CORE-PI: Non-iterative convolution-based reconstruction for parallel MRI in the wavelet domain

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 l1-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 l1-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 l1-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 l1-SPIRiT, and (d) robust fast computations.