An iteratively reweighted norm algorithm for minimization of total variation functionals

Total variation (TV) regularization has become a popular method for a wide variety of image restoration problems, including denoising and deconvolution. A number of authors have recently noted the advantages of replacing the standard ℓ² data fidelity term with an ℓ¹ norm. We propose a simple but very flexible method for solving a generalized TV functional that includes both the ℓ²-TV ℓ¹-TV and ℓ²-TV problems as special cases. This method offers competitive computational performance for ℓ²-TV and is comparable to or faster than any other ℓ¹-TV algorithms of which we are aware.