A SAR three-dimensional enhanced imaging method based on non-local tensor decomposition

Abstract

The application provides a SAR three-dimensional enhancement imaging method based on non-local tensor decomposition, and the method comprises the following steps: step 1, m+1 SAR images are searched and homogeneity data tensors are constructed according to a similarity measurement criterion, m is a positive integer; step 2, the homogeneity data tensors are analyzed for low rank, if the low rank requirement is not met, step 1 is repeated; if the low rank requirement is met, the homogeneity data tensors are low rank data tensors; step 3, for the constructed low rank data tensors, a kernel norm optimization method based on tensor Tucker decomposition is used for signal enhancement, and the method can realize high-quality three-dimensional SAR imaging under the condition of limited data resources.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, and particularly relates to a SAR three-dimensional enhancement imaging method based on nonlocal tensor decomposition. Background Technology

[0002] Microwave imaging technology, represented by Synthetic Aperture Radar (SAR), has become a key method for achieving high-precision Earth observation. It plays an indispensable role in various fields such as topographic mapping, environmental monitoring, geological exploration, and disaster assessment. However, traditional SAR systems output only two-dimensional images. This limitation becomes apparent when dealing with areas with dramatic terrain or complex environmental conditions: three-dimensional objects often overlap on a two-dimensional plane, making many details unclear and difficult to interpret effectively. In contrast, SAR three-dimensional imaging technology can directly reveal the three-dimensional electromagnetic scattering characteristics of targets, effectively overcoming distortion problems such as image compression, overlay, and top-to-bottom inversion inherent in traditional imaging mechanisms. This technology is of paramount value for constructing accurate three-dimensional environmental models, achieving high-precision target interpretation, urban area mapping, and assessing disaster impacts.

[0003] Currently, 3D SAR imaging technology faces numerous challenges due to its high requirements for signal quality and quantity, especially in urban areas where uneven distribution of terrain and buildings severely impacts 3D SAR imaging accuracy due to high noise and clutter levels. Generally, solving such problems requires a larger number of observations to improve elevation estimation accuracy; however, limited by the number of satellites in space and revisit cycles, higher data volumes significantly increase the cost of 3D SAR imaging. Therefore, improving signal quality and thus enhancing 3D SAR imaging accuracy with a limited number of observations is a crucial issue that urgently needs to be addressed.

[0004] Generally, selecting points with similar signal distributions within a SAR image for joint analysis is a common method to enhance signal quality and reduce noise. These points with similar signal distributions are called homogeneous points. Scattering points that are spatially close often exhibit similar signal characteristics due to their proximity in space and similar physical properties such as materials. Therefore, traditional methods for selecting homogeneous points are based on neighborhood search. However, limiting the search to a small surrounding area significantly restricts the potential data volume and lacks quantifiable similarity criteria. Therefore, a non-local method is adopted, utilizing similarity criteria to search for high-quality homogeneous points over a larger global scope. This method not only greatly increases the effective data volume but also provides an effective similarity criterion, improving the quality of homogeneous point selection and laying a data foundation for subsequent enhanced imaging algorithm design. Summary of the Invention

[0005] The purpose of this invention is to overcome the problems of high data cost and poor signal quality in the process of 3D SAR imaging. This invention proposes a SAR 3D enhancement imaging method based on nonlocal tensor decomposition, which can achieve high-quality 3D SAR imaging with limited data resources. This method increases the amount of data by using nonlocal methods and combines tensor decomposition to achieve high-quality 3D SAR enhancement imaging.

[0006] Technical Solution: To achieve the above-mentioned objectives, this invention provides a SAR three-dimensional enhancement imaging method based on nonlocal tensor decomposition, which includes the following steps:

[0007] Step 1: Search and construct a homogeneous data tensor for m+1 synthetic aperture radar SAR images based on the similarity metric criterion, where m is a positive integer;

[0008] Step 2: Analyze the low-rank property of the homogeneous data tensor. If the low-rank property requirement is not met, repeat Step 1; if the low-rank property requirement is met, then it is a low-rank data tensor.

[0009] Step 3: For the constructed low-rank data tensor, the nuclear norm optimization method based on tensor Tucker decomposition is used for signal enhancement.

