Tfocs function call for min quad+TV with linear constraint

TFOCS
1

I would like to solve the following problem:

||Ax -b||_2^2 + lambda*||x||_TV s.t. Cx - d <=0;

I would like to do this with TFOCS. I have been at it for too many hours, but I haven’t been able to figure out the arguments to the tfocs functions. Please can you help?

FYI, I have tried Mosek but I am not happy with the solution - x, which is an image, looks “chunky”. (Maybe I did something wrong, but I’d like to be able to compare with TFOCS).

Thank you, I do appreciate your time.

2

If this is the model you are solving with MOSEK, and it is achieving a reasonably accurate solution, then you are not going to like the solution TFOCS gives you either. If the model is the same, the image will be, too.

3

I agree with Michael: TFOCS will not give you a different answer (hopefully!). You are probably seeing a staircase effect due to TV. This is a common problem, and there has been a lot of research into fixing it. Do a google search for “staircasing TV” and there will be lots of potential solutions.