Variational Regularized Tree-Structured Wavelet Sparsity for CS-SENSE Parallel Imaging

Abstract

Both compressed sensing magnetic resonance imaging (MRI) and parallel MRI have emerged as effective techniques to accelerate MRI data acquisition in various clinical applications. The hybrid parallel imaging reconstruction methods by combining these two techniques have been developed for providing further acceleration. However, the widely used $L_{1}$ -norm of wavelet coefficients and total variation (TV) regularizer in traditional hybrid imaging methods limited further improvement in image quality. To further enhance imaging quality and reduce acquisition time, we proposed a regularized parallel imaging reconstruction method by incorporating sparsity-promoting wavelet prior and total generalized variation (TGV) regularizer. Specifically, the wavelet sparsity is effectively promoted through the $L_{0}$ quasi-norm of wavelet coefficients and tree-structured wavelet representation. This sparsity-promoting wavelet prior is capable of representing a better measure of sparseness to guarantee high-quality reconstruction even for high degrees of undersampling. Unlike TV regularizer, which preserves sharp edges but suffers from staircaselike artifacts, TGV regularizer can balance the tradeoff between edges preservation and artifacts suppression. Numerous experiments have been conducted on both simulated and in vivo MRI data sets to compare our proposed method with some state-of-the-art reconstruction methods. Experimental results have demonstrated its superior imaging performance in terms of both quantitative evaluation and visual quality.