[0010] Furthermore, the specific method for step 1 is as follows:

[0011] (1.1) Suppose that the acquired data consists of m+1 SAR images, where the first image... Main image, As auxiliary images, The main image is multiplied by the conjugate of each auxiliary image to obtain m interferograms, which are then stacked to form the interference tensor. , Represents the field of complex numbers. Indicates the direction of the dimension. Represents the distance dimension; A two-dimensional image is obtained by performing an arithmetic mean along the channel dimension. Set q=4 for the first iteration;

[0012] (1.2) Data Perform nonlocal slice selection, and record... The g-th pixel is ,by A square master slice U is defined with itself as the center and a side length of (2b+1), where b is a preset positive integer. A square region with a side length of (2qb+1) is defined as the non-local search range. ,remember The w-th pixel is ,by Determine the auxiliary slices for a square region centered at (2b+1) with side length. , Represented by pixels A secondary slice centered on the center, traversing all Obtain the set of all auxiliary slices, and compute the value of each auxiliary slice. Similarity between and U Considering and All have (2b+1) 2 A slice of pixels, U and Similarity between The calculation method is as follows:

[0013]

[0014] in, Indicates the main slice The Middle 1 pixel Indicates auxiliary slices The Middle Each pixel, i.e., a slice and The similarity is defined as the product of the similarities of each corresponding point, where the similarity between each point is calculated as follows:

[0015]

[0016]

[0017] in, express The Middle The amplitude value of each pixel. express The Middle The amplitude value of each pixel. express The Middle Phase value of each pixel express The Middle Phase value of each pixel;

[0018] (1.3) Traversing w yields each auxiliary slice within the search region W. With the main slice The similarity of the slices is determined, and the similarity is sorted. The top d most similar secondary slices are selected to form a set. Record set The coordinates of all selected slices in the m interferograms Select the slice at the same position as all slices in the master slices U and V. Slices are used to form a multi-channel homogeneous observation tensor. traverse the images sequentially Each pixel For each pixel in the image, a corresponding homogeneous data tensor is constructed. Among them, tensor The first m two-dimensional images along the third dimension are the original channel data.

[0019] Furthermore, the specific method for step 2 is as follows:

[0020] For tensors respectively Expanding along three dimensions, where modulo 1 expansion means expanding the tensor along the first dimension. Divide into (2b+1) matrices and concatenate them along the row vector direction to obtain a matrix of dimension (2b+1)×(n(2b+1)). , For the real number field, its expression is as follows:

[0021]

[0022] Modulo-2 expansion means expanding the tensor along the second dimension. Divide into (2b+1) matrices and concatenate them along the row vector direction to obtain a matrix of dimension (2b+1)×(n(2b+1)). T denotes matrix transpose, and its expression is as follows:

[0023]

[0024] Modulo 3 expansion means expanding the tensor along the third dimension. Divide the matrix into n matrices and concatenate them along the row vectors to obtain a matrix with dimension (2b+1). 2 A matrix of size ×n Its expression is as follows:

[0025]

[0026] For each of the three expanded matrices , and Perform SVD decomposition, modulo 1 decomposition yields... Its SVD decomposition form is:

[0027]

[0028] in, It is the left singular value matrix of modulo 1 decomposition. It is the right singular value matrix decomposed modulo 1. It is a singular value matrix decomposed modulo 1. For the transpose conjugate, the resulting singular value matrix... Normalize the values ​​and observe their distribution. If 80% of the values ​​are 0 and 20% are between 0 and 1, it proves that the tensor... It has low rank in the modulo 1 dimension;

[0029] Modulo 2 decomposition obtained Its SVD decomposition form is:

[0030]

[0031] in, It is the left singular value matrix of modulo 2 decomposition. It is the right singular value matrix of modulo 2 decomposition. It is the singular value matrix of modulo 2 decomposition, for the obtained Normalize the values ​​and observe their distribution. If 80% of the values ​​are 0 and 20% are between 0 and 1, it proves that the tensor... It has low rank in the modulo 2 dimension;

[0032] Modulo 3 decomposition obtained Its SVD decomposition form is:

[0033]

[0034] in, It is the left singular value matrix of modulo 3 decomposition. It is the right singular value matrix of modulo 3 decomposition. It is a singular value matrix decomposed modulo 3, and the obtained Normalize the values ​​and observe their distribution. If 80% of the values ​​are 0 and 20% are between 0 and 1, it proves that the tensor... It has low rank in the modulo 3 dimension;

[0035] If more than one modular decomposition matrix does not have low rank property, it means that the low rank property of the tensor does not hold. Return to step one, increment q by 1, until the low rank property requirement is met.

