A GPU-Accelerated Augmented Lagrangian Based L1-mean Curvature Image Denoising Algorithm Implementation

Abstract

This paper presents a graphics processing unit (GPU) implementation of a recently published augmented Lagrangian based L1-mean curvature image denoising algorithm. The algorithm uses a particular alternating direction method of multipliers to reduce the related saddle-point problem to an iterative sequence of four simpler minimization problems. Two of these subproblems do not contain the derivatives of the unknown variables and can therefore be solved point-wise without inter-process communication. Inparticular, this facilitates the efficient solution of the subproblem that deals with the non-convex term in the original objective function by modern GPUs. The two remaining subproblems are solved using the conjugate gradient method and a partial solution variant of the cyclic reduction method, both of which can be implemented relatively efficiently on GPUs. The numerical results indicate up to 33-fold speedups when compared against a single-threaded CPU implementation. The pointwise treated subproblem that takes care of the non-convex term in the original objective function was solved up to 76 times faster.