Computational Spectral Imaging: A Contemporary Overview

Spectral imaging collects and processes information along spatial and spectral coordinates quantified in discrete voxels, which can be treated as a 3D spectral data cube. The spectral images (SIs) allow identifying objects, crops, and materials in the scene through their spectral behavior. Since most spectral optical systems can only employ 1D or maximum 2D sensors, it is challenging to directly acquire the 3D information from available commercial sensors. As an alternative, computational spectral imaging (CSI) has emerged as a sensing tool where the 3D data can be obtained using 2D encoded projections. Then, a computational recovery process must be employed to retrieve the SI. CSI enables the development of snapshot optical systems that reduce acquisition time and provide low computational storage costs compared to conventional scanning systems. Recent advances in deep learning (DL) have allowed the design of data-driven CSI to improve the SI reconstruction or, even more, perform high-level tasks such as classification, unmixing, or anomaly detection directly from 2D encoded projections. This work summarises the advances in CSI, starting with SI and its relevance; continuing with the most relevant compressive spectral optical systems. Then, CSI with DL will be introduced, and the recent advances in combining the physical optical design with computational DL algorithms to solve high-level tasks

Target Detection Performance Bounds in Compressive Imaging

This paper describes computationally efficient approaches and associated theoretical performance guarantees for the detection of known targets and anomalies from few projection measurements of the underlying signals. The proposed approaches accommodate signals of different strengths contaminated by a colored Gaussian background, and perform detection without reconstructing the underlying signals from the observations. The theoretical performance bounds of the target detector highlight fundamental tradeoffs among the number of measurements collected, amount of background signal present, signal-to-noise ratio, and similarity among potential targets coming from a known dictionary. The anomaly detector is designed to control the number of false discoveries. The proposed approach does not depend on a known sparse representation of targets; rather, the theoretical performance bounds exploit the structure of a known dictionary of targets and the distance preservation property of the measurement matrix. Simulation experiments illustrate the practicality and effectiveness of the proposed approaches.Comment: Submitted to the EURASIP Journal on Advances in Signal Processin

Quantum-inspired computational imaging

Computational imaging combines measurement and computational methods with the aim of forming images even when the measurement conditions are weak, few in number, or highly indirect. The recent surge in quantum-inspired imaging sensors, together with a new wave of algorithms allowing on-chip, scalable and robust data processing, has induced an increase of activity with notable results in the domain of low-light flux imaging and sensing. We provide an overview of the major challenges encountered in low-illumination (e.g., ultrafast) imaging and how these problems have recently been addressed for imaging applications in extreme conditions. These methods provide examples of the future imaging solutions to be developed, for which the best results are expected to arise from an efficient codesign of the sensors and data analysis tools.Y.A. acknowledges support from the UK Royal Academy of Engineering under the Research Fellowship Scheme (RF201617/16/31). S.McL. acknowledges financial support from the UK Engineering and Physical Sciences Research Council (grant EP/J015180/1). V.G. acknowledges support from the U.S. Defense Advanced Research Projects Agency (DARPA) InPho program through U.S. Army Research Office award W911NF-10-1-0404, the U.S. DARPA REVEAL program through contract HR0011-16-C-0030, and U.S. National Science Foundation through grants 1161413 and 1422034. A.H. acknowledges support from U.S. Army Research Office award W911NF-15-1-0479, U.S. Department of the Air Force grant FA8650-15-D-1845, and U.S. Department of Energy National Nuclear Security Administration grant DE-NA0002534. D.F. acknowledges financial support from the UK Engineering and Physical Sciences Research Council (grants EP/M006514/1 and EP/M01326X/1). (RF201617/16/31 - UK Royal Academy of Engineering; EP/J015180/1 - UK Engineering and Physical Sciences Research Council; EP/M006514/1 - UK Engineering and Physical Sciences Research Council; EP/M01326X/1 - UK Engineering and Physical Sciences Research Council; W911NF-10-1-0404 - U.S. Defense Advanced Research Projects Agency (DARPA) InPho program through U.S. Army Research Office; HR0011-16-C-0030 - U.S. DARPA REVEAL program; 1161413 - U.S. National Science Foundation; 1422034 - U.S. National Science Foundation; W911NF-15-1-0479 - U.S. Army Research Office; FA8650-15-D-1845 - U.S. Department of the Air Force; DE-NA0002534 - U.S. Department of Energy National Nuclear Security Administration)Accepted manuscrip

Lossy Compressive Sensing Based on Online Dictionary Learning

In this paper, a lossy compression of hyperspectral images is realized by using a novel online dictionary learning method in which three dimensional datasets can be compressed. This online dictionary learning method and blind compressive sensing (BCS) algorithm are combined in a hybrid lossy compression framework for the first time in the literature. According to the experimental results, BCS algorithm has the best compression performance when the compression bit rate is higher than or equal to 0.5 bps. Apart from observing rate-distortion performance, anomaly detection performance is also tested on the reconstructed images to measure the information preservation performance

Compressive Classification

This paper derives fundamental limits associated with compressive classification of Gaussian mixture source models. In particular, we offer an asymptotic characterization of the behavior of the (upper bound to the) misclassification probability associated with the optimal Maximum-A-Posteriori (MAP) classifier that depends on quantities that are dual to the concepts of diversity gain and coding gain in multi-antenna communications. The diversity, which is shown to determine the rate at which the probability of misclassification decays in the low noise regime, is shown to depend on the geometry of the source, the geometry of the measurement system and their interplay. The measurement gain, which represents the counterpart of the coding gain, is also shown to depend on geometrical quantities. It is argued that the diversity order and the measurement gain also offer an optimization criterion to perform dictionary learning for compressive classification applications.Comment: 5 pages, 3 figures, submitted to the 2013 IEEE International Symposium on Information Theory (ISIT 2013