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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.