Compressed Sensing of Phase Varied Images Using Multi-scale eFREBAS Transform

Abstract

The use of compressive sensing (CS) in applications with rapid spatial phase variations is difficult, since not only the magnitude but also phase regularization is required in the CS framework. In this article we propose a novel image reconstruction scheme for MR phase varied images in which phase regularizer is not required in the rather simple CS reconstruction scheme. In our work, to improve the incoherence between the sampling matrix and the basis of the sparsifying transform, successive thresholding in eFREBAS transform domain using the higher feasibility in the choice of eFREBAS scaling parameter, i.e. multi-scale eFREBAS transform domain thresholding were used. Proposed method has an advantage over phase and magnitude regularization method in that the reconstruction time is almost the same as that for real-valued images and there is no need for estimating the phase variation in the iterative algorithm. Reconstruction experiments showed that proposed method using 8-scale eFREBAS transform can restore the magnitude and phase of images much better than the conventional method, especially at the region where phase changes rapidly.