[0036] Furthermore, the specific method for step 3 is as follows:

[0037] Let the desired enhanced signal be a tensor. By using the Tucker nuclear norm for relaxation, the multi-channel joint nonlocal enhancement imaging model is modeled as an optimized model:

[0038]

[0039] in, The nuclear norm of a tensor. Describing the F-norm, It is the regularization parameter, and the augmented Lagrangian form of the optimization model is:

[0040]

[0041] in, This represents the inner product operator. These are Lagrange tensor multipliers, utilizing the alternating direction multiplier method. and The two variables to be solved are obtained by alternately solving the following equation:

[0042]

[0043]

[0044] Where the superscript t represents the t-th iteration, since Directly It is concluded that The solution function is equivalent to:

[0045]

[0046] The above equation is expressed by tensor... The soft threshold constraint is used to obtain:

[0047]

[0048] in, This indicates that after expanding the tensor within the brackets with a modulus of l, the result is... The threshold is used to obtain the SVD decomposition of the expanded matrix. Apply truncation constraints. The value can be 1-3;

[0049] Based on the above method, the original observation tensor is... Enhancement yields the enhanced signal tensor. ,Will By cropping the first m two-dimensional images along the third dimension, the enhanced multi-channel data is obtained. This data is used as a new multi-channel observation signal. The compressed sensing algorithm is used to calculate the elevation estimate from the new multi-channel observation signal to form a three-dimensional SAR image.

[0050] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0051] (1) With limited observation samples, the method of the present invention improves the amplitude and phase noise suppression performance of the interferogram.

[0052] (2) By using the tensor decomposition algorithm, the method of the present invention improves the robustness of the algorithm performance when dealing with data processing of different systems. Attached Figure Description

[0053] Figure 1 This is a flowchart of the method of the present invention;

[0054] Figure 2 This is a verification diagram based on measured data from the domestically produced LuTan-1 satellite. Detailed Implementation

[0055] The embodiments of the present invention will now be described with reference to the accompanying drawings. The embodiments shown in the drawings are merely exemplary and intended to explain the principles of the present invention, and are not intended to limit the scope of the present invention.

[0056] like Figure 1 As shown, this invention provides a SAR three-dimensional enhancement imaging method based on nonlocal tensor decomposition, which includes the following steps:

[0057] Step 1: Search and construct a homogeneous data tensor for m+1 synthetic aperture radar SAR images based on the similarity metric criterion, where m is a positive integer;

[0058] Step 2: Analyze the low-rank property of the homogeneous data tensor. If the low-rank property requirement is not met, repeat Step 1; if the low-rank property requirement is met, it is a low-rank data tensor.

[0059] Step 3: For the constructed low-rank data tensor, the nuclear norm optimization method based on tensor Tucker decomposition is used for signal enhancement.

[0060] Furthermore, the specific method for step 1 is as follows:

[0061] (1.1) Suppose that the acquired data consists of m+1 SAR images, where the first image... Main image, As auxiliary images, The main image is multiplied by the conjugate of each auxiliary image to obtain m interferograms, which are then stacked to form the interference tensor. , Represents the field of complex numbers. Indicates the direction of the dimension. Represents the distance dimension; A two-dimensional image is obtained by performing an arithmetic mean along the channel dimension. Set q=4 for the first iteration;

[0062] (1.2) Data Perform nonlocal slice selection, and record... The g-th pixel is ,by A square master slice U is defined with itself as the center and a side length of (2b+1), where b is a preset positive integer. A square region with a side length of (2qb+1) is defined as the non-local search range. ,remember The w-th pixel is ,by Determine the auxiliary slices for a square region centered at (2b+1) with side length. , Represented by pixels A secondary slice centered on the center, traversing all Obtain the set of all auxiliary slices, and compute the value of each auxiliary slice. Similarity between and U Considering and All have (2b+1) 2 A slice of pixels, U and Similarity between The calculation method is as follows:

[0063]

