Hyperspectral Image Sparse Reconstruction Method with Non-Local Similarity Block 4D Correlation Constraint

Abstract

The present invention discloses a hyperspectral image sparse reconstruction method with non-local similar block 4D correlation constraint, belonging to the field of hyperspectral remote sensing image compression. For the hyperspectral image of each band group, first, for the non-local 3D similar blocks of each band, 4D similar data is formed through the spectral dimension. Then, the sparsity metric of the non-local similar data in the 4D transform domain is obtained through wavelet transform and used as the constraint prior in the hyperspectral remote sensing image reconstruction process. On this basis, a hyperspectral image sparse reconstruction model is obtained by combining the total variation regularization scheme. The present invention fully exploits the inherent correlation of hyperspectral images and has the advantages of high compression ratio, good fidelity quality, low requirement for grouping accuracy, and strong robustness.

Description

Technical Field

[0001] The present invention belongs to the field of digital image processing methods, and particularly relates to a hyperspectral image sparse reconstruction method with non-local similar block 4D correlation constraint in the field of hyperspectral remote sensing image compressive sensing reconstruction. Background Art

[0002] Hyperspectral remote sensing technology has laid a foundation for realizing fine detections such as unified and all-round discrimination of ground object attributes and geometric positioning. Through the observation and analysis of hyperspectral images, geological surveys, vegetation research, ore deposit detection, marine and atmospheric environment monitoring, etc. can be carried out, solving many application fields that cannot be achieved by traditional technologies due to the environment, and playing an important role in promoting the development of human society. However, hyperspectral remote sensing images require a huge amount of data to be saved due to the acquisition of spatial information and spectral information of ground objects, and these huge amounts of data bring great difficulties to the online transmission and subsequent practical applications of hyperspectral images. How to effectively organize and transmit hyperspectral remote sensing image information has become a frontier issue in the current field of hyperspectral image information processing and applications. Hyperspectral image sparse reconstruction under the theory of Compressed Sensing (CS) provides an important way to solve this problem.

[0003] A large number of research results show that the design of hyperspectral image sparse reconstruction algorithms and models has a great impact on the quality of the reconstructed images. Most traditional reconstruction algorithms aim to achieve fast reconstruction at the cost of sacrificing approximation accuracy, and their reconstruction quality is relatively low. In order to improve the reconstruction quality, some researchers have proposed methods such as a variable sampling rate hyperspectral image reconstruction method based on CS, a spatio-spectral joint multi-hypothesis prediction model, a fast sparse decomposition algorithm for remote sensing images based on an over-complete atom library, and a prediction method of using reference bands for ordinary bands. Among them, the variable sampling rate hyperspectral image reconstruction method based on CS theory uses different sampling rates for different groups of reference bands and non-reference bands, providing new ideas for subsequent researchers; the spatio-spectral joint multi-hypothesis prediction model uses the predicted values of each image block in the reference band image for its own and the reference blocks of adjacent reference bands in the reference band; the fast sparse decomposition algorithm for remote sensing images based on an over-complete atom library removes the spectral redundancy between remote sensing images by using a greedy clustering solution method; the prediction method of using reference bands for ordinary bands uses reference bands to predict ordinary bands to achieve reconstruction.

[0004] However, the above methods fail to fully explore and utilize the inherent spectral and spatial correlations in hyperspectral images, resulting in varying degrees of influence on the quality of the finally reconstructed hyperspectral images. Summary of the Invention

[0005] The present invention aims to solve the above-mentioned technical problems existing in the prior art, and provides a hyperspectral image sparse reconstruction method with non-local similar block 4D correlation constraint.

[0006] The technical solution of the present invention is as follows: A hyperspectral image sparse reconstruction method with non-local similar block 4D correlation constraint is carried out according to the following steps:

[0007] Step 1. Initial values of Gaussian random matrix sampling for each band of the k-th group of hyperspectral images at the reconstruction end Establish a non-local sparse representation model in the 4D transform domain according to formula (1), where N k represents the number of bands in this group, represents the i-th band image with size m×n,

[0008]

[0009] In the formula, B j is an 8×8 block in , j = 1, 2, …, (m - 8)×(n - 8) / 5; represents a group of 8×8 blocks with non-local correlation in 4D. The specific formation process is to find 5 8×8 blocks with non-local correlation with B j for each band image, and form a 3D block according to the correlation strength. Further, the 3D blocks of each band are formed into a 4D non-local similar block group in the order of bands; represents performing a 4D transform on , that is, performing a 2D wavelet and 1D discrete cosine hybrid transform on the 3D blocks formed by each band, and then performing a 1D wavelet transform between spectra;

