A sparse and prior based method for 3D image denoising

Denoising algorithms via sparse representation are among the state-of-the art for 2D image restoration. In this work, we propose a novel sparse and prior-based algorithm for 3D image denoising (SPADE). SPADE is a modification of total variation (TV) problem with an additional functional that promotes sparsity with respect to a prior image. The prior is obtained from the noisy image by combining information from neighbor slices. The functional is minimized using the split Bregman method, which leads to an efficient method for large scale 3D denoising, with computational cost given by three FFT per iteration. SPADE is compared to TV and dictionary learning on the Shepp-Logan phantom and on human knee data acquired on a spectral computerized tomography scanner. SPADE converges in approximately ten iterations and provides comparable or better results than the other methods. In addition, the exploitation of the prior image avoids the patchy, cartoon-like images provided by TV and provides a more natural texture.