Abstract
In this paper, a 3-dimension directional Haar tight framelet (3DHF) is used to detect the related features between coil images in parallel magnetic resonance imaging (pMRI). Such a Haar tight framelet has an extremely simple geometric structure in the sense that all the high-pass filters in its underlying filter bank have only two nonzero coefficients with opposite signs. A pMRI optimization model, which we coined 3DHF-SPIRiT, by regularizing the 3DHF features on the 3-D coil image data is proposed to reduce the aliasing artifacts caused by the downsampling operation in the k-space (Fourier) domain, which can be solved by alternating direction method of multipliers (ADMM) scheme. Numerical experiments are provided to demonstrate the superiority and efficiency of our 3DHF-SPIRiT model.
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