[0010] Step 2. Establish a compressive sensing reconstruction model 4DNTCoSM for the k-th group of bands according to formula (2)

[0011]

[0012] where A is the sampling matrix and Y is the sampling data; is the sum of the horizontal gradient and vertical gradient of each pixel in the i-th band of the k-th group of hyperspectral images; is the sum of the absolute values of the differences between each pixel of the i-th band and the (i - 1)-th band of the k-th group of hyperspectral images. When i is 1, i - 1 is selected as 2 according to the symmetric extension principle;

[0013] Step 3. Use formula (3) to transform the established reconstruction model (2) into an optimization problem for solution

[0014]

[0015] Among them, λ is a non - negative parameter;

[0016] Step 4. Introduce an intermediate variable u (k) , and let X (k) = u (k) , thus transforming formula (3) into formula (4);

[0017]

[0018] Step 5. Use the Alternating Direction Method based on augmented Lagrangian to solve formula (4), and transform it into the three - step iterative sub - problems shown in formulas (5) - (7):

[0019]

[0020]

[0021] b (t+1) = b (t) ((X (k) )) (t+1) - (u (k) )) (t+1) ) (7)

[0022] Among them, μ and m are positive parameters;

[0023] Step 6. Use the "Steepest Gradient Descent Method" to solve formula (5):

[0024] (X (k) ) (t+1) = (X (k) ) (t) - h(A T (A(X (k) )) (t) - Y) + m((X (k) )) (t) - (u (k) )) (t) - b (t) )) (8)

[0025] Among them, h is the optimal descent step size;

[0026] Step 7. Iteratively solve formulas (8), (6), and (7) to obtain X (k) .

[0027] The present invention first fully exploits and utilizes the strong correlation inherent in hyperspectral images. It searches for the index positions of non-locally similar small patches within the band group of the hyperspectral image in the first band and saves the index positions for the subsequent hyperspectral image to be reconstructed, which can effectively shorten the running time of the non-local regularization model and the overall algorithm time. Secondly, considering that the non-locally similar small patches searched for the reference small patch at the same position in each band within the band group not only have a certain similarity in the same band but also have a certain similarity in the entire band, the similar small patches searched at the same position in different bands are treated as a whole. In this way, it is only necessary to search for similar patches in the first band, avoiding the time consumption of searching for similar patches band by band. Finally, the requirements for the accuracy of hyperspectral band grouping are relatively low for the range and reconstruction results, improving the robustness of the algorithm. Therefore, the present invention fully explores the inherent correlation of hyperspectral images and has the advantages of high compression ratio, good fidelity quality, low requirements for grouping accuracy, and strong robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 FIG. is a schematic diagram showing the formation process of the 4D non-locally similar patch group in Embodiment 4 of the present invention.

[0029] Figure 2 FIG. is the original band of the hyperspectral image of the Dalian area taken by the EO-1 satellite used in the embodiment of the present invention.

[0030] Figure 3 FIG. is for the present invention embodiment at different bit rates Figure 2 The reconstructed band of the hyperspectral image. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0031] A method for sparse reconstruction of hyperspectral images with 4D correlation constraints of non-locally similar patches according to the present invention is carried out according to the following steps:

[0032] Step 1. For the initialization value of the Gaussian random matrix sampling of each band of the k-th group of hyperspectral images at the reconstruction end Establish a non-local sparse representation model in the 4D transform domain according to formula (1), where N k represents the number of bands in this group, represents the i-th band image with size m×n,

[0033]

[0034] In the formula, B j is an 8×8 block in , and j = 1, 2, …, (m - 8)×(n - 8) / 5; represents a group of 8×8 blocks with 4D non-local correlation, and the specific formation process is as Figure 1 shown, which is to find for each band image the one that is similar to Bj Five 8×8 blocks with non-local correlation are formed into 3D blocks according to the correlation strength, and the 3D blocks of each band are further formed into a 4D non-local similarity block group in the order of the bands; Denote the 4D transform is performed, that is, a 2D wavelet and 1D discrete cosine hybrid transform is performed on the 3D blocks formed by each band, and then a 1D wavelet transform is performed between spectra;

[0035] Step 2. Establish the compressive sensing reconstruction model 4DNTCoSM for the k-th group of bands according to formula (2)

[0036]

