Remote sensing image cloud removal method and system fusing gradient fidelity and time spectrum consistency

Abstract

The application provides a remote sensing image cloud removal method and system fusing gradient fidelity and time spectrum consistency, relates to the technical field of remote sensing image processing and tensor modeling, and comprises the following steps: firstly, acquiring multi-temporal remote sensing images and cloud mask data, and generating a fault mask through active fault identification; then, calculating a guided gradient tensor and performing low-rank approximation processing to obtain spatial feature factors and time spectrum feature factors; based on this, a multi-objective optimization model of a gradient domain fidelity term, a pixel domain fidelity term and a time spectrum consistency constraint term is constructed; a proximal alternating minimization algorithm of an embedded alternating direction multiplier method is used for efficient solution, and the reconstruction result is modified in combination with the cloud mask and the active fault mask, and a high-quality cloud-removed image sequence is output. The application can effectively maintain the image edge structure, texture details and space-time consistency under a complex cloud coverage scene, and significantly improves the availability and analysis value of remote sensing data.

Description

Technical Field

[0001] This invention relates to the fields of remote sensing image processing and tensor modeling technology, and more specifically, to a method and system for cloud removal from remote sensing images that integrates gradient fidelity and temporal-spectral consistency. Background Technology

[0002] Remote sensing images are often severely affected by cloud cover during the acquisition process. Cloud cover not only leads to the loss of surface information, but also poses a significant challenge to the continuity of multi-temporal data analysis and the integrity of multi-source data fusion.

[0003] Currently, mainstream remote sensing cloud removal methods mainly follow the traditional approach based on physical modeling, such as using time-series interpolation or spatial variational inpainting techniques to fill in cloud-contaminated areas by simply migrating cloudless temporal data or local interpolation. These methods can restore the basic structure of an image to some extent, but they heavily rely on manual parameter settings and prior assumptions. When facing complex cloud-covered scenarios, they often suffer from high computational complexity and memory consumption, and struggle to maintain image edge details and spatiotemporal consistency. Furthermore, existing technologies often design reconstruction strategies from a single dimension: time-based methods use cloudless temporal data for migration and completion, but are easily affected by changes in surface phenology, leading to temporal inconsistencies in the reconstruction results; spatial information-based methods employ interpolation or variational inpainting techniques, which have limited effectiveness in reconstructing large-scale cloud-covered areas; spectral information-based methods mine inter-band correlations, but fail in cases of full-band contamination; and while hybrid methods incorporating multi-dimensional information can improve accuracy, this comes at the cost of significantly increased model complexity and optimization difficulty.

[0004] While these outdated technologies can alleviate cloud interference in some scenarios, they ultimately lead to problems such as structural blurring, loss of detail, or artifacts in the declouding results. In particular, in the detection of active faults, they cannot effectively preserve geological features, thus limiting the usability of remote sensing data in high-precision analysis.

[0005] Therefore, there is an urgent need for a remote sensing image declouding method and system that integrates gradient fidelity and temporal consistency to solve the above-mentioned technical problems. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for cloud removal from remote sensing images that integrates gradient fidelity and temporal-spectral consistency, thereby improving the aforementioned problems. To achieve this objective, the technical solution adopted by this invention is as follows:

[0007] Firstly, this application provides a remote sensing image cloud removal method that integrates gradient fidelity and temporal-spectral consistency, including:

[0008] Acquire multi-temporal remote sensing images and their corresponding cloud mask data;

[0009] The multi-temporal remote sensing images are subjected to active fault identification to generate an object active fault mask.

[0010] The guiding gradient tensor is calculated based on the multi-temporal remote sensing images, and the guiding gradient tensor is stacked along the spectral direction according to the time series and subjected to low-rank approximation to obtain spatial feature factors and temporal spectral feature factors.

[0011] Based on the spatial feature factors and temporal feature factors, gradient domain fidelity terms, pixel domain fidelity terms, and temporal consistency constraints are constructed to obtain multiple regularization constraints.

[0012] A low-rank tensor completion model for remote sensing cloud removal is constructed based on the aforementioned multiple regularization constraints.

[0013] The low-rank tensor completion model is optimized and solved using a proximal alternating minimization algorithm based on the embedded alternating direction multiplier method. The solution is then corrected and optimized based on the cloud mask data and the active fault mask to obtain the declouded result.

[0014] The process of performing active tomography on the multi-temporal remote sensing images includes:

[0015] The multi-temporal remote sensing images are fused using multimodal data, wherein a pre-defined phase consistency algorithm is used as a preprocessor to calculate the phase consistency metric through a multi-scale Gabor filter bank to obtain preliminary tomographic data;

[0016] Based on a preset tensor voting algorithm as a post-amplifier, the preliminary fault data is subjected to tensor field voting processing. Contextual information is aggregated through preset geometric constraints to obtain optimized fault feature data.

[0017] A binary active fault mask is generated based on the optimized fault feature data.

[0018] The low-rank tensor completion model for remote sensing cloud removal, constructed based on the aforementioned multiple regularization constraints, includes:

[0019] Based on the aforementioned multiple regularization constraints, set fidelity constraints and weighting coefficients for each regularization term constraint;

[0020] Based on the fidelity constraints and the weighting coefficients of each regularization term constraint, a tensor completion model is constructed.

