Frame-based compressive sensing MR image reconstruction with balanced regularization

Shoulie Xie, Cuntai Guan, Weimin Huang, Zhongkang Lu

Abstract: This paper addresses the frame-based MR image reconstruction from undersampled k-space measurements by using a balanced ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -regularized approach. Analysis-based and synthesis-based approaches are two common methods in ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -regularized image restoration. They are equivalent under the orthogonal transform, but there exists a gap between them under redundant transform such as frame. Thus the third approach was developed to reduce the gap by penalizing the distance between the representation vector and the canonical frame coefficient of the estimated image, this balanced approach bridges the synthesis-based and analysis-based approaches and balances the fidelity, sparsity and smoothness of the solution. These frame-based approaches have been studied and compared for optical image restoration over the last few years. In this paper, we further study and compare these three approaches for the compressed sensing MR image reconstruction under redundant frame domain. These ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -regularized optimization problems are solved by using a variable splitting strategy and the classical alternating direction method of multiplier (ADMM). Numerical simulation results show that the balanced approach can reduce the gap between the analysis-based and synthesis-based approaches and are even better than these two approaches under our experimental conditions.