p-th Power total variation regularization in photon-limited imaging via iterative reweighting

Recent work in ℓ_p-norm regularized sparsity recovery problems (where 0 ≤ p ≤ 1) has shown that signals can be recovered with very high accuracy despite the fact that the solution to these nonconvex optimization problems are not necessarily the global minima but are instead potentially local minima. In particular, ℓ_p-norm regularization has been used effectively for signal reconstruction from measurements corrupted by zero-mean additive Gaussian noise. This paper describes a p-th power total variation (TV_p) regularized op timization approach for image recovery problems in photon-limited settings using iterative reweighting. The proposed method iteratively convexities a sequence of nonconvex TV_p subproblems using a weighted TV approach and is solved using a modification to the FISTA method for TV-based de-noising. We explore the effectiveness of the proposed method through numerical experiments in image deblurring.