On poisson compressed sensing and parameter estimation in sheet-of-light surface scanning

Abstract

Compressed Sensing (CS) has been successfully applied in a number of imaging systems since it can fundamentally increase frame rates and/or the resolution. In this paper, we apply CS to 3-D surface acquisition using Sheet-of-Light (SOL) scanning. The application of CS could potentially increase the speed of the measurement and/or enhance scan resolution with fewer measurements. To analyze the potential performance of a CS-SOL system, we formulate the estimation of the height profile of a target object as a compressive parameter estimation problem and investigate the achievable estimation accuracy in the presence of noise. In the context of compressed sensing, measurement models with AWGN are typically analyzed. However, in imaging applications there are multiple noise sources giving rise to different statistical noise models in which Poisson noise can be the dominating noise source. This is particularly true for photon-counting detectors that are used in low light settings. Therefore, in this paper we focus on the compressive parameter estimation problem in presence of Poisson distributed photon noise. The achievable estimation accuracy in obtaining height profiles from compressed observations is systematically analyzed with the help of the Cramer-Rao Lower Bound (CRLB). This analysis allows us to compare different CS measurement strategies and quantify the parameter estimation accuracy as a function of system parameters such as the compression ratio, exposure time, image size, etc.