A new sparse representation framework for compressed sensing MRI

Abstract

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 L1-norm regularization is developed to reconstruct piecewise-smooth information of image. For nonsmooth regions, we introduce the curvelet TF-based robust L1,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 L1,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.