CN115496662A - High-order tensor spectral image super-resolution reconstruction method based on spectral information fusion - Google Patents
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Abstract
The invention relates to a high-order Tensor spectral image super-resolution reconstruction method based on spectral information fusion, in particular to a method for realizing hyperspectral image super-resolution reconstruction by weighted low-Tensor-Train (TT) rank Tensor analysis of weighted group sparseness and spectral unmixing. The method utilizes the high spatial-spectral correlation and the non-local self-similarity of the high-multispectral image, utilizes the low TT rank tensor decomposition to approximately recover the block tensor data, and excavates the non-local self-similarity contained in the block tensor data; the weighted group sparseness is used as a regularization term to describe the spatio-spectral continuity of the hyperspectral image; linear spectral decomposition based on weighted non-convex regularization is adopted as effective spectral regularization to reduce spectral distortion. The method solves the problems of super-resolution reconstruction, high-multispectral fusion, noise removal, image detail recovery and the like, and the effectiveness and the advancement of the method are verified through experiments.
Description
Technical Field
The invention relates to super-resolution reconstruction of a hyperspectral image, in particular to a method for realizing super-resolution reconstruction of a hyperspectral image based on weighted group sparseness and weighted low TT rank tensor analysis of spectral unmixing.
Background
A Hyperspectral (HS) image consists of images of a scene in tens to hundreds of discrete spectral bands at specific frequencies. HS images have extremely high spectral resolution and coverage, and can accurately identify materials present in the scene, which facilitates characterization of the imaged scene and greatly improves performance in many applications, including remote sensing, monitoring, target detection, military applications, and tracking. However, although HS images have a high spectral resolution, there are often severe limitations in spatial resolution. In fact, HS imaging systems require a large number of exposures to acquire multiple bands simultaneously within a narrow spectral window, and often require long exposures to ensure adequate signal-to-noise ratio (SNR), which often sacrifices spatial resolution. Therefore, the spatial resolution of the HS-image is typically low, because of the large number of mixed pixels in the low resolution HS-image, which limits its wide application to some extent. Therefore, increasing the spatial resolution of HS images has become an important issue, and has received increasing attention in recent years.
Simply increasing the spatial resolution of the image sensor is not effective for HS imaging, since the average number of photons reaching the sensor will be further reduced, resulting in a lower signal-to-noise ratio, and hence increasing the resolution by post-processing is a better option. Furthermore, multispectral (MS) imaging sensors are able to capture images at increasingly higher spatial resolutions. Therefore, the low-resolution HS image can be fused with a high-resolution (HR) MS image captured by the same scene, and the low-resolution HS image can be reconstructed. This process is called HS and MS image fusion and has attracted a wide range of attention. In fact, new HS imagers are also planned to carry MS image sensors. This means that both high spectral resolution HS images and high spatial resolution MS images can be captured simultaneously and more data sources for HS and MS image fusion are expected.
There have been many fruitful studies in recent years regarding the HS and MS image fusion problem. The bayesian framework is a common method for fusing low-resolution HS images and HRHS images. Such methods typically establish a posterior distribution of the desired HRHS images based on a priori knowledge and observation models. Matrix decomposition is also a common method in HS-MS image fusion. Matrix decomposition-based fusion methods typically first expand the target HR-HS image into a matrix, which is then decomposed into a base matrix and a coefficient matrix, where the base matrix and coefficient matrix are extracted from the low resolution HS image and HR-MS image, respectively. Although matrix factorization based approaches achieve impressive performance in the HS and MS fusion problem. There are still inherent drawbacks. All matrix decomposition methods require the unfolding of the three-dimensional data structure into a matrix, and the unfolding process may destroy the spatial structure of the data, which makes it difficult to fully exploit the spatio-spectral correlation of HS images. Compared with low-rank matrix decomposition, the method based on low-rank tensor can better maintain and utilize the spatial structure of the HS image, and therefore, the method is applied to some HS image recovery problems. In order to maintain the inherent spatial structure of the HS image, the method based on tensor decomposition carries out third-order tensor modeling on high spatial spectral correlation in the HR-HS image, different from the traditional method based on matrix decomposition. Despite good performance, other effective a priori knowledge in the HS image is not fully exploited. In the past decade, deep learning based approaches have achieved impressive performance in many computer vision tasks, and are therefore introduced into the HS and MS fusion problem. Deep learning based methods, while having good performance, typically require large amounts of training data, which is often impractical in the HS image recovery problem.
