Search Results for author: Barak Sober

Found 9 papers, 1 papers with code

Mixed X-Ray Image Separation for Artworks with Concealed Designs

no code implementations23 Jan 2022 Wei Pu, Jun-Jie Huang, Barak Sober, Nathan Daly, Catherine Higgitt, Ingrid Daubechies, Pier Luigi Dragotti, Miguel Rodigues

In this paper, we focus on X-ray images of paintings with concealed sub-surface designs (e. g., deriving from reuse of the painting support or revision of a composition by the artist), which include contributions from both the surface painting and the concealed features.

Neural Network Approximation of Refinable Functions

no code implementations28 Jul 2021 Ingrid Daubechies, Ronald DeVore, Nadav Dym, Shira Faigenbaum-Golovin, Shahar Z. Kovalsky, Kung-Ching Lin, Josiah Park, Guergana Petrova, Barak Sober

Namely, we show that refinable functions are approximated by the outputs of deep ReLU networks with a fixed width and increasing depth with accuracy exponential in terms of their number of parameters.

Non-Parametric Estimation of Manifolds from Noisy Data

1 code implementation11 May 2021 Yariv Aizenbud, Barak Sober

Assuming that the data was sampled uniformly from a tubular neighborhood of $\mathcal{M}\in \mathcal{C}^k$, a compact manifold without boundary, we present an algorithm that takes a point $r$ from the tubular neighborhood and outputs $\hat p_n\in \mathbb{R}^D$, and $\widehat{T_{\hat p_n}\mathcal{M}}$ an element in the Grassmanian $Gr(d, D)$.

Image Separation with Side Information: A Connected Auto-Encoders Based Approach

no code implementations16 Sep 2020 Wei Pu, Barak Sober, Nathan Daly, Zahra Sabetsarvestani, Catherine Higgitt, Ingrid Daubechies, Miguel R. D. Rodrigues

These features are then used to (1) reproduce both of the original RGB images, (2) reconstruct the hypothetical separated X-ray images, and (3) regenerate the mixed X-ray image.

Approximating the Riemannian Metric from Point Clouds via Manifold Moving Least Squares

no code implementations20 Jul 2020 Barak Sober, Robert Ravier, Ingrid Daubechies

In this paper, we investigate the convergence of such approximations made by Manifold Moving Least-Squares (Manifold-MLS), a method that constructs an approximating manifold $\mathcal{M}^h$ using information from a given point cloud that was developed by Sober \& Levin in 2019.

Expression of Fractals Through Neural Network Functions

no code implementations27 May 2019 Nadav Dym, Barak Sober, Ingrid Daubechies

The combination of this phenomenon with the capacity, demonstrated here, of DNNs to efficiently approximate IFS may contribute to the success of DNNs, particularly striking for image processing tasks, as well as suggest new algorithms for representing self similarities in images based on the DNN mechanism.

Approximation of Functions over Manifolds: A Moving Least-Squares Approach

no code implementations2 Nov 2017 Barak Sober, Yariv Aizenbud, David Levin

The resulting approximant is shown to be a function defined over a neighborhood of a manifold, approximating the originally sampled manifold.

Dimensionality Reduction

Manifold Approximation by Moving Least-Squares Projection (MMLS)

no code implementations22 Jun 2016 Barak Sober, David Levin

We assume that the data points are located "near" the lower dimensional manifold and suggest a non-linear moving least-squares projection on an approximating $d$-dimensional manifold.

Dimensionality Reduction

Computer Aided Restoration of Handwritten Character Strokes

no code implementations23 Feb 2016 Barak Sober, David Levin

This work suggests a new variational approach to the task of computer aided restoration of incomplete characters, residing in a highly noisy document.

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