Efficient minimization method for a generalized total variation functional

Replacing the ℓ² data fidelity term of the standard Total Variation (TV) functional with an ℓ¹ data fidelity term has been found to offer a number of theoretical and practical benefits. Efficient algorithms for minimizing this ℓ¹-TV functional have only recently begun to be developed, the fastest of which exploit graph representations, and are restricted to the denoising problem. We describe an alternative approach that minimizes a generalized TV functional, including both ℓ²-TV and ℓM¹ -TV as special cases, and is capable of solving more general inverse problems than denoising (e.g., deconvolution). This algorithm is competitive with the graph-based methods in the denoising case, and is the fastest algorithm of which we are aware for general inverse problems involving a nontrivial forward linear operator.