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.
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.