An Iterative Method With Enhanced Laplacian- Scaled Thresholding for Noise-Robust Compressive Sensing Magnetic Resonance Image Reconstruction

Compressive sensing (CS) has proven to be an efficient technique for accelerating magnetic resonance imaging (MRI) acquisition through breaking the Nyquist sampling limit. However, CS measurements are often corrupted by noise in the sensing process, which greatly reduces the quality of reconstructed images and deteriorates the performance of follow-up diagnosis tasks. In this paper, we propose a novel iterative shrinkage-thresholding (IST) method based on enhanced Laplacian-scaled shrinkage operation for robust CS-MRI reconstruction. Differing to existing nonlocal Laplacian-scaled based methods that easily cause biased estimation in the presence of external noise, we design a side information-aided Laplacian-scaled sparse representation model to adapt to spatially varying image structures. Reference information obtained by performing Block-Matching 3D (BM3D) thresholding on the noisy observation is incorporated into the Laplacian-scaled thresholding operator for enhancing the accuracy of sparse coding. Furthermore, we build connections between IST algorithm and approximate message passing (AMP) algorithm and consider an approximation of the divergence of thresholding, leading to an AMP-like iterative method. Experiments validate the effectiveness of leveraging a combination of Laplacian-scaled and BM3D thresholding, and demonstrate the superior robustness of the proposed method both quantitatively and visually as compared with state-of-the-art methods.