A sequential solution for anisotropic total variation image denoising with interval constraints. (1st September 2017)

• Record Type: Journal Article
• Authors: Xu, Jingyan; Noo, Frédéric
• Is Part Of: Physics in medicine & biology. Volume 62:Number 18(2017:Sep.)
• Page Start: N428
• Page End: N435
• Publication Date: 2017-09-01
• Subjects: denoising -- total variation -- fused lasso -- interval constraints -- constrained optimization; Biophysics -- Periodicals; Medical physics -- Periodicals; 610.153
• DOI: 10.1088/1361-6560/aa837d
• Languages: English
• ISSNs: 0031-9155

Abstract

Abstract: We show that two problems involving the anisotropic total variation (TV) and interval constraints on the unknown variables admit, under some conditions, a simple sequential solution. Problem 1 is a constrained TV penalized image denoising problem; problem 2 is a constrained fused lasso signal approximator. The sequential solution entails finding first the solution to the unconstrained problem, and then applying a thresholding to satisfy the constraints. If the interval constraints are uniform, this sequential solution solves problem 1. If the interval constraints furthermore contain zero, the sequential solution solves problem 2. Here uniform interval constraints refer to all unknowns being constrained to the same interval. A typical example of application is image denoising in x-ray CT, where the image intensities are non-negative as they physically represent linear attenuation coefficient in the patient body. Our results are simple yet seem unknown; we establish them using the Karush–Kuhn–Tucker conditions for constrained convex optimization.