Abstract

The saddle point framework provides a convenient way to formulate many convex variational problems that occur in computer vi- sion. The framework unifies a broad range of data and regularization terms, and is particularly suited for nonsmooth problems such as To- tal Variation-based approaches to image labeling. However, for many interesting problems the constraint sets involved are difficult to han- dle numerically. State-of-the-art methods rely on using nested iterative pro jections, which induces both theoretical and practical convergence is- sues. We present a dual multiple-constraint Douglas-Rachford splitting approach that is globally convergent, avoids inner iterative loops, en- forces the constraints exactly, and requires only basic operations that can be easily parallelized. The method outperforms existing methods by a factor of 4 ? 20 while considerably increasing the numerical robustness.