelet transform on the image block in the horizontal and vertical directions, the power of 2 of the Haar wavelet matrix is used as a sparse basis.

[0065] Specifically, the image blocks are sparsely represented:

[0066] This paper proposes a bilateral sparse representation (BSR) method to achieve improved sparsity:

[0067] Use bidirectional wavelet decomposition to sparsely represent the image. Haar wavelet transform is an effective tool for sparse transformation of signals. It is widely used in many application fields by extracting low-frequency and high-frequency information of the signal layer by layer. Haar wavelet transform can be implemented by a Haar wavelet transform matrix. The second-order Haar wavelet transform matrix is: For a general n-order Haar wavelet transform matrix, it can be expressed as:

[0068] The bilateral sparse representation (BSR) method uses the power of 2 of the Haar wavelet matrix as the sparse basis, D = H 2 For a two-dimensional image matrix X∈R N×NPerform Haar wavelet transform in both horizontal and vertical directions at the same time. The mathematical expression is: Y = D·X·D′. Since D is an orthogonal matrix, its inverse matrix is equal to the transposed matrix, so it can also be written as: Y = D·X·D -1 , then we get the sparse matrix Y∈R N×N Then vectorize the matrix to get a one-dimensional sparse vector A N2×1 =vec(Y N×N ) in order to realize the compression and reconstruction of the signal. The processing flow of the image block is as follows Figure 3 shown.

[0069] This structure-preserving sparsification method can directly preserve the two-dimensional spatial correlation of image blocks through bidirectional decomposition of image blocks, avoiding the information loss caused by traditional vectorization. In addition, the bidirectional decomposition separates the horizontal / vertical high-frequency components, so that the energy is more concentrated in the low-frequency area, significantly reducing redundant non-zero elements.

[0070] Furthermore, obtaining the final reconstructed image includes: compressing the one-dimensional sparse vector to obtain a number of observation signals; when the original image needs to be restored, reconstructing each observation signal to obtain the corresponding sparse signal; using the corresponding sparse signal, gradually restoring each image block; and recombining the image blocks according to the original order when they were segmented to obtain the final reconstructed image.

[0071] Specifically, compression of a one-dimensional vector: The original signal can be converted into a sparse signal through a sparse transformation, but this does not achieve compression of the original signal because, although it contains many zero points, its length is not reduced compared to the original signal. The length of the compressed observation signal is actually determined by the measurement matrix, that is, the number of rows and columns of the measurement matrix determines the compression ratio. In compressed sensing methods, commonly used measurement matrices include Gaussian random matrices, Bernoulli matrices, and partial Hadamard matrices. The present invention selects the Bernoulli matrix as the measurement matrix.

[0072] The Bernoulli matrix is highly random and independent of most sparse bases. The values of the elements in the matrix are very simple, consisting of only 1 and -1, making it easy to generate and store. It is commonly used in random matrix theory, compressed sensing, signal processing, and statistical modeling. The elements of this matrix are randomly drawn from a Bernoulli distribution, meaning that each element of the Bernoulli matrix is obtained independently of the two-point distribution: Its compression of one-dimensional sparse signals can be expressed as: This results in an observed signal a that occupies less memory than the original signal M×1 .

[0073] Image reconstruction: After the original image is subjected to a series of compression processes according to the above steps, several observation signals will eventually be generated. These observation signals occupy significantly less memory than the original image, so the resources required during storage or transmission can be greatly reduced, thereby saving more costs. When the original image needs to be restored, the OMP (orthogonal matching pursuit) algorithm can be used to accurately reconstruct each observation signal to obtain the corresponding sparse signal. Because the bilateral sparse representation is reversible, these sparse signals can be used to gradually restore each image block. Finally, by recombining the image blocks in the original order in which they were cut during the compression process, a reconstructed image that is extremely close to the original image can be obtained, with very small errors. The specific steps and details of the entire reconstruction process are as follows. Figure 4 As shown in the figure, the complete process from observed signal to sparse signal and finally to reconstructed image is clearly shown.

[0074] The specific effects of the present invention include the following aspects:

[0075] 1. Improved sparsity: Compared with traditional sparse representation methods, this method has a better sparsity effect on image blocks. In a 100×100 image block, the number of elements with absolute values greater than 10 in the sparse vector generated by BSR is 1,201, which is 19.5% less than the 1,492 elements in DCT.