[0021] Secondly, this application also provides a remote sensing image cloud removal system that integrates gradient fidelity and temporal-spectral consistency, comprising:

[0022] The acquisition unit is used to acquire multi-temporal remote sensing images and their corresponding cloud mask data.

[0023] The identification unit is used to perform active fault identification on the multi-temporal remote sensing images and generate an object active fault mask.

[0024] The processing unit is used to calculate the guiding gradient tensor based on the multi-temporal remote sensing images, and to stack and perform low-rank approximation on the guiding gradient tensor along the spectral direction according to the time series to obtain spatial feature factors and temporal spectral feature factors.

[0025] The constraint unit is used to construct gradient domain fidelity terms, pixel domain fidelity terms, and temporal spectrum consistency constraint terms based on the spatial feature factors and temporal spectrum feature factors, thereby obtaining multiple regularization constraints.

[0026] The construction unit is used to construct a low-rank tensor completion model for remote sensing cloud removal based on the multiple regularization constraints.

[0027] The optimization unit is used to optimize and solve the low-rank tensor completion model based on the proximal alternating minimization algorithm with embedded alternating direction multipliers, and to correct and optimize the solution results based on the cloud mask data and active fault mask to obtain the cloud removal result.

[0028] The identification unit includes:

[0029] The first identification subunit is used to perform multimodal data fusion on the multi-temporal remote sensing images, wherein a preset phase consistency algorithm is used as a preprocessor to calculate the phase consistency metric through a multi-scale Gabor filter bank to obtain preliminary tomographic data;

[0030] The second identification subunit is used to perform tensor field voting processing on the preliminary fault data based on a preset tensor voting algorithm as a post-enhancer, and to aggregate context information through preset geometric constraints to obtain optimized fault feature data;

[0031] The third identification subunit is used to generate a binary active fault mask based on the optimized fault feature data.

[0032] The building unit includes:

[0033] The first construction subunit is used to set fidelity constraint conditions and weighting coefficients for each regularization term constraint based on the multiple regularization constraints.

[0034] The second construction subunit is used to construct a tensor completion model based on the fidelity constraints and the weighting coefficients of each regularization term constraint.

[0035] The beneficial effects of this invention are as follows:

[0036] This invention proposes a tensor completion model that integrates gradient domain fidelity and temporal spectrum consistency constraints for cloud removal and reconstruction of multi-temporal remote sensing images.

[0037] The gradient domain fidelity term proposed in this invention can effectively utilize information from cloudless areas in different time phases to accurately estimate the guiding gradient of cloud-occluded areas. Compared to the traditional pixel domain fidelity term, this method can better preserve the edge structure and texture details of the original image during image reconstruction, thus improving structural fidelity.

[0038] This invention effectively solves the aforementioned problems by introducing an active fault identification module and a multi-objective low-rank tensor completion model. The method first acquires multi-temporal remote sensing images and cloud mask data, and generates active fault masks based on phase consistency and tensor voting algorithms to accurately identify fault feature regions. Subsequently, it calculates the guiding gradient tensor, performs low-rank approximation to extract spatial and temporal spectral feature factors, and constructs gradient domain fidelity terms, pixel domain fidelity terms, and temporal spectral consistency constraint terms. Finally, it optimizes the solution using a near-end alternating minimization algorithm with embedded alternating direction multipliers, and corrects the results using cloud masks and active fault masks. This application significantly improves the structural fidelity and spatiotemporal consistency of images while maintaining low computational complexity, providing reliable support for the application of remote sensing data in geological disaster monitoring.

[0039] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0040] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a schematic diagram of the cloud removal method for remote sensing images that integrates gradient fidelity and temporal-spectral consistency, as described in an embodiment of the present invention.

[0042] Figure 2 This is a schematic diagram of the remote sensing image cloud removal system that integrates gradient fidelity and temporal-spectral consistency as described in an embodiment of the present invention.

[0043] Figure 3 The image shows the cloud removal effect in a simulated data experiment of the remote sensing image cloud removal method that integrates gradient fidelity and temporal consistency as described in this embodiment of the invention.

[0044] Figure 4The image shows the cloud removal effect in an actual data experiment of the remote sensing image cloud removal method that integrates gradient fidelity and temporal consistency as described in this embodiment of the invention.

[0045] The diagram is labeled as follows: 701, Acquisition Unit; 702, Identification Unit; 703, Processing Unit; 704, Constraint Unit; 705, Construction Unit; 706, Optimization Unit. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0047] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance. Example

[0048] This embodiment provides a method for cloud removal from remote sensing images that integrates gradient fidelity and temporal consistency.

[0049] See Figure 1 , Figure 3 and Figure 4 The figure shows that the method includes steps S1, S2, S3, S4, S5 and S6.

[0050] Step S1: Acquire the observed multi-temporal remote sensing images and their corresponding cloud mask data;

[0051] It is understandable that the multi-temporal remote sensing images in this step refer to image sequences of the same geographic area acquired at different times. These images contain rich spectral features, spatial structure, and temporal variation information, providing a data foundation for subsequent information reconstruction using temporal correlation. Cloud mask data, on the other hand, is a binary layer generated by a cloud detection algorithm. It accurately identifies areas in the image contaminated by clouds and their shadows, and its accuracy directly affects the quality of the final cloud removal effect. In practical applications, this step obtains L1 or L2 level products that have undergone radiometric calibration and atmospheric correction from satellite data platforms such as Landsat and Sentinel series, and generates high-precision cloud masks using the quality label files inherent to the satellite data.

