Regarding compressed sensing solvers

[AnouarITI]

I have a large-scale problem where I use the L1-regularized least square for compressed sensing by Stephen Boyd . However, the computation takes something like 170 seconds, which drove me to look for something more efficient. I found that also ISTA, FISTA, and Twist are able to fulfill the same task, but I did not find an implementation of the L1-regularized least square in the proximal library.

Q1: Is the L1-regularized least square already exist in the library?
Q2: Are ISTA, FISTA, and Twist capable of solving large-scale problems (A matrix shape (149600, 144))?
Q2: is the ADMM solver capable of solving such problems? If yes, is it more efficient?

[mrava87]

Hello,
thanks for the issue.

Q1: not the one in the link of your message. However this is a very different type of algorithm, not of the family of proximal algorithms so I do not think it belongs to this library
Q2: definitely. It all depends on your A matrix and how you implement it (dense, sparse, linear operator)?
Q3: yes, but I would say it is not where ADMM shines. ADMM is usually used for more complex problems where you have ||Lx||_1. Having said that, it really depends from problem to problem, so I would suggest trying it and compare its convergence properties with other competitors