Compressive Sensing and Applications Source Code

Compressive sensing, as a signal processing technique that breaks through the Nyquist sampling theorem, demonstrates unique value in remote sensing image processing. This source code repository focuses on three core application scenarios: SAR Image Compressive Sensing By leveraging the inherent sparsity of synthetic aperture radar (SAR) images, this implementation achieves high-quality imaging at sampling rates significantly lower than traditional requirements. The key technical aspects involve designing measurement matrices that align with SAR scattering characteristics and solving reconstruction optimization problems under coherent speckle noise. The code implements specialized measurement operators tailored to SAR physics and uses robust optimization algorithms to handle noise-corrupted measurements. Hyperspectral Data Reconstruction Addressing the strong correlation in the spectral dimension of hyperspectral images, the code employs a joint sparse representation model. This method effectively maintains spectral continuity across hundreds of bands while substantially reducing band sampling requirements during data acquisition. The implementation features multidimensional sparse coding techniques and utilizes tensor-based operations to preserve spectral-spatial relationships. Structure-Sparse Driven Low-Rank Reconstruction Combining spatial prior knowledge of target structures in SAR images, this approach integrates low-rank constraints with block-sparse representations. This hybrid regularization method is particularly suitable for processing scenes with repetitive structures (such as ship targets), maintaining edge sharpness while suppressing background clutter. The algorithm implements structured sparsity patterns through customized regularization terms and employs efficient matrix factorization techniques. The core advantages of this implementation include: adaptive selection of sparse transform bases (such as curvelets/3D DCT) for different remote sensing data types (single-polarization SAR/multispectral/fully-polarimetric data), and solving nonlinear optimization problems through an improved alternating direction method of multipliers (ADMM). The code features configurable transform dictionaries and optimized ADMM variants that ensure reconstruction accuracy while enhancing computational efficiency through parallelizable operations and convergence acceleration techniques.