Knowledge Enhanced Compressive Measurement Design: Detection and Estimation Tasks

Abstract

Compressive imaging exploits the inherent sparsity/compressibility of natural scenes to reduce the number of measurements required for reliable reconstruction/recovery. In many applications, however, additional scene prior information beyond sparsity (such as natural scene statistics) and task prior information may also be available. While current efforts on compressive measurement design attempt to exploit such scene and task priors in a heuristic/ad-hoc manner, in this dissertation, we develop a principled information-theoretic approach to this design problem that is able to fully exploit a probabilistic description (i.e. scene prior) of relevant scenes for a given task, along with the appropriate physical design constraints (e.g. photon count/exposure time) towards maximizing the system performance. We apply this information-theoretic framework to optimize compressive measurement designs, in EO/IR and X-ray spectral bands, for various detection/classification and estimation tasks. More specifically, we consider image reconstruction and target detection/classification tasks, and for each task we develop an information-optimal design framework for both static and adaptive measurements within parallel and sequential measurement architectures. For the image reconstruction task we show that the information-optimal static compressive measurement design is able to achieve significantly better compression ratios (and also reduced detector count, readout power/bandwidth) relative to various state-of-the-art compressive designs in the literature. Moreover, within a sequential measurement architecture our information-optimal adaptive design is able to successfully learn scene information online, i.e. from past measurement, and adapt next measurement (in a greedy sense) towards improving the measurement information efficiency, thereby providing additional performance gains beyond the corresponding static measurement design. We also develop a non-greedy adaptive measurement design framework for a face recognition task that is able to surpass the greedy adaptive design performance, by (strategically) maximizing the the long-term cumulative system performance over all measurements. Such a non-greedy adaptive design is also able to predict the optimal number of measurements for a fixed system measurement resource (e.g. photon-count). Finally, we develop a scalable (computationally) information-theoretic design framework to an X-ray threat detection task and demonstrate that information-optimized measurements can achieve a 99% threat detection threshold using 4x fewer exposures compared to a conventional system. Equivalently, the false alarm rate of the optimized measurements is reduced by nearly an order of magnitude relative to the conventional measurement design.