Compressive digital holography and Gibbs ringing

Abstract

Gibbs ringing is an artefact that occurs when a discontinuous signal is reconstructed from its Fourier coefficients. The apertures in a digital holographic system can be modelled as truncation in the Fourier domain, meaning they limit the image resolution. The process of apodization introduces Gibbs ringing to holograms of objects with discontinuities. Compressive digital holography attempts to improve image resolution using compressive sensing techniques. Hence, our hypothesis is that Gibbs ringing is reduced by compressive sensing. In this work, we simulate a compressive digital holographic system and investigate how it is affected by Gibbs ringing. We vary the size of the aperture and examine the effects of ringing. This work may aid the further development of compressive digital holography.

Reducing ringing artefact in fresnel digital holography using compressed sensing

“…A more detailed explanation of compressed sensing theory could be found in. 10,21 Our simulation in this paper is a 2D simulation of the system depicted in Fig. 1.…”

“…In another recent work, we simulated a Fourier digital holographic setup. 10 We applied a CS algorithm to suppress the ringing, and demonstrated that it is highly effective if we are not increasing the resolution by too much.…”