# Bias Reduction in Compressed Sensing

arXiv: https://arxiv.org/abs/1812.11329 · HTML: https://mlsanity.com/paper/1812.11329/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2018.

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

- [Generalized Tensor Summation Compressive Sensing Network (GTSNET): An Easy to Learn Compressive Sensing Operation](https://mlsanity.com/paper/2108.03167/) (2021)

## Abstract (arXiv)

Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy is to instead use the ℓ1- and nuclear-norms. While these are convex and can therefore be reliably optimized they suffer from a shrinking bias that degrades the solution quality in the presence of noise. In this paper we combine recently developed bias free non-convex alternatives with the nuclear- and ℓ1-penalties. This reduces bias and still enables reliable optimization properties. We develop an efficient minimization scheme using derived proximal operators and evaluate the method on several real and synthetic computer vision applications with promising results.