2015/11/29 by Sergey Voronin, Ingrid Daubechies, Voronin, Sergey +1 · 1 citation
Engineering · Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1511.08970
openalex publication_date 2015/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the idea of iteratively reweighted least squares, reducing the minimization at every iteration step to that of a functional including only ℓ2-norms. This amounts to smoothing of the absolute value function that appears in the generalized sparsity promoting penalty we consider, with the smoothing becoming iteratively less pronounced. We demonstrate that the sequence of iterates of our algorithm converges to a limit that minimizes the original functional.