The Chaotic Measurement Matrix for Compressed Sensing

Abstract

Abstract. How to construct a measurement matrix with good performance and easy hardware implementation is the core research problem in compressed sensing. In this paper, we present a simple and efficient measurement matrix named Incoherence Rotated Chaotic (IRC) matrix. We take advantage of the well pseudorandom of chaotic sequence, introduce the concept of the incoherence factor and rotation, and adopt QR decomposition to obtain the IRC measurement matrix which is suited for sparse reconstruction. Simulation results demonstrate IRC matrix has a better performance than Gaussian random matrix, Bernoulli random matrix and other state-of-the-art measurement matrices. Thus it can efficiently work on both natural image and remote sensing image.

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“…, where M is much smaller than N. Thus, significant difficulties in CS is to develop a useful measurement matrix in which the compression must preserve the information in the sparse signal and easy hardware implementation. To guarantee that, the measurement matrix is required to satisfy certain desirable properties that can ensure a certain recovery quality [30].…”

“…However, the huge memory requirement for storing the entries of random sensing matrix, its high computational complexity because of unstructured nature, and high processing time makes its hardware implementation expensive. So as to solve the problem of random measurement matrix, deterministically designing a good measurement matrix was proposed by authors of [29,30].…”

“…A chaotic system is generated by chaotic maps, which is used in the measurement matrix to achieve both determinacy and randomness properties. In this paper, the logistic chaotic sequence generated by the logistic map is used because of its exceptional characteristics such as sensitive dependence on the initial condition, non-periodicity, and pseudo-random property that introduce the idea of the incoherence factor in measurement matrix [29,30,34]:…”