Dynamic MRI Exploiting Partial Separability and Shift Invariant Discrete Wavelet Transform

This paper proposed a CS (compressed sensing) based dynamic magnetic resonance imaging (d-MRI) method, which exploits partial separability (PS) and the redundant wavelet tight frame-SIDWT (shift invariant discrete wavelet transform). Since the time domain smoothness corresponds to the frequency domain sparsity, sparsity in Fourier domain along the time dimension is widely used in d-MRI method. In redundant wavelet tight frame, SIDWT can enhance the smoothness of images in one or two dimensions, that is an image in SIDWT domain is of lower rank. We show that the Fourier coefficients along the time dimension of d-MR image in SIDWT domain are sparser than the SIDWT coefficients of d-MR image, then introduce SIDWT to enforce the sparse L1 constraint in the classical PS-L1 d-MRI method. Lastly, the proposed d-MRI model exploiting PS and SIDWT is solved by the efficient alternating direction method of multipliers (ADMM) algorithm. Experimental results verify the superior performance of the proposed method.