An adaptive directional haar framelet-based reconstruction algorithm for parallel magnetic resonance imaging
Journal
SIAM Journal on Imaging Sciences
Journal Volume
9
Journal Issue
2
Date Issued
2016
Author(s)
Abstract
© 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.
Subjects
Haar wavelet system | Parallel MRI | Proximity operator | Tight frame | Total variation
Type
journal article