Directional tensor product complex tight framelets for compressed sensing MRI reconstruction

Compressed sensing magnetic resonance imaging (CS-MRI) is an effective way of reducing the sampling data in the k-space and shortening the scanning time. Motivated by the high performance of directional tensor product complex tight framelets (TPCTFs) for the image denoising problem, the authors proposed a novel framework that integrated TPCTF for sparse representation and projected fast iterative soft-thresholding algorithm (pFISTA) for CS-MRI reconstruction. Furthermore, to take advantage of the cross-scale relations in the wavelet tree of frame coefficients, the bivariate shrinkage (BS) function with local variance estimation is proposed to shrink thresholding. Such TPCTFs can provide sparse directional representations very well for MR image. When compared with other the state-of-the-art CS-MRI algorithms in numerical experiments, the proposed TPCTF-BS method achieves a higher reconstruction quality with respect to image edge preservation and the artefact suppression.