Disclosure of Invention
Aiming at the technical defects, the invention aims to provide a method for processing the problem of hyperspectral and multispectral fusion based on weighted non-local low TT rank tensor decomposition and spectral unmixing to realize the super-resolution of spectral images. In order to fully utilize the high spatial-spectral correlation and the non-local self-similarity of a high-multispectral image, approximate recovery is carried out on block tensor data by utilizing low TT rank tensor decomposition, and the non-local self-similarity contained in the block tensor data is mined; describing spatio-spectral continuity of the hyperspectral image using group sparsity as regularization; linear spectral decomposition based on non-convex regularization is adopted as effective spectral regularization to reduce spectral distortion. Based on the prior knowledge, a unified optimization model is provided to describe the problem of hyperspectral and multispectral image fusion, and an efficient algorithm for solving the model by using an alternative direction multiplication operator is designed. Compared with the existing new work, the method has better effect in the hyperspectral and multispectral fusion problem, and has better reconstruction performance and robustness in the hyperspectral image super-resolution.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the method for reconstructing the super-resolution of the high-order tensor spectral image based on the spectral information fusion comprises the following steps of performing iterative optimization solution on the basis of an initial model, obtaining a high-order tensor spectral image super-resolution reconstruction model based on the spectral information fusion, and realizing the super-resolution reconstruction of the high-order tensor spectral image, and comprises the following steps of:
step 1, adding a weighted low TT rank high-order tensor regular term for mining the non-local self-similarity contained in the block tensor data by utilizing the high spatial-spectral correlation and the non-local self-similarity of a high-multispectral image;
step 2, adding a weighting group sparse regular term for describing the space-spectrum continuity of the hyperspectral image;
and 3, adding a weighted spectrum unmixing regularization term, and using weighted non-convex regularized linear spectrum decomposition as spectrum regularization to reduce spectrum distortion and realize high-multispectral information fusion.
The model is used for fusing the hyperspectral image and the multispectral image, and performing super-resolution reconstruction on the hyperspectral image, so that the super-resolution performance of the hyperspectral image is effectively improved.
The prior super-resolution reconstruction model is a traditional prior modeling with a prior information regular term and is recorded as:
wherein the content of the first and second substances,
in the case of a spatial domain fidelity term,
in order to be a spectral domain fidelity term,
for the observed low resolution HSI tensor data,
for high resolution MSI tensor data acquired by a multispectral imaging sensor in the same scene,
for the high resolution HSI tensor data to be recovered, B is a sampling operator, S is a blurring operator,
for the purpose of a degradation operator of the spectral domain,
is a priori information.
The high-order tensor spectral image super-resolution reconstruction model based on spectral information fusion is as follows:
wherein the content of the first and second substances,
to weight the low TT rank higher order tensor regularization term,
for the weighted set sparseness as a regularization term,
unmixing regular term for hyperspectral, multispectral weighted spectrum r Is a low rank weighting factor, λ t For the group of sparse weight factors, the weight factor,
is a weighting factor for the image to be restored,
as weight factors of the input image, W r Is a low rank weight matrix, W t For a set of sparse weight matrices,
is a weight matrix for the image to be restored,
as a weight matrix of the input image, U 1 For richness of the image to be restored, U 2 Is the richness of the input image.
The weighted low TT rank tensor item has non-local self-similarity, and the non-local self-similarity is formed by segmenting an image into a group of image blocks, finding a group of blocks most similar to a selected block, and stacking the blocks to form a 4D non-local self-similarity block.
