Reconstruction of compressively sampled MR images based on a local shrinkage thresholding algorithm with curvelet transform

To reduce the magnetic resonance imaging (MRI) data acquisition time and improve the MR image reconstruction performance, reconstruction algorithms based on the iterative shrinkage thresholding algorithm (ISTA) are widely used. However, these traditional algorithms use global threshold shrinkage, which is not efficient. In this paper, a novel algorithm based on local threshold shrinkage, which is called the local shrinkage thresholding algorithm (LSTA), was proposed. The LSTA can shrink differently for different elements from the residual matrix to adjust the shrinkage speed for each element of the image during the iterative process. Then, by taking advantage of the sparser characteristics of the curvelet transform, the LSTA combined with the curvelet transform (CLSTA) can make the construction process more efficient. Finally, compared with ISTA, the generalized thresholding iterative algorithm (GTIA) and the fast iterative shrinkage threshold algorithm (FISTA), when analysing human (brain and cervical) MR images, a conclusion can be drawn that the proposed method has better reconstruction performance in terms of the mean square error (MSE), the peak signal to noise ratio (PNSR), the structural similarity index measure (SSIM), the normalized mutual information (NMI), the transferred edge information (TEI) and the number of iterations. The proposed method can better maintain the detailed information of the reconstructed images and effectively decrease the blurring of the images edges.