[0064] in, Indicates the main slice The Middle 1 pixel Indicates auxiliary slices The Middle Each pixel, i.e., a slice and The similarity is defined as the product of the similarities of each corresponding point, where the similarity between each point is calculated as follows:

[0065]

[0066]

[0067] in, express The Middle The amplitude value of each pixel. express The Middle The amplitude value of each pixel. express The Middle Phase value of each pixel express The Middle Phase value of each pixel;

[0068] (1.3) Traversing w yields each auxiliary slice within the search region W. With the main slice The similarity of the slices is determined, and the similarity is sorted. The top d most similar secondary slices are selected to form a set. Record set The coordinates of all selected slices in the m interferograms Select the slice at the same position as all slices in the master slices U and V. Slices are used to form a multi-channel homogeneous observation tensor. traverse the images sequentially Each pixel For each pixel in the image, a corresponding homogeneous data tensor is constructed. Among them, tensor The first m two-dimensional images along the third dimension are the original channel data.

[0069] Furthermore, the specific method for step 2 is as follows:

[0070] For tensors respectively Expanding along three dimensions, where modulo 1 expansion means expanding the tensor along the first dimension. Divide into (2b+1) matrices and concatenate them along the row vector direction to obtain a matrix of dimension (2b+1)×(n(2b+1)). , For the real number field, its expression is as follows:

[0071]

[0072] Modulo-2 expansion means expanding the tensor along the second dimension. Divide into (2b+1) matrices and concatenate them along the row vector direction to obtain a matrix of dimension (2b+1)×(n(2b+1)). , The expression for matrix transpose is as follows:

[0073]

[0074] Modulo 3 expansion means expanding the tensor along the third dimension. Divide the matrix into n matrices and concatenate them along the row vectors to obtain a matrix with dimension (2b+1). 2 A matrix of size ×n Its expression is as follows:

[0075]

[0076] For each of the three expanded matrices , and Perform SVD decomposition, modulo 1 decomposition yields... Its SVD decomposition form is:

[0077]

[0078] in, It is the left singular value matrix of modulo 1 decomposition. It is the right singular value matrix decomposed modulo 1. It is a singular value matrix decomposed modulo 1. For the transpose conjugate, the resulting singular value matrix... Normalize the values ​​and observe their distribution. If 80% of the values ​​are 0 and 20% are between 0 and 1, it proves that the tensor... It has low rank in the modulo 1 dimension;

[0079] Modulo 2 decomposition obtained Its SVD decomposition form is:

[0080]

[0081] in, It is the left singular value matrix of modulo 2 decomposition. It is the right singular value matrix of modulo 2 decomposition. It is the singular value matrix of modulo 2 decomposition, for the obtained Normalize the values ​​and observe their distribution. If 80% of the values ​​are 0 and 20% are between 0 and 1, it proves that the tensor... It has low rank in the modulo 2 dimension;

[0082] Modulo 3 decomposition obtained Its SVD decomposition form is:

[0083]

[0084] in, It is the left singular value matrix of modulo 3 decomposition. It is the right singular value matrix of modulo 3 decomposition. It is a singular value matrix decomposed modulo 3, and the obtained Normalize the values ​​and observe their distribution. If 80% of the values ​​are 0 and 20% are between 0 and 1, it proves that the tensor... It has low rank in the modulo 3 dimension;

[0085] If more than one modular decomposition matrix does not have low rank property, it means that the low rank property of the tensor does not hold. Return to step one, increment q by 1, until the low rank property requirement is met.

[0086] Furthermore, the specific method for step 3 is as follows:

[0087] Let the desired enhanced signal be a tensor. By using the Tucker nuclear norm for relaxation, the multi-channel joint nonlocal enhancement imaging model is modeled as an optimized model:

[0088]

[0089] in, The nuclear norm of a tensor. Describing the F-norm, It is the regularization parameter, and the augmented Lagrangian form of the optimization model is:

[0090]

[0091] in, This represents the inner product operator. These are Lagrange tensor multipliers, utilizing the alternating direction multiplier method. and The two variables to be solved are obtained by alternately solving the following equation:

[0092]

[0093]

[0094] Where the superscript t represents the t-th iteration, since Directly It is concluded that The solution function is equivalent to:

[0095]

[0096] The above equation is expressed by tensor... The soft threshold constraint is used to obtain:

[0097]

[0098] in, This indicates that after expanding the tensor within the brackets with a modulus of l, the result is... The threshold is used to obtain the SVD decomposition of the expanded matrix. Apply truncation constraints. The value ranges from 1 to 3.

