Objectives The conventional group sparse representation (GSR) model encounters challenges in precisely estimating the sparsity of individual image groups, because the influence of noise results in distortion in the restoration of original image group.

Methods This paper introduces a strategy denominated as the group sparse residual constraint. This strategy leverages non-local self-similarity priors to derive precise estimate of sparse coefficients for each original image group. Subsequently, the sparse coefficients of corresponding degraded image groups are constrained to approximate this estimate. Furthermore, the intricate nature of noise in area-array satellite images (e.g., Luojia3-01 satellite images), surpasses the simplicity of additive white Gaussian noise (AWGN). Consequently, conventional GSR model tailored for AWGN exhibits a reduction in efficacy when deployed in real image denoising scenarios. To address this, this paper introduces two distinct weight matrices into the data fidelity term and regularization, respectively, with the intent of characterizing the statistical features inherent in both images and noise. This paper adopts the alternating direction method of multipliers for optimizing the proposed image denoising task.

Results The effectiveness of the proposed model is validated by the experiments using simulated data and real images obtained from the Luojia3-01 satellite. In the experiments of simulated data, the proposed model outperforms other methods in removing AWGN and spatially variant noise. In the experiments of real images, the entropy of denoised images by the proposed model shows improvements of 2.03%, 1.18%, 1.26%, 1.24%, and 2.10% , compared to the block-matching and 3-D filtering method, multi-channel weighted nuclear norm minimization method, nonlocally centralized sparse representation method, low-rankness guided group sparse representation method, and trilateral weighted sparse coding method, respectively.

Conclusions The proposed method exhibits good performance in processing area-array satellite images with low signal-to-noise ratios and complex noise structures, significantly enhancing the quality of the image. By effectively reducing noise while preserving crucial details and edges, it provides a reliable solution for enhancing the usability and interpretability of area-array satellite images, particularly in challenging conditions.