Abstract : Quantization, deﬁned as the act of attributing a ﬁnite number of grey-levels to an image, is an essential task in image acquisition and coding. It is also intricately linked to various image analysis tasks, such as denoising and segmentation. In this paper, we investigate quantization combined with regularity constraints, a little-studied area which is of interest, in particular, when quantizing in the presence of noise or other acquisition artifacts. We present an optimization approach to the problem involving a novel two-step, iterative, ﬂexible, joint quantizing-regularization method featuring both convex and combinatorial optimization techniques. We show that when using a small number of grey-levels, our approach can yield better quality images in terms of SNR, with lower entropy, than conventional optimal quantization methods.