An improved reconstruction method for CS-MRI based on exponential wavelet transform and iterative shrinkage/thresholding algorithm

In this paper, we propose a novel sparse transform dubbed exponential wavelet transform (EWT), which provides sparser coefficients than the conventional wavelet transform. We also propose a reconstruction algorithm EWT-ISTA that takes advantages of both EWT and ISTA. Experiments compare the proposed EWT-ISTA with conventional ISTA method that takes wavelet transform as sparsity domain. We employ five different kinds of MR images, i.e. the phantom, the brain, the leg, the arm, and the uterus images. The results demonstrate that: (1) EWT is more efficient than wavelet transform in terms of sparsity representation, and (2) the proposed EWT-ISTA can obtain less MAE & MSE, and higher PSNR than ISTA, with comparable computation time.