[0052] Step S2: Perform active fault identification on the multi-temporal remote sensing images to generate an object active fault mask;

[0053] Understandably, this step first performs registration and radiometric correction on multimodal data (such as optical imagery and SAR data) to enhance the contrast of fault features. Then, a phase consistency algorithm is applied as a pre-processor, using a multi-scale Gabor filter bank to calculate local phase consistency metrics, effectively capturing weak linear features (fault lines). Its insensitivity to illumination changes ensures that preliminary fault clues can still be extracted under complex cloud cover. Next, a tensor voting algorithm is used as a post-enhancer, aggregating contextual information through a geometrically constrained voting mechanism to reduce noise interference and enhance the continuity and directional consistency of fault lines, outputting optimized fault feature data. Finally, an adaptive thresholding process generates a binarized active fault mask, where high-confidence regions identify suspected fault locations. In this step, step S2 includes steps S21, S22, and S23.

[0054] Step S21: Perform multimodal data fusion on the multi-temporal remote sensing images, wherein a preset phase consistency algorithm is used as a preprocessor to calculate the phase consistency metric through a multi-scale Gabor filter bank to obtain preliminary tomographic data;

[0055] Understandably, this step first performs spatiotemporal registration and radiometric correction on optical data and synthetic aperture radar (SAR) data from multi-temporal remote sensing images. An enhanced data cube is constructed through feature-level fusion—optical images provide rich spectral texture information, while SAR data carries backscattering features sensitive to surface deformation. This complementary fusion significantly improves the signal-to-noise ratio of fault linear features. Subsequently, a phase consistency algorithm acts as a pre-processor, extracting local phase consistency features in the frequency domain using a multi-scale Gabor filter bank. The filter bank, designed with different center frequencies and direction parameters, covers full-scale feature detection, from coarse-scale fault contours to fine-scale crack textures. Its phase consistency metric calculation, by comparing the amplitude consistency of each filter's response vector, effectively overcomes the sensitivity of traditional gradient detection to illumination changes and contrast differences. The preliminary fault data generated in this process not only contains the spatial distribution of fault lines but also retains vector information of edge directions, providing structured input for subsequent tensor voting processing.

[0056] This multimodal fusion strategy complements physical mechanisms (optical spectroscopy and SAR coherence), effectively overcoming the limitations of a single data source under cloud cover and shadow interference in less common scenarios such as polar regions and mountainous areas. Secondly, the phase consistency algorithm abandons the traditional amplitude-based edge detection approach and utilizes the illumination invariance of phase information to stably extract weak fault traces in low-contrast geological environments.

[0057] Step S22: Based on a preset tensor voting algorithm as a post-amplifier, tensor field voting processing is performed on the preliminary fault data, and context information is aggregated through preset geometric constraints to obtain optimized fault feature data;

[0058] Understandably, this step converts the initial fault data (including edge points and orientation information detected by phase consistency detection) into a tensor field representation. Each pixel's orientation and confidence are modeled using a second-order symmetric tensor. Then, a voting mechanism aggregates contextual information: each pixel projects a vote to its neighboring pixels, with voting weights based on geometric constraints (the Gaussian kernel function and orientation consistency condition during the voting process). This strengthens the continuity of linear structures (such as fault lines) while suppressing noise and isolated points. This step significantly improves the continuity and robustness of fault features, laying a solid foundation for generating high-precision active fault masks and directly supporting accurate analysis in geological hazard risk assessment. It also maintains stable enhancement of fault features even in the face of cloud cover or terrain interference, providing high-precision input for subsequent mask generation.

[0059] Step S23: Generate a binarized active fault mask based on the optimized fault feature data.

[0060] Understandably, this step first performs statistical analysis on the feature data output by the tensor voting algorithm (containing the confidence score and orientation information of each pixel), and automatically determines the optimal segmentation point using the Otsu thresholding method to balance recall and precision and avoid human bias. Subsequently, an opening operation (erosion followed by dilation) is applied to smooth the mask edges, fill small gaps, and remove isolated noise points, enhancing the mask's connectivity and topological consistency. This step ensures that the mask can capture subtle fault traces while suppressing unstructured noise.

[0061] Step S3: Calculate the guiding gradient tensor based on the multi-temporal remote sensing images, and stack the guiding gradient tensor along the spectral direction according to the time series and perform low-rank approximation to obtain spatial feature factors and temporal spectral feature factors;

[0062] It is understandable that this step effectively captures the high-dimensional redundancy of remote sensing data through low-rank priors, compressing massive amounts of data into a small number of core features, greatly reducing model complexity and computational overhead. It achieves the extraction of essential features from the original data, providing a compact and highly representative initialization model for subsequent optimization, significantly improving the iteration convergence speed and final reconstruction accuracy. In this step, step S3 includes steps S31, S32, and S33.

[0063] Step S31: Divide the multi-temporal remote sensing images into cloud-covered image sequences and cloudless image sequences, and calculate the cloudless image sequences obtained by division according to a preset average value calculation formula to obtain the average value image of the cloudless sequence.

