Chaotic Analog-to-information Conversion: Sparse Signal Reconstruction with Multiple Shooting Method

Chaotic Compressive Sensing (CS) is a nonlinear compressive sensing theory which utilizes the randomness-like characteristic of chaos systems to measure sparse signals. This paper focuses on the chaotic compressive sensing for the acquisition and reconstruction of analog signals, i.e., Chaotic Analog-to-Information (ChaA2I) converter. ChaA2I generates the low-rate samples by sampling the output of chaotic system excited by the sparse signals, and implements the signal reconstruction by solving the sparsity-regularized nonlinear least squares problem. With the view on chaotic parameter estimation, a highly-efficient reconstruction algorithm (MS-IRNLS) is developed by combing the Multiple Shooting (MS) method with the Iteratively Reweighted Nonlinear Least-Squares (IRNLS) algorithm. With the Lorenz system as an example, the paper conducts extensive simulations for the reconstruction performance of MS-IRNLS algorithm. The simulations demonstrate the effectiveness of the proposed ChaA2I.