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An adaptive directional Haar framelet-based reconstruction algorithm for parallel magnetic resonance imaging. (English) Zbl 1366.94057

Summary: 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 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.

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
65K10 Numerical optimization and variational techniques
65T60 Numerical methods for wavelets
68U10 Computing methodologies for image processing

Software:

DLMRI-Lab
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Full Text: DOI

References:

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