[0037] where A is the sampling matrix and Y is the sampling data; is the sum of the horizontal gradient and the vertical gradient of each pixel in the i-th band of the k-th group of hyperspectral images; is the sum of the absolute values of the differences of each pixel between the i-th band and the (i - 1)-th band of the k-th group of hyperspectral images. When i is 1, i - 1 is selected as 2 according to the symmetric extension principle;

[0038] Step 3. Use formula (3) to transform the established reconstruction model (2) into an optimization problem for solution

[0039]

[0040] where λ is a non-negative parameter;

[0041] Step 4. Introduce an intermediate variable u (k) , and let X (k) = u (k) , thus transforming formula (3) into formula (4);

[0042]

[0043] Step 5. Solve formula (4) by the alternating direction method based on the augmented Lagrangian, and transform it into the three-step iterative sub-problems shown in formulas (5)-(7):

[0044]

[0045]

[0046] b (t+1) = b (t) ((X (k) ) (t+1) - (u (k) ) (t+1) ) (7)

[0047] where μ and m are positive parameters;

[0048] Step 6. Solve formula (5) using the "steepest gradient descent method":

[0049] (X (k) ) (t+1) =(X (k) ) (t) -h(A T (A(X (k) ) (t) -Y)+m((X (k) ) (t) -(u (k) ) (t) -b (t) )) (8)

[0050] where h is the optimal descent step size;

[0051] Step 7. Iteratively solve formulas (8), (6), and (7) to obtain X (k) .

[0052] Experiment:

[0053] Using the embodiments of the present invention, the original bands of the hyperspectral images of the Dalian area taken by the EO-1 satellite shown in Figure 1 are reconstructed at different coding rates (0.2, 0.3, 0.4), and the reconstructed bands are as shown in Figure 2 . The peak signal-to-noise ratios of the reconstructed bands at different coding rates are shown in Table 1.

[0054] Table 1

[0055]

[0056]

[0057] The results show that the present invention fully exploits the inherent correlation of hyperspectral images and has the advantages of high compression ratio, good fidelity quality, low requirement for grouping accuracy, and strong robustness.

Claims

1. A hyperspectral image sparse reconstruction method based on non-local similar block 4D correlation constraint, characterized in that Proceed as follows: Step 1. Initial values of Gaussian random matrix sampling for each band of the k-th group of hyperspectral images at the reconstruction end Establish a non-local sparse representation model in the 4D transform domain according to formula (1), where N k represents the number of bands in this group, represents the i-th band image with size m×n, Where B j is an 8×8 block in, j = 1, 2, …, (m - 8)×(n - 8) / 5; represents a 4D group of 8×8 blocks with non-local correlation. The specific formation process is to find 5 8×8 blocks with non-local correlation with B j for each band image, and form a 3D block according to the correlation strength. Further, the 3D blocks of each band are formed into a 4D non-local similar block group in the order of the bands; represents performing a 4D transform on , that is, performing a hybrid 2D wavelet and 1D discrete cosine transform on the 3D blocks formed by each band, and then performing a 1D wavelet transform between spectra; Step 2. Establish the compressive sensing reconstruction model 4DNTCoSM for the k-th group of bands according to Formula (2). Where A is the sampling matrix and Y is the sampling data; is the sum of the horizontal gradient and the vertical gradient of each pixel in the i-th band of the k-th group of hyperspectral images; is the sum of the absolute values of the differences of each pixel between the i-th band and the (i - 1)-th band of the k-th group of hyperspectral images. When i is 1, i - 1 is selected as 2 according to the principle of symmetric extension; Step 3. Use Formula (3) to transform the established reconstruction model (2) into an optimization problem for solution: where λ is a non-negative parameter; Step 4. Introduce an intermediate variable u (k) , and let X (k) = u (k) , thus transforming formula (3) into formula (4); Step 5. Solve Formula (4) using the alternating direction method based on augmented Lagrangian, and transform it into three-step iterative sub-problems shown in Formulas (5)-(7): b (t+1) = b (t) ((X (k) ) (t+1) -(u (k) ) (t+1) ) (7) where μ and m are positive parameters; Step 6. Solve Formula (5) using the "steepest gradient descent method": (X (k) ) (t+1) =(X (k) ) (t) -h(A T (A(X (k) ) (t) -Y)+m((X (k) ) (t) -(u (k) ) (t) -b (t) )) (8) where h is the optimal descent step size; Step 7. Iteratively solve equations (8), (6), and (7) to obtain X (k) .

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