Magnetic resonance image restoration via dictionary learning under spatially adaptive constraints.

This paper proposes a spatially adaptive constrained dictionary learning (SAC-DL) algorithm for Rician noise removal in magnitude magnetic resonance (MR) images. This algorithm explores both the strength of dictionary learning to preserve image structures and the robustness of local variance estimation to remove signal-dependent Rician noise. The magnitude image is first separated into a number of partly overlapping image patches. The statistics of each patch are collected and analyzed to obtain a local noise variance. To better adapt to Rician noise, a correction factor is formulated with the local signal-to-noise ratio (SNR). Finally, the trained dictionary is used to denoise each image patch under spatially adaptive constraints. The proposed algorithm has been compared to the popular nonlocal means (NLM) filtering and unbiased NLM (UNLM) algorithm on simulated T1-weighted, T2-weighted and PD-weighted MR images. Our results suggest that the SAC-DL algorithm preserves more image structures while effectively removing the noise than NLM and it is also superior to UNLM at low noise levels.