I'm fairly new to compressive sensing, and I have been looking for a MATLAB implementation of the problem:
$$ A x = b $$
where $ A \in \mathbb{C}^{m \times n} $, $ b \in \mathbb{C}^{m} $ and $ x \in \mathbb{C}^{n} $.
Until now I was solving this problem with Least Squares framework:
$$ \arg \min_{x} \frac{1}{2} {\left\| A x - b \right\|}_{2}^{2} $$
Recently I have been having problems with ill conditioned matrices.
Hence I wanted to give $ {L}_{1} $ minimization a try:
$$ \arg \min_{x} \frac{1}{2} {\left\| A x - b \right\|}_{2}^{2} + \lambda {\left\| x \right\|}_{1} $$
Anything you can recommend how to solve such problem?
CVX is robust but a bit slow. YALL1 is another good choice. Simple and fast. SPGL is also good.