Single-pixel microscopy compressive sampling strategy supported by pupils’ prior information

Abstract

This contribution presents a compressive sampling method for single-pixel microscopy (SPM) which takes into account the properties of the optical system. In SPM, structured patterns are demagnified over the sample plane in order to retrieve an image of the object under study. The quality of the recovered image depends on proper pattern projection. We simulate the pattern projection given by the optical system aperture pupil and compare each sampling pattern and its projection. Those whose contrast and spatial structure are poorly preserved are then discarded. The structural similarity index measure (SSIM) is used as the performance metric to achieve this. This procedure effectively reduces the sampling basis to patterns that can be transferred through the optical system and therefore contribute meaningfully to reconstruction. The proposed method has been tested for infrared-regime SPM. This sampling approach enables efficient, high-fidelity SPM imaging within the practical limits imposed by diffraction resolution at long wavelengths, using typical microscope optics.