Total Variation (TV) regularization has become a popular method for a wide variety of image restoration problems, including denoising and deconvolution. Recently, a number of authors have noted the advantages, including superior performance with certain non-Gaussian noise, of replacing the standard ℓ2 data fidelity term with an ℓ1 norm. We propose a simple but very flexible and computationally efficient method, the Iteratively Reweighted Norm algorithm, for minimizing a generalized TV functional which includes both the ℓ2 -TV and and ℓ1-TV problems.