Chaotic Compressed Sensing and Its Application to Magnetic Resonance Imaging

Abstract

Fast image acquisition in magnetic resonance imaging (MRI) is important, due to the need to find ways that help relieve patient’s stress during MRI scans. Methods for fast MRI have been proposed, most notably among them are pMRI (parallel MRI), SWIFT (SWeep Imaging with Fourier Transformation), and compressed sensing (CS) based MRI. Although it promises to significantly reduce acquisition time, applying CS to MRI leads to difficulties with hardware design because of the randomness nature of the measurement matrix used by the conventional CS methods. In this paper, we propose a novel method that combines the above-mentioned three approaches for fast MRI by designing a compound measurement matrix from a series of single measurement matrices corresponding to pMRI, SWIFT, and CS. In our method, the CS measurement matrix is designed to be deterministic via chaotic systems. This chaotic compressed sensing (CCS) measurement matrix, while retaining most features of the random CS matrix, is simpler to realize in hardware. Several compound measurement matrices have been constructed and examined in this work, including CCS-MRI, CCS-pMRI, CCS-SWIFT, and CCS-pSWIFT. Simulation results showed that the proposed method allows an increase in the speed of the MRI acquisition process while not compromising the quality of the acquired MR images.

Design and Implementation of a Digital Dual Orthogonal Outputs Chaotic Oscillator

“…Various modulation schemes, like the chaos shift keying, use a chaotic carrier in order to secure the transmission and to reinforce its confidentiality [13,14]. Chaotic sequences are also used in compressive sensing to build a measurement matrix that satisfies the restricted isometry property [15][16][17]. In the literature [18], the authors show that a chaotic generator can be used to create a reliable and efficient wireless communication system.…”