Adaptive Weighted Minimax-Concave Penalty Based Dictionary Learning for Brain MR Images

We consider adaptive weighted minimax-concave (WMC) penalty as a generalization of the minimax-concave penalty (MCP) and vector MCP (VMCP). We develop a computationally efficient algorithm for sparse recovery considering the WMC penalty. Our algorithm in turn employs the fast iterative soft-thresholding algorithm (FISTA) but with the key difference that the threshold is adapted from one iteration to the next. The new sparse recovery algorithm when used for dictionary learning has a better representation capability as demonstrated by an application to magnetic resonance image denoising. The denoising performance turns out to be superior to the state-of-the-art techniques considering the standard performance metrics namely peak signal-to-noise ratio (PSNR) and structural similarity index metric (SSIM).