Spread spectrum in chaotic compressed sensing with application to MRI

Abstract

This paper concerns the deterministic and structured designs of the measurement matrix in compressed sensing (CS). The deterministic design is approached using chaotic sequences while the structured one is with a spread-spectrum technique using chirp modulation. We propose to combine these two approaches to take advantage of the simple hardware implementation of chaotic sequences, and of reduced the mutual coherence by a chirp modulation, which spreads the data in the acquired domain. The method is illustrated by the well-known application of CS for fast acquisition in magnetic resonance imaging (MRI). Results and performance comparison are provided by numerical simulation, showing that the proposed method outperforms state-of-the-art CS techniques for MRI acquisition in terms of image reconstruction quality.