This paper presents a novel comparative study between two prominent compressed sensing algorithms – Orthogonal Matching Pursuit (OMP) and Iterative Hard Thresholding (IHT) – within the context of digital holography, specifically focusing on their efficacy in handling phase discontinuities. Previous research has predominantly centered on Gibbs ringing artifacts in image reconstruction and their mitigation. However, the aspect of phase discontinuities, which are critical in holographic imaging, has not been extensively explored. Our study implement both OMP and IHT algorithms in a simulated digital holographic environment, where phase discontinuities are inherent due to the nature of holographic imaging. We analyze how these algorithms perform in the presence of phase discontinuities. We quantitatively analyze the performance of each algorithm in handling phase discontinuities. Additionally, our study delves into the computational efficiency of both algorithms, considering their practical applicability in real-time holographic imaging systems. The results of our comparative analysis provide insights into the advantages and limitations of OMP and IHT in the context of phase discontinuities. Our findings have significant implications for advancing digital holography, particularly in applications requiring precise phase information, such as medical imaging, microscopy, and non-destructive testing.
Hard apertures in imaging systems create artifacts at discontinuous points in an image. When we zoom in on such an image, Gibbs ringing can be a factor in the confusion of small features with artifacts, or in errors in measurements made of the features. In previous works, we have systemically analysed certain algorithms for suppressing artifacts, and developed metrics and procedures to make a quantifiable comparison between algorithms in that field. A common assumption in the literature is that zero-padding in the Fourier domain (sinc interpolation) is used for the zoom algorithm. Other algorithms make use of linear interpolation for a similar reason. In this paper, we analyse several interpolation formulae and compare them with sinc interpolation in a quantitative fashion. We further consider the interaction of the interpolation formulae with filtered Fourier reconstruction. Our results are foundational to establishing a quantitative evidence base for preferring certain ringing suppression algorithms over others, and provide grounds for revisiting assumptions that have long stood in commercial imaging pipelines.
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.
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.
Gibbs ringing is an artefact that occurs when a discontinuous signal is truncated in the Fourier domain. It is a phenomenon which occurs frequently in optics as apodization - the action of an aperture - and which can be interpreted as an idealised low pass filtering process. Diffraction can be approximately modelled using the Fresnel transform. The spectral method of calculating the Fresnel transform, a workhorse in digital holography and other fields, interprets the Fresnel transform as an all-pass filter. In this paper, we analyse the relationship between these phenomena and propose how to use this interpretation to improve image quality.
KEYWORDS: Digital holography, Holograms, Digital imaging, Diffraction, 3D image reconstruction, Image processing algorithms and systems, Holography, Error analysis, Phase imaging
A quantitative phase image is often obtained by refocussing or by an iterative algorithm containing refocussing steps. The required propagation distance is judged by a manual search. Autofocus algorithms attempt to estimate this propagation distance. In this paper, we report novel approaches to autofocus for quantitative phase images using neural networks.
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