Wavelet-Based Compressive Sensing for Point Scatterers

Abstract

Compressive Sensing (CS) allows for the sam- pling of signals at well below the Nyquist rate but does so, usually, at the cost of the suppression of lower amplitude sig- nal components. Recent work suggests that important infor- mation essential for recognizing targets in the radar context is contained in the side-lobes as well, which are often sup- pressed by CS. In this paper we extend existing techniques and introduce new techniques both for improving the accu- racy of CS reconstructions and for improving the separa- bility of scenes reconstructed using CS. We investigate the Discrete Wavelet Transform (DWT), and show how the use of the DWT as a representation basis may improve the ac- curacy of reconstruction generally. Moreover, we introduce the concept of using multiple wavelet-based reconstructions of a scene, given only a single physical observation, to derive reconstructions that surpass even the best wavelet-based CS reconstructions. Lastly, we specifically consider the effect of the wavelet-based reconstruction on classification. This is done indirectly by comparing outputs of different algo- rithms using a variety of separability measures. We show that various wavelet-based CS reconstructions are substan- tially better than conventional CS approaches at inducing (or preserving) separability, and hence may be more useful in classification applications.