CORE‐PI: Non‐iterative convolution‐based reconstruction for parallel MRI in the wavelet domain. Issue 1 (20th November 2018) - Shimron, Efrat; Webb, Andrew G.; Azhari, Haim
Abstract : Purpose: To develop and test a novel parameter‐free non‐iterative wavelet domain method for reconstruction of undersampled multicoil MR data. Theory and Methods: A linear parallel MRI method that operates in the Stationary Wavelet Transform (SWT) domain is proposed. The method is coined COnvolution‐based REconstruction for Parallel MRI (CORE‐PI). This method computes the SWT of the unknown MR image directly from subsampled k‐space measurements, without modifying the RF excitation pulse. It then reconstructs the image using the wavelet filter bank approach, with simple linear computations. The CORE‐PI implementation is demonstrated by experiments with a numeric brain phantom and in vivo brain scans data, with various wavelet types and high reduction factors. It is compared to the well‐known parallel MRI methods GRAPPA and l 1‐SPIRiT. Results: The experimental results show that CORE‐PI is suitable for different 1D Cartesian k‐space undersampling schemes, including regular and irregular ones, and for wavelets of different families. CORE‐PI accurately reconstructs the SWT coefficients of the unknown MR image; this wavelet‐domain decomposition is fully computed despite the k‐space undersampling. Furthermore, CORE‐PI provides high‐quality final reconstructions, with an average NRMSE of 0.013, which is significantly lower than that obtained by GRAPPA and l 1‐SPIRiT. Moreover, CORE‐PI offers significantly faster computation times: the typical CORE‐PI runtime is about 60 seconds, which is about 20% shorter than that of l 1‐SPIRiT and 55%–75% shorter than that of GRAPPA. Conclusion: COnvolution‐based REconstruction for Parallel MRI advantageously offers: (a) flexible 1D undersampling of a Cartesian k‐space, (b) a parameter‐free non‐iterative implementation, (c) reconstruction performance comparable or better than that of GRAPPA and l 1‐SPIRiT, and (d) robust fast computations.