The weighting group sparse term is used for describing the smoothness of the spectral images of different spectral bands and mining the difference of the line space structures of the image blocks of the spectral bands and the shared sparse structure.
The weighted spectrum unmixing term adopts the non-convex regularized linear spectrum decomposition as spectrum regularization so as to reduce spectrum distortion.
In the repeated iteration optimization solving process, when the error of the two adjacent image recovery result data is within the threshold range, the image is judged to be in accordance with the convergence from the image reconstruction to the current turn, and the iteration is stopped.
The error function is:
wherein K is the number of iterations,
for the high resolution HSI tensor data to be recovered,
for the observed low resolution HSI tensor data, the algorithm converges to stop timing when the error function is within a set threshold range.
The repeated iteration optimization solution adopts an ADMM algorithm.
The invention has the following beneficial effects and advantages:
1. the method adopts weighted low TT rank tensor decomposition to approximately recover the block tensor data, and excavates the non-local self-similarity contained in the block tensor data.
2. The method adopts a weighting group sparse regular term to excavate the difference of the spatial structure of the image block line of each spectral band and the shared sparse structure.
3. The method adopts the non-convex regularized linear spectrum decomposition as an effective spectrum regularization term to reduce the spectrum distortion.
4. The method is superior to the existing algorithm in the aspects of hyperspectral and multispectral fusion, and has better hyperspectral reconstruction performance and robustness.
Drawings
FIG. 1 is a general framework diagram of the process herein;
FIG. 2 is a 38 th spectral band and corresponding error map of a reconstructed high resolution hyperspectral image on a Pavia University dataset with different methods.
FIG. 3 is a 38 th spectral band of a reconstructed high resolution hyperspectral image on Washington DC Mall dataset with different methods and the corresponding error map.
Detailed Description
The present invention will be described in further detail with reference to examples.
A unified optimization model is proposed to describe the hyperspectral and multispectral image fusion problem, and an efficient algorithm for solving the model by using an alternate direction multiplication operator is designed.
In order to improve the spatial resolution of the hyperspectral image, the invention provides an effective fusion method of the hyperspectral image and the multispectral image by utilizing the low-rank tensor analysis and the spectrum unmixing thought.
The super-resolution reconstruction method of the high-order tensor spectral image based on the spectral information fusion comprises four items: the super items are used for ensuring the fidelity of the observation data and the original data; carrying out approximate recovery on the block tensor data by weighted low TT rank tensor decomposition, and mining the non-local self-similarity contained in the block tensor data; weighting group sparseness as regularization to describe spatio-spectral continuity of the HS images; linear spectral decomposition based on weighted non-convex regularization is adopted as effective spectral regularization to reduce spectral distortion. The model solves the problem of hyperspectral and multispectral fusion, can perform super-resolution reconstruction on the spectral image, and effectively improves the super-resolution performance and robustness of the spectral image. The hyperspectral image data and the multispectral image data are input as models in a tensor form, and observation data are generated by setting different sampling rates and fuzzy operators. And when the error of the data recovery for two times needs to be calculated after each image reconstruction, judging the convergence of the image reconstruction according to whether the error function meets the threshold requirement.
The error function is
Wherein, K is the number of iterations,
in order to recover the data it is necessary to,
to observe the data.
1. Problem modeling
High resolution tensor for HSI to be restored
Where W, H, S represent the width, height and spectral band pattern, respectively, of the high resolution HSI tensor data. The observed low resolution HSI tensor data is recorded as
Where the spectral bands are consistent with high resolution HSI but are spatially down-sampled.
