Anonymous Attendee       09:56 AM
For Jean-Luc, the compressed sparsity assume a foreground and noise free problem, as y = Hx = H \phi \alpha have no noise accountability. How would you account for noise and foregrounds in compressed sparisty w.r.t to image recovery?

Jean-Luc Starck       10:08 AM
This is right, but there are also results by Candes et al showing that the sparse recovery lin the noisy case leads  to a solution with an error norm below a given value, 2sigma / k_min,  where sigma is the  noise standard deviation and k_min is the minimum of H eigen values. In practive, we see that proximal algorithms are very robust to noise and this is not surprising since the l_1 proximal operator is also a denoiser. There are also some works showing that sparse recovery is robust if we have an error on the H operator, i.e. H is not perfectly known.