Blue-noise sampling for human retinal cone spatial distribution modeling

Lanaro, Matteo Paolo; Perrier, Hélène; Cœurjolly, David; Ostromoukhov, Victor; Rizzi, Alessandro

doi:10.1088/2399-6528/ab8064

Cited by 5 publications

(4 citation statements)

References 65 publications

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“…Instead, our main hypotheses are the blue noise distribution and the nearest-neighbor connectivity pattern. For the blue noise distribution and given the physical nature of neurons (Blazquez-Llorca et al, 2014;Lanaro, Perrier, Coeurjolly, Ostromoukhov, & Rizzi, 2020), we think it makes sense to consider neurons to be at a minimal distance from each other and randomly distributed and to have a nearest-neighbor connectivity as it is known to occur in the cortex (van Pelt & van Ooyen, 2013). The case of reorganization, where neurons physically migrate (Lloyd relaxation), is probably the most dubious hypothesis but seems to be partially supported by experimental results (Kaneko, Sawada, & Sawamoto, 2017).…”

Section: Discussionmentioning

confidence: 99%

Randomized Self-Organizing Map

Rougier

Detorakis

2021

Neural Computation

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We propose a variation of the self-organizing map algorithm by considering the random placement of neurons on a two-dimensional manifold, following a blue noise distribution from which various topologies can be derived. These topologies possess random (but controllable) discontinuities that allow for a more flexible self- organization, especially with high-dimensional data. The proposed algorithm is tested on one-, two- and three-dimensional tasks, as well as on the MNIST handwritten digits data set and validated using spectral analysis and topological data analysis tools. We also demonstrate the ability of the randomized self-organizing map to gracefully reorganize itself in case of neural lesion and/or neurogenesis.

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Section: Discussionmentioning

confidence: 99%

Randomized Self-Organizing Map

Rougier

Detorakis

2021

Neural Computation

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“…CVTs give rise to cells in a close near-hexagonal packing, whose centroids follow a blue noise distribution. For this reason, they can be observed in many biological imaging systems, for example in the distribution of cones in the human retina 15 or in the arrangement of ommatidia in compound eyes 16,17 (cf. Fig.…”

Section: Optimization and Propertiesmentioning

confidence: 99%

Compound eye inspired flat lensless imaging with spatially-coded Voronoi-Fresnel phase

Fu¹,

Yan²,

Heidrich³

2021

Preprint

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Lensless cameras are a class of imaging devices that shrink the physical dimensions to the very close vicinity of the image sensor by integrating flat optics and computational algorithms. Here we report a flat lensless camera with spatially-coded Voronoi-Fresnel phase, partly inspired by biological apposition compound eye, to achieve superior image quality. We propose a design principle of maximizing the information in optics to facilitate the computational reconstruction. By introducing a Fourier domain metric, Modulation Transfer Function volume (MTFv), we devise an optimization framework to guide the optimal design of the optical element. The resulting Voronoi-Fresnel phase features an irregular array of quasi-Centroidal Voronoi cells containing a base first-order Fresnel phase function. We demonstrate and verify the imaging performance with a prototype Voronoi-Fresnel lensless camera on a 1.6-megapixel image sensor in various illumination conditions. The proposed design could benefit the development of compact imaging systems working in extreme physical conditions.

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“…Poisson-disk sampling (Kazimierczuk et al 2008), and Poisson-gap (PG) sampling (Hyberts et al 2010). Together, these solutions are often referred to as "blue-noise sampling", especially in non-NMR literature (Tang et al 2009;Correa et al 2016;Lanaro et al 2020). As shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

Clustered sparsity and Poisson-gap sampling

2021

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Non-uniform sampling (NUS) is a popular way of reducing the amount of time taken by multidimensional NMR experiments. Among the various non-uniform sampling schemes that exist, the Poisson-gap (PG) schedules are particularly popular, especially when combined with compressed-sensing (CS) reconstruction of missing data points. However, the use of PG is based mainly on practical experience and has not, as yet, been explained in terms of CS theory. Moreover, an apparent contradiction exists between the reported effectiveness of PG and CS theory, which states that a “flat” pseudo-random generator is the best way to generate sampling schedules in order to reconstruct sparse spectra. In this paper we explain how, and in what situations, PG reveals its superior features in NMR spectroscopy. We support our theoretical considerations with simulations and analyses of experimental data from the Biological Magnetic Resonance Bank (BMRB). Our analyses reveal a previously unnoticed feature of many NMR spectra that explains the success of ”blue-noise” schedules, such as PG. We call this feature “clustered sparsity”. This refers to the fact that the peaks in NMR spectra are not just sparse but often form clusters in the indirect dimension, and PG is particularly suited to deal with such situations. Additionally, we discuss why denser sampling in the initial and final parts of the clustered signal may be useful.

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Blue-noise sampling for human retinal cone spatial distribution modeling

Cited by 5 publications

References 65 publications

Randomized Self-Organizing Map

Randomized Self-Organizing Map

Compound eye inspired flat lensless imaging with spatially-coded Voronoi-Fresnel phase

Clustered sparsity and Poisson-gap sampling

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