Denoising of the Speckle Noise by Robust Low-rank Tensor Decomposition

Abstract

Speckle noise is commonly assumed to be multiplicative. Non-local speckle denoising algorithms stack the correlated data patches into a tensor and take the logarithm such that the noise becomes additive. The log-transformed speckle noise is commonly assumed to be white Gaussian noise. The denoising is done through the low-rank approximation techniques applied to the non-local data patches. However, the log-transformed speckle noise can be better approximated as white Gaussian noise with sparse outliers. In this paper, we model the log-transformed speckle noise with this assumption and assess the importance of the noise model under various SNRs. In addition, we propose a weighting scheme for the tensor-based low-rank convex denoising method that utilizes the known ranks. The performance of the proposed algorithm is benchmarked against truncated multilinear singular value decomposition, higher-order orthogonal iteration, and robust tensor decomposition methods that use the sum of the nuclear norm and the tubal nuclear norm. Robust tensor decomposition methods that use the tubal nuclear norm perform better in low SNR scenarios. For high SNR scenarios, the proposed algorithm is found to perform better.