Approximate Methods for Constrained Total Variation Minimization

Constrained total variation minimization and related convex optimization problems have applications in many areas of image processing and computer vision such as image reconstruction, enhancement, noise removal, and segmentation. We propose a new method to approximately solve this problem. Numerical experiments show that this method gets close to the globally optimal solution, and is 15-100 times faster for typical images than a state-of-the-art interior point method. Our method’s denoising performance is comparable to that of a stateof-the-art noise removal method of [4]. Our work extends our previously published algorithm for solving the constrained total variation minimization problem for 1D signals [13] which was shown to produce the globally optimal solution exactly in O(N logN) time where N is the number of data points.