Iterative Compressed Sensing Reconstruction Algorithm

Iterative compressed sensing reconstruction algorithms represent a popular research direction in signal processing in recent years. These algorithms employ iterative optimization techniques to reconstruct original signals with high precision from limited measurement data. The core principle leverages sparsity priors, where each iteration progressively refines the signal estimate toward the true signal. Implementation typically involves sparse transformation functions (e.g., FFT or wavelet transforms) and optimization solvers.

The algorithm generally comprises three key phases: First, sparse signal representation using appropriate basis functions like Fourier or wavelet bases through transform matrix multiplication. Second, formulation of optimization objectives, commonly L1-norm minimization problems implemented via linear programming or convex optimization libraries. Third, iterative optimization strategies such as gradient descent or proximal gradient methods, where each iteration updates signal estimates using update rules until convergence criteria are met. Code implementations often involve loops with residual calculations and thresholding operations.

Compared to traditional compressed sensing methods, iterative algorithms demonstrate superior reconstruction quality and robustness, effectively handling noise interference and non-ideal measurement conditions. They show significant application potential in medical imaging (e.g., MRI reconstruction) and wireless communications (e.g., sparse channel estimation), where implementations may incorporate regularization parameters and stopping conditions based on relative error thresholds.