Search Results for author: Ingrid Daubechies

Found 15 papers, 1 papers with code

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.

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.

Non-Oscillatory Pattern Learning for Non-Stationary Signals

no code implementations21 May 2018 Jieren Xu, Yitong Li, David Dunson, Ingrid Daubechies, Haizhao Yang

This paper proposes a novel non-oscillatory pattern (NOP) learning scheme for several oscillatory data analysis problems including signal decomposition, super-resolution, and signal sub-sampling.

Super-Resolution

Stop memorizing: A data-dependent regularization framework for intrinsic pattern learning

no code implementations ICLR 2019 Wei Zhu, Qiang Qiu, Bao Wang, Jianfeng Lu, Guillermo Sapiro, Ingrid Daubechies

Deep neural networks (DNNs) typically have enough capacity to fit random data by brute force even when conventional data-dependent regularizations focusing on the geometry of the features are imposed.

Robust and Resource Efficient Identification of Shallow Neural Networks by Fewest Samples

no code implementations4 Apr 2018 Massimo Fornasier, Jan Vybíral, Ingrid Daubechies

In the case of the shallowest feed-forward neural network, second order differentiation and tensors of order two (i. e., matrices) suffice as we prove in this paper.

Gaussian Process Landmarking on Manifolds

no code implementations9 Feb 2018 Tingran Gao, Shahar Z. Kovalsky, Ingrid Daubechies

As a means of improving analysis of biological shapes, we propose an algorithm for sampling a Riemannian manifold by sequentially selecting points with maximum uncertainty under a Gaussian process model.

Experimental Design

LDMNet: Low Dimensional Manifold Regularized Neural Networks

no code implementations CVPR 2018 Wei Zhu, Qiang Qiu, Jiaji Huang, Robert Calderbank, Guillermo Sapiro, Ingrid Daubechies

To resolve this, we propose a new framework, the Low-Dimensional-Manifold-regularized neural Network (LDMNet), which incorporates a feature regularization method that focuses on the geometry of both the input data and the output features.

Face Recognition Small Data Image Classification

Recursive Diffeomorphism-Based Regression for Shape Functions

1 code implementation12 Oct 2016 Jieren Xu, Haizhao Yang, Ingrid Daubechies

This paper proposes a recursive diffeomorphism based regression method for one-dimensional generalized mode decomposition problem that aims at extracting generalized modes $\alpha_k(t)s_k(2\pi N_k\phi_k(t))$ from their superposition $\sum_{k=1}^K \alpha_k(t)s_k(2\pi N_k\phi_k(t))$.

Multi-modal dictionary learning for image separation with application in art investigation

no code implementations14 Jul 2016 Nikos Deligiannis, Joao F. C. Mota, Bruno Cornelis, Miguel R. D. Rodrigues, Ingrid Daubechies

Our dictionary learning framework can be tailored both to a single- and a multi-scale framework, with the latter leading to a significant performance improvement.

Dictionary Learning

X-ray image separation via coupled dictionary learning

no code implementations20 May 2016 Nikos Deligiannis, João F. C. Mota, Bruno Cornelis, Miguel R. D. Rodrigues, Ingrid Daubechies

In support of art investigation, we propose a new source sepa- ration method that unmixes a single X-ray scan acquired from double-sided paintings.

Dictionary Learning

Painting Analysis Using Wavelets and Probabilistic Topic Models

no code implementations26 Jan 2014 Tong Wu, Gungor Polatkan, David Steel, William Brown, Ingrid Daubechies, Robert Calderbank

In this paper, computer-based techniques for stylistic analysis of paintings are applied to the five panels of the 14th century Peruzzi Altarpiece by Giotto di Bondone.

Topic Models

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