Compressive sampling strategies for integrated microspectrometers

We consider compressive sensing in the context of optical spectroscopy. With compressive sensing, the ratio between the number of measurements and the number of estimated values is less than one, without compromising the fidelity in estimation. A compressive sensing system is composed of a measurement subsystem that maps a signal to digital data and an inference algorithm that maps the data to a signal estimate. The inference algorithm exploits both the information captured in the measurement and certain a priori information about the signals of interest, while the measurement subsystem provides complementary, signal-specific information at the lowest sampling rate possible. Codesign of the measurement strategies, the model of a priori information, and the inference algorithm is the central problem of system design. This paper describes measurement constraints specific to optical spectrometers, inference models based on physical or statistical characteristics of the signals, as well as linear and nonlinear reconstruction algorithms. We compare the fidelity of sampling and inference strategies over a family of spectral signals.