Step adaptive fast iterative shrinkage thresholding algorithm for compressively sampled MR imaging reconstruction

In order to accelerate magnetic resonance imaging (MRI) scanning, fast MRI technique based on compressed sensing (CS) was proposed. The shrinkage thresholding algorithm (STA) is an efficient method in related algorithms to decrease the incoherent artifacts produced by the undersampling in k-space directly. The traditional STA uses the fixed iteration step size during the reconstruction progress, and it is not conducive to accelerate the convergence speed. In order to improve global iteration efficiency, in this paper, step adaptive fast iterative shrinkage thresholding algorithm (SAFISTA) was proposed for MRI reconstruction based on STA. It used a feedback to dynamically adjust the iteration step size. The feedback parameter was calculated from the total variations (TV) of two previous iterations. It can effectively improve the efficiency of iteration. Experiments over three kinds of MR images (human head, blood vessels and knee) under different sample ratios indicated that the proposed algorithm SAFISTA showed better reconstruction performance than iterative shrinkage thresholding algorithm (ISTA), fast iterative shrinkage thresholding algorithm (FISTA) and generalized thresholding iterative algorithm (GTIA) in terms of mean square error (MSE), peak signal to noise ratio (PSNR) and structural similarity index measure (SSIM).