CONVERGENCE OF AN ITERATIVE METHOD FOR TOTAL VARIATION DENOISING

In total variation denoising, one attempts to remove noise from a sign al or image by solving a nonlinear minimization problem involving a to tal variation criterion. Several approaches based on this idea have re cently been shown to be very effective, particularly for denoising fun ctions with discontinuities. This paper analyzes the convergence of an iterative method for solving such problems. The iterative method invo lves a ''lagged diffusivity'' approach in which a sequence of linear d iffusion problems are solved. Global convergence in a finite-dimension al setting is established, and local convergence properties, including rates and their dependence on various parameters, are examined.