Total-variation minimization with bound constraints

2015/05/21 by Musa Maharramov, Maharramov, Musa, Stewart A. Levin +1
Engineering · Computer Science · #Sparse and Compressive Sensing Techniques #Medical Image Segmentation Techniques #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.1505.05694

Abstract

We present a powerful and easy-to-implement algorithm for solving constrained optimization problems that involve L₁/total-variation regularization terms, and both equality and inequality constraints. We discuss the relationship of our method to earlier works of Goldstein and Osher (2009) and Chartrand and Wohlberg (2010), and demonstrate that our approach is a combination of the augmented Lagrangian method with splitting and model projection. We test the method on a geomechanical problem and invert highly compartmentalized pressure change from noisy surface uplift observations. We conclude the paper with a discussion of possible extension to a wide class of regularized optimization problems with bound and equality constraints.

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