[0064] It is understandable that this step involves inputting multi-temporal remote sensing images. ,in, Indicates the spatial resolution of a sequence of cloud-covered images. Indicates the spatial resolution of a cloudless image sequence. Indicates spectral resolution, Indicates temporal resolution. Multi-temporal remote sensing images are split into cloudless image sequences based on whether they are cloudy or clear. Image sequences with clouds ,in The formula for calculating the average value of the remote sensing image during a cloudless phase is shown below:

[0065] ;

[0066] in, The average value image of a remote sensing image during a cloudless period. This represents the total number of cloudless images. The dimension label of a cloudless image. Indicates the first A sequence of cloudless images.

[0067] In this step, the average image serves as the guiding basis for subsequent estimation of cloud-polluted area values, providing crucial prior information for gradient calculation and low-rank reconstruction. This effectively ensures the authenticity and consistency of ground structure and spectral features during cloud removal, and is one of the core guarantees for the robustness and high-precision cloud removal of the entire algorithm.

[0068] Step S32: Calculate the average image of the cloudless sequence based on the preset cloud pollution time phase image estimation formula to obtain the cloud pollution time phase image for each spectral band.

[0069] It is understandable that this step uses the average image of the cloudless sequence to estimate the cloud pollution phase image for each spectral band:

[0070] ;

[0071] in, Temporal images of cloud contamination for each spectral band. For the first Phase parameters, For the first Spectral parameters, The image shows the average value of the cloudless sequence, which is estimated by least squares regression of the cloudless region.

[0072] This step provides a near-realistic data foundation for the next step of building the guiding gradient tensor, and is an indispensable bridge for achieving high precision, structural fidelity, and cloud-free operation throughout the entire process.

[0073] Step S33: Stack the cloud pollution time-phase images of all spectral bands, and perform differential calculation on the stacked guided remote sensing images to obtain guided gradient tensor data.

[0074] Understandably, this step involves replacing the cloud-polluted areas in the observed multi-temporal remote sensing images with cloud-polluted temporal images from all spectral bands to obtain the guiding remote sensing image. The guided gradient tensor is obtained through difference calculation, and its difference calculation formula is shown below:

[0075] ;

[0076] in, This refers to the guiding gradient tensor. Indicates along the first Perform matrix operations on dimensions. It is a difference matrix. To guide remote sensing images, it is defined as:

[0077] ;

[0078] This step provides the core constraint objective for the gradient domain fidelity term in the subsequently constructed low-rank tensor completion model, ensuring that the gradient field (i.e., spatial details) of the reconstructed image remains highly consistent with this reliable guiding gradient field during the iterative optimization process.

[0079] In this step, step S3 also includes steps S34 and S35.

[0080] Step S34: Stack each phase of the guided gradient tensor data along the spectral dimension using the reshape operator to obtain third-order tensor data with spatial row number, spatial column number, and spectral-temporal combined dimension;

[0081] It is understandable that this step involves multi-temporal remote sensing images. Each phase Stack them into a third-order tensor using the reshape operator along the third dimension. The reshape operator is defined as follows: ,in, Indicates the spatial resolution of a sequence of cloud-covered images. Indicates the spatial resolution of a cloudless image sequence. Indicates spectral resolution, This indicates the temporal resolution. This step organizes massive amounts of multi-temporal remote sensing data into a low-rank, user-friendly format, which not only significantly reduces the computational complexity and memory overhead of subsequent optimization solutions, but more importantly, it fully preserves the inherent spatial-temporal coupling information in the data, laying a solid foundation for the model to simultaneously utilize spatial details and temporal correlations for accurate cloud removal and reconstruction.

[0082] Step S35: Perform a low-rank approximation of the third-order tensor data according to a preset approximation formula to obtain spatial feature factors and temporal feature factors.

[0083] It is understandable that the multi-temporal remote sensing images stacked in this step... Approximately expressed as:

[0084] ;

[0085] in, For stacked multi-temporal remote sensing images, Indicates along the first Perform matrix operations on dimensions. Represents spatial characteristic factors, , Characterizes spatial information from multi-temporal remote sensing images. It is a temporal-spectral feature factor that characterizes the temporal-spectral information of multi-temporal remote sensing images; Describe the predefined rank of the low-rank decomposition of the tensor and satisfy the following conditions: .

[0086] Step S4: Construct gradient domain fidelity term, pixel domain fidelity term, and temporal spectrum consistency constraint term based on the spatial feature factor and temporal spectrum feature factor to obtain multiple regularization constraints;

[0087] It is understandable that the gradient domain fidelity term constructed in this step is as follows:

[0088] ;

[0089] in, It is the Frobenius norm. Representing dimension, It is a difference matrix. This is the guiding gradient tensor.

[0090] The low-rank representation constraints obtained are as follows:

[0091] ;

[0092] The constructed temporal spectrum consistency constraints are shown below:

[0093] ;

[0094] in, The target tensor weighting factor, For element-wise multiplication, Let L2 and L1 norms be represented.

[0095] Step S5: Construct a low-rank tensor completion model for remote sensing cloud removal based on the multiple regularization constraints.