[0099] Based on the above method, the original observation tensor is... Enhancement yields the enhanced signal tensor. ,Will The enhanced multi-channel data is obtained by cropping the first m two-dimensional images along the third dimension. This data is used as a new multi-channel observation signal. The elevation estimate is calculated from the new multi-channel observation signal using a compressed sensing algorithm to form a three-dimensional SAR image.

[0100] To verify the beneficial effects of the present invention, the following experiments were conducted:

[0101] Under the same data conditions, a simulated experimental dataset for L-band SAR tomography of individual buildings was constructed. The dataset was processed for 3D imaging using the generalized likelihood detection algorithm, compressed sensing algorithm, and the algorithm of this invention, respectively. The results are shown in Table 1, demonstrating that the proposed algorithm has higher accuracy. Furthermore, high-resolution 3D SAR imaging was verified using data from the domestically produced LuTan-1 satellite, successfully achieving high-resolution 3D images of urban areas. Figure 2 .

[0102] Table 1 Comparison of Elevation Accuracy of Three Methods

[0103]

[0104] As shown in Table 1, under the same data conditions, a simulated experimental dataset for L-band SAR tomography of a single building was constructed. The dataset was processed using the generalized likelihood detection algorithm, the compressed sensing algorithm, and the algorithm of this invention. The Euclidean distance between the actual elevation and the estimated elevation of each pixel was calculated. A distance less than 1 meter was considered a successful restoration, and a distance greater than or equal to 1 meter was considered a failed restoration. The percentage of all pixels that were successfully restored was calculated, and the data is shown in Table 1. The experiment shows that the method proposed in this invention has a significantly higher elevation restoration accuracy than other algorithms.

[0105] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A SAR three-dimensional enhancement imaging method based on nonlocal tensor decomposition, characterized in that, The method includes the following steps: Step 1: Search and construct a homogeneous data tensor for m+1 synthetic aperture radar SAR images based on the similarity metric criterion, where m is a positive integer; Step 2: Analyze the low-rank property of the homogeneous data tensor. If the low-rank property requirement is not met, repeat Step 1; if the low-rank property requirement is met, then it is a low-rank data tensor. Step 3: For the constructed low-rank data tensor, the nuclear norm optimization method based on tensor Tucker decomposition is used for signal enhancement; The specific method for step 1 is as follows: (1.1) Suppose that the acquired data consists of m+1 synthetic aperture radar SAR images, where the first image... Main image, As auxiliary images, The main image is multiplied by the conjugate of each auxiliary image to obtain m interferograms, which are then stacked to form the interference tensor. , Represents the field of complex numbers. Indicates the direction of the dimension. Represents the distance dimension; A two-dimensional image is obtained by performing an arithmetic mean along the channel dimension. Set q=4 for the first iteration; (1.2) Data Perform nonlocal slice selection, and record... The g-th pixel is ,by A square master slice U is defined with itself as the center and a side length of (2b+1), where b is a preset positive integer. A square region with a side length of (2qb+1) is defined as the non-local search range. ,remember The w-th pixel is ,by Determine the auxiliary slices for a square region centered at (2b+1) with side length. , Represented by pixels A secondary slice centered on the center, traversing all Obtain the set of all auxiliary slices, and compute the value of each auxiliary slice. Similarity between and U ; (1.3) Traversing w yields each auxiliary slice within the search region W. With the main slice The similarity of the slices is determined, and the similarity is sorted. The top d most similar secondary slices are selected to form a set. Record set The coordinates of all selected slices in the m interferograms Select the slice at the same position as all slices in the master slices U and V. Slices are used to form a multi-channel homogeneous observation tensor. traverse the image sequentially Each pixel For each pixel in the image, a corresponding homogeneous data tensor is constructed. Among them, tensor The first m two-dimensional images along the third dimension are the original channel data; Step 2 is explained in the following steps: For tensors respectively Expanding along three dimensions, where modulo 1 expansion means expanding the tensor along the first dimension. Divide into (2b+1) matrices and concatenate them along the row vector direction to obtain a matrix of dimension (2b+1)×(n(2b+1)). , For the real number field, its expression is as follows: ； Modulo-2 expansion means expanding the tensor along the second dimension. Divide into (2b+1) matrices and concatenate them along the row vector direction to obtain a matrix of dimension (2b+1)×(n(2b+1)). T represents the matrix transpose, and its expression is as follows: ； Modulo-3 expansion means expanding the tensor along the third dimension. Divide the matrix into n matrices and concatenate them along the row vectors to obtain a matrix with dimension (2b+1). 2 A matrix of size ×n Its expression is as follows: ； For each of the three expanded matrices , and Perform SVD decomposition, modulo 1 decomposition yields... Its SVD decomposition form is: ,in, It is a left singular value matrix decomposed modulo 1. It is the right singular value matrix decomposed modulo 1. It is a singular value matrix decomposed modulo 1. For the transpose conjugate, the resulting singular value matrix... Normalize the values ​​and observe their distribution. If 80% of the values ​​are 0 and 20% are between 0 and 1, it proves that the tensor... It has low rank in the modulo 1 dimension; Modulo 2 decomposition obtained Its SVD decomposition form is: ,in, It is the left singular value matrix of modulo 2 decomposition. It is the right singular value matrix of modulo 2 decomposition. It is the singular value matrix of modulo 2 decomposition, for the obtained Normalize the values ​​and observe their distribution. If 80% of the values ​​are 0 and 20% are between 0 and 1, it proves that the tensor... It has low rank in the modulo 2 dimension; Modulo 3 decomposition obtained Its SVD decomposition form is: ,in, It is the left singular value matrix of modulo 3 decomposition. It is the right singular value matrix of modulo 3 decomposition. It is a singular value matrix decomposed modulo 3, and the obtained Normalize the values ​​and observe their distribution. If 80% of the values ​​are 0 and 20% are between 0 and 1, it proves that the tensor... It has low rank in the modulo 3 dimension; If more than one modular decomposition matrix does not have low rank property, it means that the low rank property of the tensor does not hold. Return to step one, increment q by 1, until the low rank property requirement is met.

