Performance Analysis of Low-Flux Least-Squares Single-Pixel Imaging

A single-pixel camera is able to computationally form spatially resolved images using one photodetector and a spatial light modulator. The images it produces in low-light-level operation are imperfect, even when the number of measurements exceeds the number of pixels, because its photodetection measurements are corrupted by Poisson noise. Conventional performance analysis for single-pixel imaging generates estimates of mean-square error (MSE) from Monte Carlo simulations, which require long computational times. In this letter, we use random matrix theory to develop a closed-form approximation to the MSE of the widely used least-squares inversion method for Poisson noise-limited single-pixel imaging. We present numerical experiments that validate our approximation and a motivating example showing how our framework can be used to answer practical optical design questions for a single-pixel camera.

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