Coherence Analysis of Compressive Sensing Based Magnetic Resonance Imaging Reconstruction

Abstract

Fourier encoding is commonly used in modern magnetic resonance imaging (MRI) scanners. However, the partial Fourier matrix is weakly incoherent with the wavelet transform matrix. It implies that the subsampled $k$-space data set may not be a satisfactory option for compressive sensing (CS) based image reconstruction. On the contrary, noiselet matrix has proven to be perfectly incoherent with Haar wavelet matrix, which makes it superior to Fourier matrix for CS applications. Recently, noiselet encoded MRI scan has been studied and resulted in improved image reconstruction performance. In this paper, empirical analysis of Fourier encoding and noiselet encoding is carried out to gain further understanding of their incoherence properties for CS based MRI reconstruction. It is shown that when multiple coils are used, noiselet encoding can provide a better means than Fourier encoding does for CS based MRI reconstruction.