Li, Y.-R.Y.-R.LiChan, R.H.R.H.ChanLI-JIUAN SHENHsu, Yung-ChinYung-ChinHsuWEN-YIH TSENG2019-10-032019-10-0320161936-4954https://scholars.lib.ntu.edu.tw/handle/123456789/425873© 2016 Society for Industrial and Applied Mathematics. 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 twodimensional 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 ±45° 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.enHaar wavelet system | Parallel MRI | Proximity operator | Tight frame | Total variationjournal article10.1137/15M1033964http://www.scopus.com/inward/record.url?eid=2-s2.0-84976632944&partnerID=MN8TOARS276281982-s2.0-84976632944http://www.scopus.com/inward/record.url?eid=2-s2.0-84976632944&partnerID=MN8TOARS27628198