Reconstruction of apertured Fourier Transform Hologram using compressed sensing

Vetal, Akshay Pandit; Singh, Darshika; Singh, Rakesh Kumar; Mishra, Deepak

doi:10.1016/j.optlaseng.2018.08.008

Cited by 5 publications

(4 citation statements)

References 25 publications

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“…The hologram contains both the amplitude and phase information of the object, which allows the 3D image to be reconstructed with high accuracy and resolution. CS has been applied to DH in recent years, as detailed in a comprehensive review by Rivenson et al 8 CS was first introduced to DH by Brady et al 9 It was first introduced to apertured Fourier transform holography by Vetal et al 10 In this paper, we simulated a Fourier digital holographic setup shown in Fig. 1, reproduced from our previous research.…”

Section: Introductionmentioning

confidence: 99%

Orthogonal matching pursuit vs. iterative hard thresholding: addressing phase discontinuities in digital holography

Wang,

Healy

2024

Optics, Photonics, and Digital Technologies for Imaging Applications VIII

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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.

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Section: Introductionmentioning

confidence: 99%

Orthogonal matching pursuit vs. iterative hard thresholding: addressing phase discontinuities in digital holography

Wang,

Healy

2024

Optics, Photonics, and Digital Technologies for Imaging Applications VIII

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“…5 Fourier Transform Holography (FTH) is a type of DH that encodes object information as the Fourier spectrum in an interference pattern with the help of a reference point source. 6 A Fourier-transform holographic microscope was shown to achieve a spatial resolution approaching the diffraction limit. 7 In this paper, the digital holography system that we simulated is a FTH system.…”

Section: Introductionmentioning

confidence: 99%

“…CS has been successfully introduced in digital holography (DH) in recent years. 8 The first published formulation of holography as a CS problem was suggested by Brady et al 9 Reconstruction of apertured Fourier transform hologram using compressed sensing was proposed by Vetal et al 6 Compressive sensing was also applied to digital Fresnel holography by Rivenson et al 10 Gibbs ringing is an artefact created when a discontinuous function is approximated by its Fourier transform. The more truncated the Fourier transform is, the more severe the ringing grows.…”

Section: Introductionmentioning

confidence: 99%

Compressive digital holography and Gibbs ringing

Wang¹,

Healy

2023

Holography: Advances and Modern Trends VIII

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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.

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“…During Scanning Transmission X-ray Microscopy (STXM) or X-ray Fluorescence (XRF) experiments [ 24 ], CS has been employed to dramatically reduce the time acquired for a single scan [ 25 , 26 ]: based on a rough STXM measurement, indeed, a spatial mask can be used to discriminate areas of sparse or fine scanning (for the subsequent XRF/STXM fine-measure). A different application is in Fourier Holography, where a CS framework is employed to solve for the values of the diffraction pattern, which are covered by a beam-stop at the detector plane [ 27 ].…”

Section: Introductionmentioning

confidence: 99%

Automatic Differentiation for Inverse Problems in X-ray Imaging and Microscopy

Guzzi

Gianoncelli

Billè

et al. 2023

Life

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Computational techniques allow breaking the limits of traditional imaging methods, such as time restrictions, resolution, and optics flaws. While simple computational methods can be enough for highly controlled microscope setups or just for previews, an increased level of complexity is instead required for advanced setups, acquisition modalities or where uncertainty is high; the need for complex computational methods clashes with rapid design and execution. In all these cases, Automatic Differentiation, one of the subtopics of Artificial Intelligence, may offer a functional solution, but only if a GPU implementation is available. In this paper, we show how a framework built to solve just one optimisation problem can be employed for many different X-ray imaging inverse problems.

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Reconstruction of apertured Fourier Transform Hologram using compressed sensing

Cited by 5 publications

References 25 publications

Orthogonal matching pursuit vs. iterative hard thresholding: addressing phase discontinuities in digital holography

Orthogonal matching pursuit vs. iterative hard thresholding: addressing phase discontinuities in digital holography

Compressive digital holography and Gibbs ringing

Automatic Differentiation for Inverse Problems in X-ray Imaging and Microscopy

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