Compressed Sensing Reconstruction Algorithm Collection

Compressed sensing reconstruction algorithms constitute a class of mathematical methods for recovering sparse signals from limited observational data. These algorithms find significant applications in signal processing, medical imaging, wireless communications, and other fields. Below is a characteristic analysis of several mainstream reconstruction algorithms:

Greedy Algorithms: MP (Matching Pursuit) serves as the foundational greedy algorithm, reconstructing signals by iteratively selecting atoms that best match the residual. Implementation typically involves calculating inner products between residuals and dictionary atoms. OMP (Orthogonal Matching Pursuit) improves upon MP by performing orthogonalization processing on all selected atoms after each iteration, enhancing stability through Gram-Schmidt or matrix inversion operations. CoSaMP (Compressive Sampling Matching Pursuit) and SP (Subspace Pursuit) incorporate backtracking mechanisms that dynamically adjust the support set during iterations, requiring careful management of candidate sets and pruning operations.

Optimization-Based Algorithms: IHT (Iterative Hard Thresholding) enforces solution sparsity by applying hard thresholding constraints, where each iteration involves gradient descent followed by thresholding operations to maintain sparsity. IRLS (Iteratively Reweighted Least Squares) approximates l0-norm optimization problems using weighted l2-norms, with weights updated iteratively based on current solutions to emphasize sparse components. GBP (Generalized Alternating Projection) iterates between two constraint sets through alternating projections, often implemented using projection operators onto sparsity and measurement consistency sets.

The core principle shared by these algorithms involves leveraging sparse prior information of signals. Different algorithms exhibit distinct advantages in convergence speed, computational complexity, and reconstruction accuracy. Practical applications require selecting appropriate reconstruction algorithms based on specific problem scale, real-time requirements, and noise levels. Code implementations typically involve careful parameter tuning and stopping criterion selection to optimize performance.