Representing a high resolution MSI acquired by a multi-spectral imaging sensor in the same scene. The above three mathematical relationships are described as
Wherein
The degradation operators representing the spatial domain comprise a down-sampling operator B, a fuzzy operator S and a degradation operator of the spectral domain
Namely:
since the above problem is an underdetermined problem, the solution of equation (2) is not unique. Conventional a priori modeling is performed by combining one or more data
As a regular term, to constrain the solution space, denoted as:
wherein the content of the first and second substances,
in the case of a spatial domain fidelity term,
in order to be a spectral domain fidelity term,
for the observed low resolution HSI tensor mode 3 data,
for high resolution MSI tensor mode 3 data acquired by a multispectral imaging sensor in the same scene,
for the high resolution HSI tensor mode 3 data to be recovered, B is the sampling operator, S is the blurring operator,
for the purpose of a degradation operator of the spectral domain,
is a priori information.
So far, a spectral image super-resolution reconstruction problem model is obtained.
1.1. Weighted low TT rank higher order tensor regularization term
In recent years, low rank priors have shown their effectiveness and superiority in image processing tasks. Setting:
representing a low rank prior of the image data. The problem model can be written as
Wherein λ is r Is a low rank weighting factor.
The non-local similarity of HSI describes the fact that each three-dimensional block of HSI has many similar blocks in the nearby space. Generally, to exploit the self-similarity implied in images, the HSI is first segmented into overlapping three-dimensional blocks, and then non-locally similar blocks are clustered by the k-means algorithm. The simultaneous mining of non-locally similar blocks takes advantage of the spectral and spatial low rank characteristics of HSI. Furthermore, the low rank tensor super-resolution reconstruction model based on the non-local block can be recorded as
Wherein k is the order of the non-local similarity block,
is an operator for taking similar blocks in the spectral image spatial domain.
For the high-order tensor data processing problem, the traditional tensor decomposition is limited in performance in tensor approximation due to the problem of NP difficulty in calculation and the problem of mode imbalance. The method herein is based on exploiting the better TT decomposition for pattern equality. For a given tensor
Its weighted low TT rank norm may be defined as:
in the formula, W r In the form of a low-rank weight matrix,
is a diagonal matrix whose elements are n-order matrices
Singular value of alpha n Is the weight of each n-order matrix, defined as
Wherein
Based on this weighted low TT rank norm, the relaxed form of equation (5) can be expressed as
1.2. Weighted group sparse regularization term
In addition to spatial spectral correlation and non-local self-similarity,
it also exhibits spatial spectral continuity, which can be represented by a Total Variation (TV) regularization term. The TV regularization term is widely applied to exploring a spatial piecewise smooth structure to solve the HS image restoration task. Consider that there is also a strong local smoothing structure of the HS image along its spectral pattern. Simulation using 3D-TV in general
Spatial spectral continuity of (a). However, the image is usually represented by strong sparsity of a shared structure along a spectrum mode, so that the group sparse regular term is more reasonable and effective than the traditional TV regular term in the aspects of describing the smoothness of spectrum images of different spectral bands, and mining the difference of the line space structures of image blocks of the spectral bands and the shared sparsity structure. For a given tensor
With a weight set of sparse regularization terms of
Wherein the content of the first and second substances,(i, j,: is the pixel position,
for the weight in the x-direction,
for weights in the y-direction, D is two differential operators, i.e., D x And D y The difference between the width and height along the space is calculated.
Using the weighted set sparsity of the spatial domain, the proposed model equation (7) can be rewritten as
Wherein λ is t As a group sparse weight factor, W t Is a group sparse weight matrix.
1.3. Weighted spectral unmixing regularization term
The above model (8) only considers spatial domain resolution enhancement, a processing scheme that is susceptible to spectral distortion. Spectral unmixing has become an important way of spectral regularization to reduce spectral distortion. The sparse spectral unmixing for a given matrix X can be expressed as
Wherein E is an end member set, lambda is a weight factor, and U is the image richness.
Its non-convex relaxation form formula based on the weighting MCP penalty function can be written as
Where W is a weight matrix.
