Signal reconstruction from partial data for sensor array imaging applications

Abstract

In this paper, the problem of signal recovery from partial information with special reference to sensor array imaging situations is examined. In sensor array imaging, as used for viewing underwater objects, the complex wave field is measured at a discrete set of points on a receiver airier. This data is used to reconstruct an image of the object using a suitable transformation. This data can be viewed as partial magnitude and phase data, which after appropriate phase modification, is transformed to obtain the object information. Recently, algorithms have been proposed in the literature for reconstruction of signals from partial information such as magnitude or phase (1-bit phase in some cases) of the Fourier transform. We examine the relevance of these algorithms to sensor array imaging situations. We propose new algorithms that are applicable to these situations. In particular, we show that measurement at multiple frequencies with suitable phase quantization reduces the receiver complexity and sometimes the effects of noise. The proposed new algorithms are demonstrated with several illustrations of simulated field data for a simplified model of an imaging setup.