Phase-Pole-Free Images and Smooth Coil Sensitivity Maps by Regularized Nonlinear Inversion

Phase singularities are a common problem in image reconstruction with auto-calibrated sensitivities due to an inherent ambiguity of the estimation problem. The purpose of this work is to develop a method for detecting and correcting phase poles in non-linear inverse (NLINV) reconstruction of MR images and coil sensitivity maps.

Phase poles are detected in individual coil sensitivity maps by computing the curl in each pixel. A weighted average of the curl in each coil is computed to detect phase poles. Phase pole detection and correction is then integrated into the iteratively regularized Gauss-Newton method of the NLINV algorithm. In addition, we demonstrate the algorithm can also remove phase poles in ESPIRiT coil sensitivity maps. Phase pole correction is evaluated for reconstruction of accelerated Cartesian MPRAGE data of the brain and interactive radial real-time MRI of the human heart.

For both applications, phase pole correction can be used for estimation of coil sensitivity profiles free from singularities. For NLINV, we demonstrate reliable and efficient estimation even from very small ( $7\times 7$ ) auto-calibration (AC) regions.

With the proposed method, phase poles can be reliably removed in reconstructions and coil sensitivities.