Non-monotonic dependence of compressive sensing in ghost imaging with an LC-SLM under noisy conditions

Ghost imaging, which relies on single-pixel detection, offers advantages in spectral flexibility and sensitivity compared to conventional imaging systems. However, its performance is inherently limited by noise and the characteristic square-root dependence of image quality on the number of measurements. This study investigates how compressive sensing methods-specifically L₁ and L₂ norm minimization-alter this dependence under noisy conditions, transforming it into a non-monotonic relationship. We analyze four illumination patterns (non-shifted random binary, subpixel-shifted, displacement, and color-noise patterns) in numerical simulation and an experimental setup, comparing their reconstruction via compressive sensing and second-order correlation methods. Our results provide practical guidelines for pattern and algorithm selection. These insights establish a framework for optimizing ghost imaging systems in noisy environments, including speckle noise from liquid crystal spatial light modulators, dynamic scattering, and source instabilities. The observed non-monotonic quality dependence underscores the need for careful measurement-number optimization in ghost imaging systems with compressive sensing.