# A Nonconvex Nonsmooth Regularization Method for Compressed Sensing and Low-Rank Matrix Completion

arXiv: https://arxiv.org/abs/1605.00479 · HTML: https://mlsanity.com/paper/1605.00479/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 May 2016.

## Built on by (most cited first, 1 of 1)

- [Physics-Informed DeepMRI: Bridging the Gap from Heat Diffusion to k-Space Interpolation](https://mlsanity.com/paper/2308.15918/) (2023)

## Abstract (arXiv)

In this paper, nonconvex and nonsmooth models for compressed sensing (CS) and low rank matrix completion (MC) is studied. The problem is formulated as a nonconvex regularized leat square optimization problems, in which the l0-norm and the rank function are replaced by l1-norm and nuclear norm, and adding a nonconvex penalty function respectively. An alternating minimization scheme is developed, and the existence of a subsequence, which generate by the alternating algorithm that converges to a critical point, is proved. The NSP, RIP, and RIP condition for stable recovery guarantees also be analysed for the nonconvex regularized CS and MC problems respectively. Finally, the performance of the proposed method is demonstrated through experimental results.