Euler’s elastica-based algorithm for Parallel MRI reconstruction using SENSitivity Encoding

SENSitivity Encoding (SENSE) is an effective mathematical formulation for reconstructing under-sampled MRI data obtained in Parallel Magnetic Resonance Imaging (Parallel MRI). The functional model includes a regularization term and a data fidelity term which need to be minimized to obtain a high quality MRI result. The proper choice of regularization is essential for image quality. In this paper, we show that Euler’s elastica is an effective regularization for Parallel MRI data reconstruction, and has advantages over the Total Variation (TV) regularization in improving image signal to noise ratio and image relative error. The Euler’s elastica functional is however complex to minimize as it is non-convex, non-smooth, and highly nonlinear. In this paper, we propose a new numerical method to solve Euler’s elastica regularized SENSE efficiently. This algorithm is based on a variable splitting approach and proper relaxation of the functional. Numerical examples are presented to show the effectiveness of the proposed Euler’s elastica algorithm in comparison to Bregman Operator Splitting with Variable Stepsize, a TV based algorithm.