Compressed sensing using FREBAS transform in magnetic resonance phase scrambling Fourier transform technique

The application of compressed sensing (CS) to MRI has the potential for significant scan time reductions. The signal obtained in the phase-scrambling Fourier transform (PSFT) imaging technique shows better performances compared to standard Fourier transform base imaging when it is applied to CS. Sparsity of signal is an essential condition for compressed sensing. In this work, we adopt a FREBAS transform as a sparsifying transform function instead of wavelet transform to improve the quality of images in PSFT based CS. It was shown that the directionality of FREBAS transform and the usage of successive thresholding in FREBAS domain offers fairly good images, particularly at low sampling rates. In addition, proposed method is robust to the choice of sampling trajectory of NMR signal.