[0096] Understandably, this step combines the regularization term with the low-rank representation constraint that characterizes the essence of the data to construct a multi-objective convex optimization problem. The model's uniqueness lies in its multi-constraint collaborative architecture: the gradient domain fidelity term ensures that the spatial structure of the reconstructed image remains consistent with the guiding gradient tensor, effectively protecting edge and texture details; the pixel domain fidelity term, as a hard constraint, guarantees the absolute authenticity of data in cloud-free areas; the temporal consistency constraint provides supplementary information for the reconstruction of cloud-polluted areas by mining temporal correlations; and the low-rank constraint captures the inherent characteristics of remote sensing data, achieving dimensionality reduction and denoising of high-dimensional data. In this step, step S5 includes steps S51 and S52.

[0097] Step S51: Set fidelity constraints and weighting coefficients for each regularization term constraint based on the multiple regularization constraints;

[0098] It is understandable that this step involves selecting a weighting coefficient (i.e., a penalty parameter) for each regularization term. and In practical applications, It controls the strength of the low-rank constraint. The larger the value, the stronger the low-rank characteristics of the reconstruction result. It is suitable for scenarios with simple land cover types and smooth temporal changes. This controls the importance of the gradient fidelity term. Increasing its value can better preserve edge and texture details, making it suitable for scenarios with complex terrain and requiring high spatial fidelity.

[0099] Step S52: Based on the fidelity constraints and the weighting coefficients of each regularization term constraint, construct a tensor completion model.

[0100] Understandably, this step constructs a low-rank representation and a tensor completion model based on gradient domain fidelity and temporal spectrum consistency constraints, using the gradient domain fidelity term as an example. The objective function is as follows:

[0101] ;

[0102] in, An index set representing the location of cloudless areas. For stacked multi-temporal remote sensing images, Indicates will A projection operator that maps the pixel at a given location to itself and sets other pixels to 0. and For a penalty parameter greater than zero, For element-wise multiplication, It is a difference matrix. This refers to the guiding gradient tensor. Represents multi-temporal remote sensing images. This represents multi-temporal remote sensing images observed. It is the Frobenius norm.

[0103] Step S6: The low-rank tensor completion model is optimized and solved using the near-end alternating minimization algorithm based on the embedded alternating direction multiplier method. The solution results are then corrected and optimized based on the cloud mask data and the active fault mask to obtain the cloud removal result.

[0104] It is understandable that this step updates the spectral characteristic factor, spatial characteristic factor, and multi-temporal remote sensing image using the Alternating Proximal Minimization (PAM) method, with the specific formula as follows:

[0105] ;

[0106] in, And it is a penalty parameter. , and This step involves updating the temporal spectral feature factors, spatial feature factors, and multi-temporal remote sensing images from the previous iteration. Step S6 includes steps S61, S62, S63, S64, and S65.

[0107] Step S61: Iteratively update the temporal spectral feature factors according to the low-rank tensor completion model and the proximal alternating minimization algorithm to obtain the iteratively updated temporal spectral feature factors;

[0108] It is understandable that this step updates the time-spectral characteristic factor variable by fixing other variables, as shown in the following formula:

[0109] ;

[0110] Solve for the variables by taking the derivative and expanding all tensors along the third dimension:

[0111] ;

[0112] in, and These are the tensors updated in the previous iteration. and The third-dimensional expansion matrix, For the transpose operator, It is an identity matrix.

[0113] Step S62: Iteratively update the spatial feature factors according to the low-rank tensor completion model, the preset auxiliary variables, and the proximal alternating minimization algorithm with embedded alternating direction multipliers, to obtain the iteratively updated spatial feature factors.

[0114] It is understandable that, with other variables fixed, the objective function for the characteristic factors in the variable space is:

[0115] ;

[0116] This step involves introducing auxiliary variables. The alternating direction multiplier algorithm is used to solve the above formula, and its Lagrangian function is as follows:

[0117] ;

[0118] ;

[0119] in, To augment the Lagrange function, It is a Lagrange multiplier. The penalty parameters for the alternating direction multiplier algorithm; , and Both methods use the alternating direction multiplier algorithm to alternately update variables. This is the spatial feature tensor updated in the previous iteration.

[0120] ;

[0121] Among them, superscript The labeled variable represents the variable from the previous iteration. The variable to be updated, For the updated spatial feature factors, This represents the updated auxiliary variable. This represents the updated Lagrange multipliers. This represents the auxiliary variable from the previous iteration. Represents the Lagrange multiplier of the previous iteration;

[0122] Next, by fixing other variables, the following objective function is minimized to update the variables. :

[0123] ;

[0124] According to the minimization criterion, setting the first derivative to zero, the optimal values ​​of the variables are as follows:

[0125] ;

[0126] in, , Let the target gradient tensor be represented. Expanding the above tensor along the spectral dimension yields the following formula:

[0127] ;

[0128] in, This is a set of difference operators. The expanded formula can be solved quickly by the Sylvester tensor equation, where the variables... Updated formula:

[0129] ;

[0130] in, and Diagonalized by singular value decomposition and , and It is a two-dimensional DFT matrix. and It is a diagonal matrix. , Indicates dot division. Represents the folding operator. It is the size of A matrix in which all elements are set to 1.

[0131] Next, with other iteration variables fixed, the auxiliary variables are updated by minimizing the following objective function. :

[0132] ;

[0133] in, These are auxiliary variables updated in the previous iteration.

