Compressed Sensing for Thoracic MRI with Partial Random Circulant Matrices

Abstract

The use of circulant matrix as the sensing matrix in compressed sensing (CS) scheme has recently been proposed to overcome the limitation of random or partial Fourier matrices. Aside from reducing computational complexity, the use of circulant matrix for magnetic resonance (MR) image offers the feasibility in hardware implementations. This paper presents the simulation of compressed sensing for thoracic MR imaging with circulant matrix as the sensing matrix. The comparisons of reconstruction of three different type MR images using circulant matrix are investigated in term of number of samples, number of iteration and signal to noise ratio (SNR). The simulation results showed that circulant matrix works efficiently for encoding the MR image of respiratory organ, especially for smooth and sparse image in spatial domain.