There has recently been considerable interest in applying Total Variation regularization with an ℓ¹ data fidelity term to the denoising of images subject to salt and pepper noise, but the extension of this formulation to more general problems, such as deconvolution, has received little attention. We consider this problem, comparing the performance of ℓ¹-TV deconvolution, computed via our Iteratively Reweighted Norm algorithm, with an alternative variational approach based on Mumford-Shah regularization. The ℓ¹-TV deconvolution method is found to have a significant advantage in reconstruction quality, with comparable computational cost.