[0134] Using the group sparsity operator Update auxiliary variables The definition of the group sparsity operator is:

[0135] ;

[0136] in, The set of gradient values ​​for all channels at a given pixel location. This is a preset scalar threshold parameter.

[0137] The formula for the auxiliary variable is as follows:

[0138] ;

[0139] in, For auxiliary variables in spatial location A vector consisting of the values ​​of all bands or time phases. It is a weighted combination of gradient tensors. For tensor The line, number The absolute values ​​of the elements in the column are taken.

[0140] Finally, update the Lagrange multipliers of the variables until the convergence condition is met. The ADMM algorithm stops iterating when the maximum number of iterations is reached; otherwise, it returns to the step of updating the time-spectral feature factors.

[0141] Step S63: Update the multi-temporal remote sensing image according to the low-rank tensor completion model and the near-end alternation minimization algorithm to obtain the updated multi-temporal remote sensing image;

[0142] It is understandable that this step updates the multi-temporal remote sensing image by fixing other variables and minimizing the following objective function, which is shown below:

[0143] ;

[0144] Transform the stacked / fourth-order tensor in the above formula into the first... The temporal tensor, expanded along the third dimension:

[0145]

[0146] ;

[0147] in, and Both are two-dimensional difference operators constructed using the Kronecker product. To guide the gradient tensor in the th case A slice of time, This indicates that the reconstructed cloudless image is in the [missing information - likely a specific location or region]. The estimated value of the time phase, For the target tensor The transpose expansion matrix of the phase.

[0148] To find the optimal solution, we differentiate the above formula and set the derivative to zero, thus obtaining the analytical solution:

[0149] ;

[0150] in, For the composite gradient operator matrix, Let be the proximal regularization parameter, the th The formula for updating multi-temporal remote sensing images is as follows:

[0151] ;

[0152] in, For the first Multi-temporal remote sensing images reconstructed from time phases. A folding operator for refolding a matrix back into its original three-dimensional tensor form. It is the conjugate transpose of the two-dimensional discrete Fourier transform (DFT) matrix. It is a diagonal matrix. It is an orthogonal matrix. It is a two-dimensional discrete Fourier transform (DFT) matrix. Let be the target gradient matrix.

[0153] Step S64: Stack the updated multi-temporal remote sensing images to restore them into a fourth-order multi-temporal remote sensing image, and combine it with the corresponding cloud mask and active fault mask to correct the updated multi-temporal remote sensing image to obtain the corrected multi-temporal remote sensing image.

[0154] Understandably, this step reorganizes the optimized third-order tensor (number of spatial rows, number of spatial columns, and spectral-temporal combination dimension) into the original fourth-order structure, ensuring the integrity of data dimensions and temporal consistency. It supplements the data reconstruction details that may be omitted in the low-rank approximation process, such as restoring the spatial-spectral-temporal correlation of multi-temporal sequences through tensor expansion and folding operations.

[0155] Subsequently, mask correction is applied: cloud masks are used to directly recover the original pixel values ​​of cloudless areas (avoiding over-modification), while active fault masks serve as weighting factors to adjust the pixel correction intensity in the gradient domain fidelity term, prioritizing the protection of fault feature regions (through weighted averaging) and preventing the loss of edge details during cloud removal. The updated multi-temporal remote sensing images are stacked and restored to a fourth-order multi-temporal remote sensing image. The target tensor is then corrected using the cloud mask, with the following formula:

[0156] ;

[0157] in, For the corrected multi-temporal remote sensing images, Indicates cloud mask, This represents multi-temporal remote sensing images from the original observations. Indicates the active fault mask. This indicates the preset weight.

[0158] The integrated multi-mask collaborative correction strategy in this step not only inherits the denoising advantages of the low-rank model, but also enhances the fidelity of geological features in the image through mask guidance. Technically, it directly produces high-quality de-clouded image sequences, providing a directly analyzable remote sensing data foundation for practical applications such as dynamic monitoring of geological disasters.

[0159] Step S65: Calculate the relative error between the corrected multi-temporal remote sensing image of the current iteration number and the corrected multi-temporal remote sensing image of the previous iteration number, and determine whether the relative error meets the preset convergence condition or whether the iteration number has reached the preset maximum iteration number. If the determination result is that the preset convergence condition is met or the iteration number has reached the maximum iteration number, the corrected multi-temporal remote sensing image of the current iteration number is used as the final cloud-removed multi-temporal remote sensing image.

[0160] It is understandable that this step calculates the relative error between the corrected multi-temporal remote sensing image at the current iteration number and the corrected multi-temporal remote sensing image at the previous iteration number. The process continues until the error reaches the convergence condition. When the maximum number of iterations is reached, the proximal alternating minimization algorithm iteration is stopped; otherwise, the process returns to the step of updating the temporal spectral feature factors. This step, through the deep integration of gradient fidelity constraints, low-rank tensor modeling, and temporal spectral consistency optimization, addresses the problems of detail ambiguity, temporal inconsistency, and low computational efficiency inherent in traditional methods under complex cloud coverage scenarios.

[0161] Example 2:

[0162] like Figure 2 As shown, this embodiment provides a remote sensing image cloud removal system that integrates gradient fidelity and temporal spectrum consistency. The system includes an acquisition unit 701, an identification unit 702, a processing unit 703, a constraint unit 704, a construction unit 705, and an optimization unit 706.

