Exponential wavelet iterative shrinkage thresholding algorithm with random shift for compressed sensing magnetic resonance imaging

We propose the use of exponent of wavelet transform (EWT) coefficients as a sparse representation which is combined with the iterative shrinkage/threshold algorithm (ISTA) for the reconstruction of compressed sensing magnetic resonance imaging. In addition, random shifting (RS) is employed to guarantee the translation invariance property of discrete wavelet transform. The proposed method is termed the exponential wavelet iterative shrinkage/threshold algorithm with random shifting (EWISTARS), which takes advantages of the sparse representation of EWT, the simplicity of ISTA, and the translation invariance of RS. Simulation results on brain, vertebrae, and knee MR images demonstrate that EWISTARS is superior to existing algorithms with regard to reconstruction quality and computation time.