no code implementations • 6 Mar 2022 • Shan Shan, Ingrid Daubechies
The DM procedure consists in constructing a spectral parametrization for the manifold from simulated random walks or diffusion paths on the data set.
no code implementations • 23 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.
no code implementations • 28 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.
no code implementations • 16 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.
no code implementations • 20 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.
no code implementations • 27 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.
no code implementations • 21 May 2018 • Jieren Xu, Yitong Li, Haizhao Yang, David Dunson, Ingrid Daubechies
This paper proposes a novel kernel-based optimization scheme to handle tasks in the analysis, e. g., signal spectral estimation and single-channel source separation of 1D non-stationary oscillatory data.
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.
no code implementations • 4 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.
no code implementations • 9 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.
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.
1 code implementation • 12 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 $\sum_{k=1}^K \alpha_k(t)s_k(2\pi N_k\phi_k(t))$.
no code implementations • 14 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.
no code implementations • 4 Jun 2016 • Rujie Yin, Tingran Gao, Yue M. Lu, Ingrid Daubechies
We propose an image representation scheme combining the local and nonlocal characterization of patches in an image.
no code implementations • 20 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.
no code implementations • 26 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.
no code implementations • 22 Apr 2013 • Bruno Cornelis, Yun Yang, Joshua T. Vogelstein, Ann Dooms, Ingrid Daubechies, David Dunson
The preservation of our cultural heritage is of paramount importance.