[0163] Acquisition unit 701 is used to acquire observed multi-temporal remote sensing images and their corresponding cloud mask data;

[0164] The identification unit 702 is used to perform active fault identification on the multi-temporal remote sensing images and generate an object active fault mask.

[0165] Processing unit 703 is used to calculate the guiding gradient tensor based on the multi-temporal remote sensing image, and stack the guiding gradient tensor along the spectral direction according to the time series and perform low-rank approximation to obtain spatial feature factors and temporal spectral feature factors;

[0166] Constraint unit 704 is used to construct gradient domain fidelity term, pixel domain fidelity term and time spectrum consistency constraint term according to the spatial feature factor and the temporal spectrum feature factor, so as to obtain multiple regularization constraints;

[0167] Construction unit 705 is used to construct a low-rank tensor completion model for remote sensing cloud removal based on the multiple regularization constraints.

[0168] The optimization unit 706 is used to optimize and solve the low-rank tensor completion model based on the near-end alternating minimization algorithm of the embedded alternating direction multiplier method, and to correct and optimize the solution results based on the cloud mask data and the active fault mask to obtain the cloud removal result.

[0169] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0170] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0171] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A remote sensing image cloud removal method fusing gradient fidelity and time spectrum consistency, characterized in that, The method comprises the following steps: Obtaining observed multi-temporal remote sensing images and corresponding cloud mask data; Performing active fault identification on the multi-temporal remote sensing images to generate object active fault masks; Calculating a guided gradient tensor from the multi-temporal remote sensing images, and stacking and low-rank approximating the guided gradient tensor along the spectral direction in time sequence to obtain spatial feature factors and time-spectral feature factors; Constructing a gradient domain fidelity term, a pixel domain fidelity term, and a time-spectral consistency constraint term from the spatial feature factors and the time-spectral feature factors to obtain multiple regularization constraints; Constructing a low-rank tensor completion model for remote sensing cloud removal based on the multiple regularization constraints; Optimizing and solving the low-rank tensor completion model based on a proximal alternating direction multiplier method, and correcting and optimizing the solution based on the cloud mask data and the active fault masks to obtain a cloud removal result; Wherein, the active fault identification on the multi-temporal remote sensing images comprises: Performing multi-modal data fusion on the multi-temporal remote sensing images, wherein a preset phase consistency algorithm is used as a front-end processor to calculate a phase consistency measure through a multi-scale Gabor filter bank to obtain preliminary fault data; A preset tensor voting algorithm is used as a back-end enhancer to perform tensor field voting processing on the preliminary fault data, and a preset geometric constraint is used to aggregate context information to obtain optimized fault feature data; Generating a binary active fault mask based on the optimized fault feature data; Wherein, the construction of the low-rank tensor completion model for remote sensing cloud removal based on the multiple regularization constraints comprises: Setting a fidelity constraint condition and a weighting coefficient of each regularization term constraint based on the multiple regularization constraints; Based on the fidelity constraint condition and the weighting coefficient of each regularization term constraint, a tensor completion model is constructed.

2. The remote sensing image cloud removing method of fusing gradient fidelity and time spectrum consistency according to claim 1, characterized in that The guided gradient tensor is calculated from the multi-temporal remote sensing images, which comprises: The multi-temporal remote sensing images are divided into cloud image sequences and cloud-free image sequences, and the cloud-free image sequences obtained by the division are calculated according to a preset average value calculation formula to obtain cloud-free sequence average value images; The cloud pollution phase image of each spectral band is calculated based on a preset cloud pollution phase image estimation formula. Stack all spectral band cloud pollution phase images, and perform difference calculation on the stacked guided remote sensing images to obtain guided gradient tensor data.

3. The remote sensing image cloud removing method of fusing gradient fidelity and time spectrum consistency according to claim 1, characterized in that The guided gradient tensor is stacked and low-rank approximated along the spectral direction in time sequence, which comprises: Each phase of the guided gradient tensor data is stacked along the spectral dimension using a reshape operator to obtain three-order tensor data with spatial row number, spatial column number, and spectral-time combined dimension; The three-order tensor data is low-rank approximated according to a preset approximation formula to obtain spatial feature factors and time-spectral feature factors.

4. The remote sensing image cloud removing method of fusing gradient fidelity and time spectrum consistency according to claim 1, characterized in that ,The low-rank tensor completion model is optimized and solved based on a proximal alternating minimization algorithm of an embedded alternating direction multiplier method, and the solving result is corrected and optimized based on the cloud mask data and the active fault mask to obtain a cloud removal result, including: Spectrum feature factors are obtained by iteratively updating the spectrum feature factors according to the low-rank tensor completion model and the proximal alternating minimization algorithm. Spatial feature factors are obtained by iteratively updating the spatial feature factors according to the low-rank tensor completion model, the preset auxiliary variable and the proximal alternating minimization algorithm of the embedded alternating direction multiplier method. The multi-temporal remote sensing image is updated according to the low-rank tensor completion model and the proximal alternating minimization algorithm to obtain an updated multi-temporal remote sensing image. The updated multi-temporal remote sensing image is stacked and restored to a four-order multi-temporal remote sensing image, and the updated multi-temporal remote sensing image is corrected in combination with the corresponding cloud mask and active fault mask to obtain a corrected multi-temporal remote sensing image. The relative error of the corrected multi-temporal remote sensing image of the current iteration number and the corrected multi-temporal remote sensing image of the last iteration number is calculated, and it is determined whether the relative error meets a preset convergence condition or whether the iteration number reaches a preset maximum iteration number, if the determination result is that the preset convergence condition is met or the iteration number reaches the maximum iteration number, the corrected multi-temporal remote sensing image of the current iteration number is taken as the final cloud-removed multi-temporal remote sensing image.

