Reducing ringing artefact in fresnel digital holography using compressed sensing

Compressed sensing is a signal processing technique used for signal reconstruction with significantly smaller number of samples than the requirements of the Nyquist-Shannon theorem. In this work, we simulate a lensless digital holographic system. We investigate the ringing-like artefact introduced by truncation by the camera aperture. We present the results of using the orthogonal matching pursuit based compressed sensing algorithms to combat this ringing-like artefact. We demonstrate that compressed sensing achieves remarkable reconstructions and suppresses ringing well, but only up to a point in terms of the size of the aperture. This research could help the advancement of compressive digital holography.