Image smoothing using spatial iterative methods based on accelerated iterative shrinkage

In recent years, much research interest has developed in image smoothing techniques. With increasing application in various fields, there is a motivation to explore various modes of algorithm implementation of image smoothing. Recently, edge-aware image smoothing techniques have been developed based on fast Fourier transformation methods. In this paper, we present an alternative implementation for an existing image smoothing algorithm using spatial iterative methods. The motivation of this is to create a performance baseline using spatial iterative methods such as multigrid (MG), conjugate gradient (CG), and preconditioned conjugate gradient (PCG) methods, for the purpose that the algorithm can be easily adapted to parallel computing systems. We also determine the competitiveness compared with FFT implementation in terms of computational cost. From experimental results, multigrid preconditioned conjugate gradient (MGCG) method provides superior results both in smoothing quality and computational cost compared to all the spatial iterative methods considered. Furthermore, with relaxed tolerance, it demonstrates lower computational complexity compared with FFT implementation, with similar smoothing results but having minor quality compromise. Hence, MGCG provides a relatively competitive spatial domain alternative to frequency domain solver, FFT. In applications which do not require computation of an exact solution, spatial iterative methods can provide a reasonable computation alternative to FFT implementation as their convergence conditions can easily be altered by the user to fit a specific application, as well as possessing the ease for parallel computing adaptation.