Yan-Ran Li, Raymond H. Chan, Lixin Shen, Yung-Chin Hsu, Wen-Yih Isaac Tseng
Abstract: Parallel magnetic resonance imaging (pMRI) is a technique to accelerate the magnetic resonance
imaging process. The problem of reconstructing an image from the collected pMRI data is ill-posed.
Regularization is needed to make the problem well-posed. In this paper, we first construct a 2-dimensional
tight framelet system whose filters have the same support as the orthogonal Haar filters and are able to
detect edges of an image in the horizontal, vertical, and ±45o directions. This system is referred to as
directional Haar framelet (DHF). We then propose a pMRI reconstruction model whose regularization
term is formed by the DHF. This model is solved by a fast proximal algorithm with low computational
complexity. The regularization parameters are updated adaptively and determined automatically during
the iteration of the algorithm. Numerical experiments for in-silico and in-vivo data sets are provided to
demonstrate the superiority of the DHF-based model and the efficiency of our proposed algorithm for
pMRI reconstruction.
Preprint