By utilizing the prior regularization terms of the spatial domain and the spectral band domain, a higher-order tensor spectral image super-resolution reconstruction model based on spectral information fusion is provided, namely
Wherein the content of the first and second substances,
in order to be a spatial domain fidelity term,
in order to be a spectral domain fidelity term,
to weight the low TT rank higher order tensor regularization term,
for weighted group sparseness as the regularization term,
unmixing regularization term, λ, for hyperspectral, multispectral weighted spectra r Is a low rank weight factor, λ t For the purpose of the group sparse weight factor,
is a weighting factor for the image to be restored,
as a weighting factor of the input image, W r Is a low rank weight matrix, W t Is a set of sparse weight matrices
Is a weight matrix for the image to be restored,
as a weight matrix of the input image, U 1 For richness of the image to be restored, U 2 Is the richness of the input image.
2. Algorithm solution
In order to solve the coupling problem in the process of variable solution, auxiliary variables are introduced into corresponding variables
s.t.
V 1 ＝U 1 ,V 2 ＝U 2 ) (12)
Furthermore, we have their Lagrangian functional form
The variables are updated in sequence, including
Updating
The problem is a strong convex one, and a solution can be obtained by forcing its derivative. w.r.t
Is zero, i.e.
Wherein
C 2 ＝BS(BS) T
Updating Z n ：
Closed type solution
Updating
Order to
The closed form solution of the fiber is calculated by the following formula
Updating
Linear system solution
Updating
Closed type solution
Updating U 1 ，U 2 ：
Closed type solution
The same can be obtained
Closed type solution
Update V 1 ，V 2 ：
Closed type solution
The same can be obtained
Closed type solution
Updating lagrange multipliers
Experiments are carried out on the public hyperspectral image datasets Pavia University and Washington DC Mall, and compared with a representative method, as shown in figures 2 and 3, the hyperspectral image details which are over-divided and reconstructed by the method are clearer. The blueness and smoothness of the blue error image of the method indicate that the reconstruction error is smaller.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (10)
1. The method for reconstructing the super-resolution of the high-order tensor spectral image based on the spectral information fusion is characterized by comprising the following steps of performing iterative optimization solution on the basis of an initial model, obtaining a high-order tensor spectral image super-resolution reconstruction model based on the spectral information fusion, and realizing the reconstruction of the high-order tensor spectral image super-resolution, wherein the steps comprise:
step 1, adding a weighted low TT rank high-order tensor regular term for mining the non-local self-similarity contained in the block tensor data by utilizing the high spatial-spectral correlation and the non-local self-similarity of a high-multispectral image;
step 2, adding a weighting group sparse regular term for describing the space-spectrum continuity of the hyperspectral image;
and 3, adding a weighted spectrum unmixing regular term, and using the linear spectrum decomposition of weighted non-convex regular as spectrum regular, so as to reduce spectrum distortion and realize high-multispectral information fusion.
2. The higher-order tensor spectral image super-resolution reconstruction method based on spectral information fusion as claimed in claim 1, wherein the model is used for the fusion of the hyperspectral image and the multispectral image, and the super-resolution reconstruction is carried out on the hyperspectral image, so that the super-resolution performance of the spectral image is effectively improved.
3. The method for super-resolution reconstruction of the higher-order tensor spectral image based on spectral information fusion as claimed in claim 1, wherein the prior super-resolution reconstruction model is a traditional prior modeling with a prior information regular term, and is recorded as:
wherein, the first and the second end of the pipe are connected with each other,
in the case of a spatial domain fidelity term,
in order to be a spectral domain fidelity term,
for the observed low resolution HSI tensor data,
for high resolution MSI tensor data acquired by a multispectral imaging sensor in the same scene,
for the high resolution HSI tensor data to be recovered, B is a sampling operator, S is a blurring operator,
for the purpose of a degradation operator of the spectral domain,
is a priori information.
