Multiplicative updates algorithm to minimize the generalized total variation functional with a non-negativity constraint

We propose an efficient algorithm to solve the generalized Total Variation (TV) functional with a non-negativity constraint. This algorithm, which does not involve the solution of a linear system, but rather multiplicative updates only, can be used to solve the denoising and deconvolution problems. The derivation of our method is straightforward once the generalized TV functional is cast as a Non-negative Quadratic Programming (NQP) problem. The proposed algorithm offers a fair computational performance to solve the ℓ²-TV and ℓ¹-TV denoising and deconvolution problems and it is the fastest algorithm of which we are aware for general inverse problems involving a nontrivial forward linear operator and a non-negativity constraint.