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

@article{Li2016AnAD,
title={An Adaptive Directional Haar Framelet-Based Reconstruction Algorithm for Parallel Magnetic Resonance Imaging},
author={Yan-Ran Li and Raymond H. Chan and Lixin Shen and Yung-Chin Hsu and Wen-Yih Isaac Tseng},
journal={SIAM J. Imaging Sci.},
year={2016},
volume={9},
pages={794-821}
}
• Published 7 June 2016
• Mathematics
• SIAM J. Imaging Sci.
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 two-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 $\pm 45^o$ directions. This…

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