4. The method for reconstructing super-resolution of high-order tensor spectral image based on spectral information fusion as claimed in claim 1, wherein the model for reconstructing super-resolution of high-order tensor spectral image based on spectral information fusion is as follows:
wherein the content of the first and second substances,
to weight the low TT rank higher order tensor regularization term,
for the weighted set sparseness as a regularization term,
unmixing regular term for hyperspectral, multispectral weighted spectrum r Is a low rank weight factor, λ t For the group of sparse weight factors, the weight factor,
is a weighting factor for the image to be restored,
as weight factors of the input image, W r Is a low rank weight matrix, W t To form a set of sparse weight matrices,
is a weight matrix for the image to be restored,
as a weight matrix of the input image, U 1 For richness of the image to be restored, U 2 Is the richness of the input image.
5. The method for super-resolution reconstruction of higher-order tensor spectral image based on spectral information fusion as claimed in claim 4, wherein the weighted low TT rank tensor term, the non-local self-similarity, is formed by dividing the image into a set of image blocks, finding a set of blocks most similar to the selected block, and stacking the blocks to form a 4D non-local self-similar block.
6. The method for super-resolution reconstruction of the higher-order tensor spectral image based on spectral information fusion as claimed in claim 1, wherein the weighted set sparse term is used for describing smoothness of spectral images in different spectral bands, and mining spatial structure difference and shared sparse structure of image blocks in each spectral band.
7. The super-resolution reconstruction method for the higher-order tensor spectral image based on the spectral information fusion as claimed in claim 1, wherein the weighted spectral unmixing term adopts a non-convex regularized linear spectral decomposition as the spectral regularization to reduce the spectral distortion.
8. The hyperspectral image anomaly detection method based on high-order tensor representation according to claim 1 is characterized in that in the repeated iterative optimization solution process, when the error of the image recovery result data of two adjacent times is within a threshold range, the image is judged to be in accordance with convergence when being reconstructed to the current turn, and the iteration is stopped.
9. The method for detecting the abnormality of the hyperspectral image based on the higher-order tensor representation according to claim 8, wherein the error function is:
wherein K is the number of iterations,
for the high resolution HSI tensor data to be recovered,
for the observed low resolution HSI tensor data, the algorithm converges to stop timing when the error function is within a set threshold range.
10. The method for detecting the abnormality of the hyperspectral image based on the high-order tensor representation according to claim 1, wherein the repeated iterative optimization solution adopts an ADMM algorithm.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115719309A (en) * | 2023-01-10 | 2023-02-28 | 湖南大学 | Spectrum super-resolution reconstruction method and system based on low-rank tensor network |
| CN116245779A (en) * | 2023-05-11 | 2023-06-09 | 四川工程职业技术学院 | Image fusion method and device, storage medium and electronic equipment |
| CN116433534A (en) * | 2023-06-09 | 2023-07-14 | 四川工程职业技术学院 | Hyperspectral image restoration method and device, storage medium and electronic equipment |
| CN117197627A (en) * | 2023-09-13 | 2023-12-08 | 长春理工大学 | Multi-mode image fusion method based on high-order degradation model |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115719309A (en) * | 2023-01-10 | 2023-02-28 | 湖南大学 | Spectrum super-resolution reconstruction method and system based on low-rank tensor network |
| CN116245779A (en) * | 2023-05-11 | 2023-06-09 | 四川工程职业技术学院 | Image fusion method and device, storage medium and electronic equipment |
| CN116245779B (en) * | 2023-05-11 | 2023-08-22 | 四川工程职业技术学院 | Image fusion method and device, storage medium and electronic equipment |
| CN116433534A (en) * | 2023-06-09 | 2023-07-14 | 四川工程职业技术学院 | Hyperspectral image restoration method and device, storage medium and electronic equipment |
| CN116433534B (en) * | 2023-06-09 | 2023-08-22 | 四川工程职业技术学院 | Hyperspectral image restoration method and device, storage medium and electronic equipment |
| CN117197627A (en) * | 2023-09-13 | 2023-12-08 | 长春理工大学 | Multi-mode image fusion method based on high-order degradation model |
| CN117197627B (en) * | 2023-09-13 | 2024-03-01 | 长春理工大学 | Multi-mode image fusion method based on high-order degradation model |
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