An Adaptive Directional Haar Framelet-Based Reconstruction Algorithm for Parallel Magnetic Resonance Imaging

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Original languageEnglish
Pages (from-to)794-821
Journal / PublicationSIAM Journal on Imaging Sciences
Issue number2
Online published7 Jun 2016
Publication statusPublished - 2016
Externally publishedYes


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.

Research Area(s)

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