An adaptive directional haar framelet-based reconstruction algorithm for parallel magnetic resonance imaging

Yan Ran LI, Raymond H. CHAN, Lixin SHEN, Yung Chin HSU, Wen Yih Isaac TSENG

Research output: Journal PublicationsJournal Article (refereed)peer-review

14 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)794-821
Number of pages28
JournalSIAM Journal on Imaging Sciences
Volume9
Issue number2
DOIs
Publication statusPublished - Jan 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 Society for Industrial and Applied Mathematics.

Keywords

  • Haar wavelet system
  • Parallel MRI
  • Proximity operator
  • Tight frame
  • Total variation

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