Direct Under-Sampling Compressive Sensing Method for Underwater Echo Signals and Physical Implementation

Abstract

Compressive sensing can guarantee the recovery accuracy of suitably constrained signals by using sampling rates much lower than the Nyquist limit. This is a leap from signal sampling to information sampling. The measurement matrix is key to implementation but limited in the acquisition systems. This article presents the critical elements of the direct under-sampling—compressive sensing (DUS–CS) method, constructing the under-sampling measurement matrix, combined with a priori information sparse representation and reconstruction, and we show how it can be physically implemented using dedicated hardware. To go beyond the Nyquist constraints, we show how to design and adjust the sampling time of the A/D circuit and how to achieve low-speed random non-uniform direct under-sampling. We applied our method to data measured with different compression ratios (volume ratios of collected data to original data). It is shown that DUS-CS works well when the SNR is 3 dB, 0 dB, −3 dB, and −5 dB and the compression ratio is 50%, 20%, and 10%, and this is validated with both simulation and actual measurements. The method we propose provides an effective way for compressed sensing theory to move toward practical field applications that use underwater echo signals.

Compressive Sensing Based Active Imaging System Using Programable Coded Mask and a Photodiode

“…CS is an emerging data acquisition technique that enables the acquisition of signals at sampling rates below the Nyquist criterion [45], [46], [47]. CS substitutes traditional sampling with measurements of the inner products of the signal and mathematical vectors [48].…”

Analysis of Compressed Sensing for Efficient Signal Acquisition and Reconstruction

“…Sensing matrix ΦΨ must adhere to the constrained isometric property in order to create x from y. Significant improvements have been made in CS theory and applications [7,8]. Sensing and reconstruction are the two main essential parts of computational science.…”

“…As an illustration, consider the Chebyshev chaotic system [15]: The following equations serve as a representation of the Chebyshev chaotic system: x(n + 1) = a − b * x(n) 2 + y(n)…………………………. (7) y(n + 1) = x(n) …………………………….. (8) In this system, a and b are system parameters, and x(n) and y(n) are the state variables at time step n. These equations can be repeated starting with the initial conditions to create a pseudorandom sequence. When compared to employing a wholly random matrix, this sequence can subsequently be utilized as a measurement matrix in CCS.…”

Overview of Compressed Sensing: Sensing Model, Reconstruction Algorithm, and Its Applications

“…y = Θ s, (5) which is a convex-optimization problem. A large amount of work has been done on CS theory and applications [7,8]. Based on the CS introduction above, CS is principally composed of two important parts, sensing and reconstruction.…”