Integrated variable projection approach (IVAPA) for parallel magnetic resonance imaging

Parallel magnetic resonance imaging (pMRI) is a fast method which requires algorithms for the reconstructing image from a small number of measured k-space lines. The accurate estimation of the coil sensitivity functions is still a challenging problem in parallel imaging. The joint estimation of the coil sensitivity functions and the desired image has recently been proposed to improve the situation by iteratively optimizing both the coil sensitivity functions and the image reconstruction. It regards both the coil sensitivities and the desired images as unknowns to be solved for jointly. In this paper, we propose an integrated variable projection approach (IVAPA) for pMRI, which integrates two individual processing steps (coil sensitivity estimation and image reconstruction) into a single processing step to improve the accuracy of the coil sensitivity estimation using the variable projection approach. The method is demonstrated to be able to give an optimal solution with considerably reduced artifacts for high reduction factors and a low number of auto-calibration signal (ACS) lines, and our implementation has a fast convergence rate. The performance of the proposed method is evaluated using a set of in vivo experiment data.