A new sparse representation framework for compressed sensing MRI

Compressed sensing based Magnetic Resonance imaging (MRI) via sparse representation (or transform) has recently attracted broad interest. The tight frame (TF)-based sparse representation is a promising approach in compressed sensing MRI. However, the conventional TF-based sparse representation is difficult to utilize the sparsity of the whole image. Since the whole image usually has different structure textures and a kind of tight frame can only represent a particular kind of ground object, how to reconstruct high-quality of magnetic resonance (MR) image is a challenge. In this work, we propose a new sparse representation framework, which fuses the double tight frame (DTF) into the mixed norm regularization for MR image reconstruction from undersampled k-space data. In this framework, MR image is decomposed into smooth and nonsmooth regions. For the smooth regions, the wavelet TF-based weighted L-1-norm regularization is developed to reconstruct piecewise-smooth information of image. For nonsmooth regions, we introduce the curvelet TF-based robust L-1,L-a-norm regularization with the parameter to preserve the edge structural details and texture. To estimate the reasonable parameter, an adaptive parameter selection scheme is designed in robust L-1,L-a-norm regularization. Experimental results demonstrate that the proposed method can achieve the best image reconstruction results when compared with other existing methods in terms of quantitative metrics and visual effect. (C) 2019 Elsevier B.V. All rights reserved.