Compressed Sensing-Based Simultaneous Recovery of Magnitude and Phase MR Images via Dual Trigonometric Sparsity

Complex-valued Magnetic Resonance Imaging (MRI) is widely used in clinical diagnosis. The magnitude images are mainly used for structure visualization, and the phase images reveal tissue properties, such as magnetic susceptibility and fluid flow information. While MRI is slow, compressed sensing (CS) can be used to reconstruct the accelerated acquisitions. Current CS-based MRI reconstruction algorithms mostly focus on magnitude image recovery, with less attention to the recovery of phase images. In this paper, we propose a novel CS algorithm to simultaneously recover the magnitude and phase MR images based on the sparsity of the trigonometric function. The CS method requires a sparse representation of the original images, and it is observed the trigonometric functions of phase images in the Wavelet domain promote sparsity. Therefore, rather than transforming the phase images directly into the Wavelet domain, we calculate the sine and cosine of the phase images whose Wavelet transforms are set as the L1-norm regularization term. The combination of the dual trigonometric functions captures a unique, faithful four-quadrant phase information, which also improves the reconstructed magnitude images through an alternating optimization procedure. Reconstructions of simulated images and in vivo images are studied, and both show the superiority of the proposed method over compared phase recovery algorithms.