Construction of efficient and structural chaotic sensing matrix for compressive sensing

An effective sensing matrix can sample sparse or compressible signals without distortion provided that the matrix satisfies the low mutual coherence in the compressive sensing paradigm. In this work, we propose a novel structural chaotic sensing matrix (ScSM), which has the merits of both structured random sensing matrix and chaotic construction. The proposed ScSM first flips original signal, then fast and pseudo-randomly measures the flipped coefficients using a chaotic-based circulant operator, and at last, down-samples the resulting measurements to obtain the final samples. We elaborate the flipping permutation operator, chaotic-based circulant matrix, and down-sampling operator for the ScSM based on Chebyshev chaotic sequence. Moreover, the proposed ScSM is proven to yield low mutual coherence, which guarantees the desirable sampling efficiency. Experimental validations demonstrate the validity of the theory. Because of its well-designed structurally deterministic construction, the proposed ScSM has inherent superiority for storage, fast calculation, and hardware realization.