[0076] 2. Optimizing attenuation characteristics: The attenuation characteristics of sparse vectors (i.e., the proportion of large coefficients) directly affect the reconstruction stability of compressed sensing. The attenuation coefficient energy of traditional DCT decays at a rate of 1 / √k, and the proportion of elements with an absolute value greater than 70 begins to approach zero. However, the sparsely represented image blocks of the BSR method decay more quickly, and elements with an absolute value greater than 40 begin to approach zero.

[0077] 3. Improvement of reconstruction quality and efficiency: In the experiment, the BSR method is selected to perform sparse representation of image blocks, and the OMP algorithm is used to reconstruct the observation signal. The experiment is conducted on images selected from the CVG-UGR image library. The results are shown in Table 1.

[0078]

[0079] Figure 5 The process of using the BSR method to sparsely represent and compress images in the compressed sensing method is as follows: 1. Cut the original image into several image blocks; 2. Sparsely represent each image block to obtain several sparse matrices; 3. Vectorize each sparse matrix to obtain a sparse vector; 4. Use the Bernoulli random matrix to compress the sparse vector to obtain several one-dimensional observation vectors, and combine the observation vectors together to obtain the observation signal after image compression, so as to save memory in storage and transmission.

[0080] Figure 5 The compressed sensing method reconstructs the original image based on the compressed observation signal: 1. Use the OMP algorithm to reconstruct a sparse vector based on each one-dimensional observation signal; 2. Inverse quantize (matrix) the sparse vector to obtain a sparse matrix; 3. Because the BSR method is reversible, the image block can be restored based on the sparse matrix; 4. Combine the image blocks in the order of cutting to obtain a reconstructed image with very small error from the original image to meet the requirements for high-definition pixels during use.

[0081] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. An image compression sensing method based on bilateral sparse representation, characterized in that: include: Acquire an original image, segment the original image, and obtain a plurality of image blocks; Performing a bidirectional Haar wavelet transform on the image block to obtain a sparse matrix, and vectorizing the sparse matrix to obtain a one-dimensional sparse vector; The one-dimensional sparse vector is compressed and an image is reconstructed to obtain a final reconstructed image.

2. The image compression sensing method based on bilateral sparse representation according to claim 1, characterized in that: Obtaining the sparse matrix includes: Performing Haar wavelet transform on the image block in horizontal and vertical directions to obtain the sparse matrix.

3. The image compression sensing method based on bilateral sparse representation according to claim 2, characterized in that: When performing Haar wavelet transform on the image block in the horizontal and vertical directions, the power of 2 of the Haar wavelet matrix is used as a sparse basis.

4. The image compression sensing method based on bilateral sparse representation according to claim 3, characterized in that: The method of performing Haar wavelet transform on the image block in the horizontal and vertical directions using the power of 2 of the Haar wavelet matrix as a sparse basis includes: Y=D·X·D -1 Among them, Y is the sparse matrix, D is the sparse basis, X is the image block, D -1 is the inverse matrix of the sparse basis.

5. The image compression sensing method based on bilateral sparse representation according to claim 1, characterized in that: Obtaining the one-dimensional sparse vector includes: in, is a one-dimensional sparse vector, vec(·) represents the vectorization process of the matrix, Y N×N is an N×N image block matrix.

6. The image compression sensing method based on bilateral sparse representation according to claim 1, characterized in that: Acquiring the final reconstructed image includes: The one-dimensional sparse vector is compressed to obtain a plurality of observation signals. When the original image needs to be restored, each observation signal is reconstructed to obtain a corresponding sparse signal. The corresponding sparse signals are used to gradually restore each image block, and the image blocks are recombined according to the original order when they were segmented to obtain the final reconstructed image.

7. The image compression sensing method based on bilateral sparse representation according to claim 6, characterized in that: Compressing the one-dimensional sparse vector includes: Among them, a M×1 is the observation signal, a one-dimensional sparse vector, is the measurement matrix, M is the sparse vector a M×1 The length of N is the image block matrix Y N×N Length and height, N 2 is a sparse vector length.

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