5. A remote sensing image cloud removal system fusing gradient fidelity and temporal consistency, characterized in that, including: An acquisition unit is configured to acquire observed multi-temporal remote sensing images and corresponding cloud mask data thereof; An identification unit is configured to identify active faults of the multi-temporal remote sensing images to generate object active fault masks; A processing unit is configured to calculate a guided gradient tensor based on the multi-temporal remote sensing images, and stack and low-rank approximate the guided gradient tensor along a spectral direction according to a time sequence to obtain spatial feature factors and time-spectral feature factors; A constraint unit is configured to construct a gradient domain fidelity term, a pixel domain fidelity term and a time-spectral consistency constraint term based on the spatial feature factors and the time-spectral feature factors to obtain multiple regularization constraints; A construction unit is configured to construct a low-rank tensor completion model for remote sensing cloud removal based on the multiple regularization constraints; An optimization unit is configured to optimize and solve the low-rank tensor completion model based on a proximal alternating minimization algorithm of an embedded alternating direction multiplier method, and correct and optimize the solving result based on the cloud mask data and the active fault mask to obtain a cloud removal result. The identification unit includes: A first identification subunit is configured to perform multi-modal data fusion on the multi-temporal remote sensing images, wherein a preset phase consistency algorithm is used as a front-end processor to calculate a phase consistency metric through a multi-scale Gabor filter bank to obtain preliminary fault data. A second identification subunit is configured to perform tensor field voting processing on the preliminary fault data based on a preset tensor voting algorithm as a back-end enhancer, and aggregate context information through a preset geometric constraint to obtain optimized fault feature data. The third identification subunit is configured to generate a binary active fault mask based on the optimized fault feature data. The construction unit comprises: The first construction subunit is configured to set a fidelity constraint condition and a weighted coefficient of each regularization term constraint based on the multiple regularization constraints. The second construction subunit is configured to construct a tensor completion model based on the fidelity constraint condition and the weighted coefficient of each regularization term constraint.

6. The remote sensing image cloud removing system fusing gradient fidelity and temporal consistency according to claim 5, characterized in that, The processing unit comprises: The first processing subunit is configured to divide the multi-temporal remote sensing image into a cloud image sequence and a cloud-free image sequence, and calculate the cloud-free image sequence according to a preset average value calculation formula to obtain a cloud-free sequence average value image. The second processing subunit is configured to calculate the cloud-free sequence average value image according to a preset cloud pollution temporal image estimation formula to obtain a cloud pollution temporal image of each spectral band. The third processing subunit is configured to stack the cloud pollution temporal images of all spectral bands, and perform difference calculation on the stacked guided remote sensing image to obtain guided gradient tensor data.

7. The remote sensing image cloud removing system fusing gradient fidelity and temporal consistency consistency according to claim 5, characterized in that, The processing unit further comprises: The fourth processing subunit is configured to perform stack processing on each temporal phase of the guided gradient tensor data along the spectral dimension using a reshape operator to obtain three-order tensor data of a spatial row number, a spatial column number and a spectral-temporal combined dimension. The fifth processing subunit is configured to perform low-rank approximation processing of a preset rank on the three-order tensor data according to a preset approximate representation formula to obtain spatial feature factors and time-spectral feature factors.

8. The remote sensing image cloud removing system fusing gradient fidelity and temporal consistency consistency according to claim 5, characterized in that, The optimization unit comprises: The first optimization subunit is configured to iteratively update the time-spectral feature factors according to the low-rank tensor completion model and a proximal alternating minimization algorithm to obtain iteratively updated time-spectral feature factors. The second optimization subunit is configured to iteratively update the spatial feature factors according to the low-rank tensor completion model, a preset auxiliary variable and a proximal alternating minimization algorithm of an embedded alternating direction multiplier method to obtain iteratively updated spatial feature factors. The second optimization subunit is configured to update the multi-temporal remote sensing image according to the low-rank tensor completion model and the proximal alternating minimization algorithm to obtain an updated multi-temporal remote sensing image. The third optimization subunit is configured to stack and restore the updated multi-temporal remote sensing image into a four-order multi-temporal remote sensing image, and correct the updated multi-temporal remote sensing image in combination with a corresponding cloud mask and an active fault mask to obtain a corrected multi-temporal remote sensing image. The fourth optimization subunit is configured to calculate a relative error of the corrected multi-temporal remote sensing image of the current iteration number and the corrected multi-temporal remote sensing image of the last iteration number, and determine whether the relative error satisfies a preset convergence condition or whether the iteration number reaches a preset maximum iteration number, and if the determination result is that the preset convergence condition is satisfied or the iteration number reaches the maximum iteration number, the corrected multi-temporal remote sensing image of the current iteration number is taken as a final multi-temporal remote sensing image after cloud removal.

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