2. The SAR three-dimensional enhancement imaging method based on nonlocal tensor decomposition according to claim 1, characterized in that, In step (1.2), considering and All have (2b+1) 2 A slice of pixels, U and Similarity between The calculation method is as follows: ,in, Indicates the main slice The Middle 1 pixel Indicates auxiliary slices The Middle Each pixel, i.e., a slice and The similarity is defined as the product of the similarities of each corresponding point.

3. The SAR three-dimensional enhancement imaging method based on nonlocal tensor decomposition according to claim 2, characterized in that, The similarity between each point is calculated as follows: ， ; in, express The Middle The amplitude value of each pixel. express The Middle The amplitude value of each pixel. express The Middle Phase value of each pixel express The Middle The phase value of each pixel.

4. The SAR three-dimensional enhancement imaging method based on nonlocal tensor decomposition according to claim 1, characterized in that, The specific method for step 3 is as follows: Let the desired enhanced signal be a tensor. By using the Tucker nuclear norm for relaxation, the multi-channel joint nonlocal enhancement imaging model is modeled as an optimization model: ,in, The nuclear norm of a tensor. Describing the F-norm, It is the regularization parameter, and the augmented Lagrangian form of the optimization model is: ,in, This represents the inner product operator. These are Lagrange tensor multipliers, utilizing the alternating direction multiplier method. and The two variables to be solved are obtained by alternately solving the following equation: , Where the superscript t denotes the t-th iteration, since Directly It is concluded that The solution function is equivalent to: The above equation is obtained by applying tensors The soft threshold constraint is used to obtain: ,in, This indicates that after expanding the tensor within the brackets with a modulus of l, the result is... The threshold is obtained from the SVD decomposition of the expanded matrix. Apply truncation constraints. The value can be 1-3; Based on the above method, the original observation tensor is... Enhancement yields the enhanced signal tensor. ,Will By cropping the first m two-dimensional images along the third dimension, the enhanced multi-channel data is obtained. This data is used as a new multi-channel observation signal. The compressed sensing algorithm is used to calculate the elevation estimate from the new multi-channel observation signal to form a three-dimensional SAR image.

Images