CDF 9/7 wavelets as sparsifying operator in compressive holography

Yan, Hao; Blinder, David; Bettens, Stijn; Ottevaere, Heidi; Munteanu, Adrian; Schelkens, Peter

doi:10.1109/icip.2015.7351154

Cited by 3 publications

(3 citation statements)

References 20 publications

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“…The Cohen-Daubechies-Fauveau (CDF) wavelets 17 for instance have been retained as an ideal choice for its multi-scale and smooth wavelet transformation that match relatively well the human visual system. Fast transforms based on lifting schemes exist for CDF wavelets, 18 and hologram compression schemes 19 as well as reconstruction from few hologram samples 20 have been proposed based on this representation. Fast transforms implemented with lifting scheme are optimally efficient algorithms, requiring a constant processing time per pixel.…”

Section: Scene Representationmentioning

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: Scene Representationmentioning

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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“…In this work, the Gini index is proposed as a sparsifying measure for justifying the choice of the orthogonal wavelet basis, a Projected Gradient Method (PGM) is introduced for solving (1) with regard to x, and the resilience of the reconstruction to random subsampling of the image wavefield is investigated for TwIST, PGM and Projection Over Convex Sets (POCS). For the details on POCS and TwIST we refer respectively to [5] and [6].…”

Section: Introductionmentioning

confidence: 99%

Reconstruction Resilience to Subsampling in Compressive Fresnel Holography

Bettens¹,

Yan²,

Bundervoet

et al. 2015

Digital Holography &Amp; 3-D Imaging Meeting

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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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CDF 9/7 wavelets as sparsifying operator in compressive holography

Cited by 3 publications

References 20 publications

Compressed digital holography: from micro towards macro

Compressed digital holography: from micro towards macro

Reconstruction Resilience to Subsampling in Compressive Fresnel Holography

Bounds and Conditions for Compressive Digital Holography Using Wavelet Sparsifying Bases

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