Reconstruction Resilience to Subsampling in Compressive Fresnel Holography

Bettens, Stijn; Yan, Hao; Bundervoet, Shaun; Schretter, Colas; Dooms, Ann; Schelkens, Peter

doi:10.1364/dh.2015.dt1a.3

Cited by 2 publications

(2 citation statements)

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“…32 A similar study considered two alternatives to TwIST, namely the projection onto convex set (POCS) and the projected gradient method (PGM). 33 These methods solve a strict basis pursuit problem and therefore implicitly assume that holograms are noise-free. Nevertheless, the sparse reconstructions were resilient to noise, suggesting that noise issues are not significant in compressed digital holography.…”

Section: Light Wave Propagationmentioning

confidence: 99%

“…For example, Wavelets combined with a backpropagation kernel are typically used as a sparsifying operator on the recorded hologram. 20,33 Unfortunately, this model is inadequate for macroscopic scenes for several reasons. First, large hologram apertures results in a small depth of field and the extended scene depth make it impossible to have the whole scene in focus simultaneously.…”

Section: Volumetric Scene Modelingmentioning

confidence: 99%

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Compressed digital holography: from micro towards macro

Schretter

Bettens

Blinder

et al. 2016

Applications of Digital Image Processing XXXIX

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The age of computational imaging is merging the physical hardware-driven approach of photonics with advanced signal processing methods from software-driven computer engineering and applied mathematics. The compressed sensing theory in particular established a practical framework for reconstructing the scene content using few linear combinations of complex measurements and a sparse prior for regularizing the solution. Compressed sensing found direct applications in digital holography for microscopy. Indeed, the wave propagation phenomenon in free space mixes in a natural way the spatial distribution of point sources from the 3-dimensional scene. As the 3-dimensional scene is mapped to a 2-dimensional hologram, the hologram samples form a compressed representation of the scene as well. This overview paper discusses contributions in the field of compressed digital holography at the micro scale. Then, an outreach on future extensions towards the real-size macro scale is discussed. Thanks to advances in sensor technologies, increasing computing power and the recent improvements in sparse digital signal processing, holographic modalities are on the verge of practical high-quality visualization at a macroscopic scale where much higher resolution holograms must be acquired and processed on the computer.

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Section: Light Wave Propagationmentioning

confidence: 99%

Section: Volumetric Scene Modelingmentioning

confidence: 99%

Compressed digital holography: from micro towards macro

Schretter

Bettens

Blinder

et al. 2016

Applications of Digital Image Processing XXXIX

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Bounds and Conditions for Compressive Digital Holography Using Wavelet Sparsifying Bases

Bettens

Schretter

Deligiannis

et al. 2017

IEEE Trans. Comput. Imaging

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In compressive digital holography, we reconstruct sparse object wavefields from undersampled holograms by solving an 1 -minimization problem. Applying wavelet transformations to the object wavefields produces the necessary sparse representations, but prior work clings to transformations with too few vanishing moments. We put several wavelet transformations belonging to different wavelet families to the test by evaluating their sparsifying properties, the number of hologram samples that are required to reconstruct the sparse wavefields perfectly, and the robustness of the reconstructions to additive noise and sparsity defects. In particular, we recommend the CDF 9/7 and 17/11 wavelet transformations, as well as their reverse counterparts, because they yield sufficiently sparse representations for most accustomed wavefields in combination with robust reconstructions. These and other recommendations are procured from simulations and are validated using biased, noisy holograms.

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Reconstruction Resilience to Subsampling in Compressive Fresnel Holography

Abstract: The reconstruction resilience of a Projected Gradient Method (PGM), POCS and TwIST to randomly subsampled image wavefields is investigated. POCS and PGM do not consider noisy data, but they return a better reconstruction than TwIST.

Cited by 2 publications

References 9 publications

Compressed digital holography: from micro towards macro

Compressed digital holography: from micro towards macro

Bounds and Conditions for Compressive Digital Holography Using Wavelet Sparsifying Bases

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