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Data Learning on Manifolds and Future Challenges

Deliverables

Super-resolution and interpolation of the Euclid PSF

Report on applying dictionary learning on manifolds developed in DEDALE in combination with interpolation methods which are used extensively by the UCL group (e.g neural networks and Gaussian processes) to build a model for the Euclid PSF.

Optimization for manifold-valued signal restoration.

Report on optimization methods for signal restoration with manifold-valued representations: designing and implementing algorithms to solve linear inverse problems with non-linear signal representations; The case of non-linear and potentially non-convex problems will be discussed.

Adaptive transforms for manifold-valued data.

Report on the development of adapted multiscale transforms. The final learned dictionary is restricted to a class of dictionaries generated from a structured dictionary such as shearlet. Existence of fast transform/reconstruction will be discussed.

Non-linear learning on complex imaging data.

Report on Non-linear learning on complex imaging data: learning representations for data lying on unknown low-dimensional manifolds. The use of deep learning architectures like stacked sparse autoencoders will be particularly studied in this task.

Large-scale learning schemes.

Evaluation of cutting edge distributed processing platforms, such as GraphLab, Mahout and MLI, for benchmarking large-scale test sets for machine learning. Real time parallel processing considerations will be actively taken under account into this task.

Optimizations for non-linear learning.

Report on building upon proximal methods and problem splitting techniques to design highly-parallelizable sparse solvers (e.g. sparse/low-rank multivariate signal decompositions.)

Learning-based photometric and spectroscopic redshift estimation

Report on the development of a dictionary learning based method for spectroscopic and photometric redshift estimation of Euclid data.

Dictionary learning for multivariate/multispectral data.

Report on Dictionary Learning on multi-valued data. The case of multi-channel polarized data on the sphere will be considered.

Linear inverse problems with sparsity constraints.

Report on the development of dedicated solvers for the recovery of multivariate signals with adapted sparse priors, either in fixed representations from Task 2.1 or learnt representations from task 2.2. Convergence and Computation time will be discussed.

Numerical toolbox and benchmarking platform.

Development of a numerical toolbox and benchmark test set. The code will be in Python and/orC++. The algorithms related to tasks 3.1 and 3.2 will be included in the toolbox, and benchmark data will also be joined to the toolbox for test and evaluation.

Toolbox and benchmarking platform for large scale learning.

Toolbox for parallel linear and non-linear sparsity based learning architectures.

Evaluation/validation of the mass mapping algorithms

Report on using dictionary methods for 2D and 3D mass mapping from weak lensing data. Data available in the framework of the Open Research Data Pilot concept.

Project Website & Factsheet

Realization of web site, contains informations about the project (publications, technical notes, etc).

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Publications

Cosmic microwave background reconstruction from WMAP and Planck PR2 data

Author(s): J. Bobin, F. Sureau, J.-L. Starck
Published in: Astronomy & Astrophysics, Issue 591, 2016, Page(s) A50, ISSN 0004-6361
DOI: 10.1051/0004-6361/201527822

Sparsity and inverse problems in astrophysics

Author(s): Jean-Luc Starck
Published in: Journal of Physics: Conference Series, Issue 699, 2016, Page(s) 012010, ISSN 1742-6588
DOI: 10.1088/1742-6596/699/1/012010

High resolution weak lensing mass mapping combining shear and flexion

Author(s): F. Lanusse, J.-L. Starck, A. Leonard, S. Pires
Published in: Astronomy & Astrophysics, Issue 591, 2016, Page(s) A2, ISSN 0004-6361
DOI: 10.1051/0004-6361/201628278

Point Spread Function Field Learning Based on Optimal Transport Distances

Author(s): F. Ngolé, J.-L. Starck
Published in: SIAM Journal on Imaging Sciences, Issue 10/3, 2017, Page(s) 1549-1578, ISSN 1936-4954
DOI: 10.1137/16M1093677

α -Molecules

Author(s): Philipp Grohs, Sandra Keiper, Gitta Kutyniok, Martin Schäfer
Published in: Applied and Computational Harmonic Analysis, Issue 41/1, 2016, Page(s) 297-336, ISSN 1063-5203
DOI: 10.1016/j.acha.2015.10.009

Sparse Reconstruction of the Merging A520 Cluster System

Author(s): Austin Peel, François Lanusse, Jean-Luc Starck
Published in: The Astrophysical Journal, Issue 847/1, 2017, Page(s) 23, ISSN 1538-4357
DOI: 10.3847/1538-4357/aa850d

Space variant deconvolution of galaxy survey images

Author(s): S. Farrens, F. M. Ngolè Mboula, J.-L. Starck
Published in: Astronomy & Astrophysics, Issue 601, 2017, Page(s) A66, ISSN 0004-6361
DOI: 10.1051/0004-6361/201629709

Singular spectrum-based matrix completion for time series recovery and prediction

Author(s): Grigorios Tsagkatakis, Baltasar Beferull-Lozano, Panagiotis Tsakalides
Published in: EURASIP Journal on Advances in Signal Processing, Issue 2016/1, 2016, ISSN 1687-6180
DOI: 10.1186/s13634-016-0360-0

Land Classification Using Remotely Sensed Data: Going Multilabel

Author(s): Konstantinos Karalas, Grigorios Tsagkatakis, Michael Zervakis, Panagiotis Tsakalides
Published in: IEEE Transactions on Geoscience and Remote Sensing, Issue 54/6, 2016, Page(s) 3548-3563, ISSN 0196-2892
DOI: 10.1109/TGRS.2016.2520203

Matrix and Tensor Completion on a Human Activity Recognition Framework

Author(s): Sofia Savvaki, Grigorios Tsagkatakis, Athanasia Panousopoulou, Panagiotis Tsakalides
Published in: IEEE Journal of Biomedical and Health Informatics, Issue 21/6, 2017, Page(s) 1554-1561, ISSN 2168-2194
DOI: 10.1109/JBHI.2017.2716112

Compressed sensing for finite-valued signals

Author(s): Sandra Keiper, Gitta Kutyniok, Dae Gwan Lee, Götz E. Pfander
Published in: Linear Algebra and its Applications, Issue 532, 2017, Page(s) 570-613, ISSN 0024-3795
DOI: 10.1016/j.laa.2017.07.006

Wasserstein Dictionary Learning: Optimal Transport-Based Unsupervised Nonlinear Dictionary Learning

Author(s): Morgan A. Schmitz, Matthieu Heitz, Nicolas Bonneel, Fred Ngolè, David Coeurjolly, Marco Cuturi, Gabriel Peyré, Jean-Luc Starck
Published in: SIAM Journal on Imaging Sciences, Issue 11/1, 2018, Page(s) 643-678, ISSN 1936-4954
DOI: 10.1137/17M1140431

A Haar wavelet-based perceptual similarity index for image quality assessment

Author(s): Rafael Reisenhofer, Sebastian Bosse, Gitta Kutyniok, Thomas Wiegand
Published in: Signal Processing: Image Communication, Issue 61, 2018, Page(s) 33-43, ISSN 0923-5965
DOI: 10.1016/j.image.2017.11.001

Unsupervised feature-learning for galaxy SEDs with denoising autoencoders

Author(s): J. Frontera-Pons, F. Sureau, J. Bobin, E. Le Floc’h
Published in: Astronomy & Astrophysics, Issue 603, 2017, Page(s) A60, ISSN 0004-6361
DOI: 10.1051/0004-6361/201630240

Optimal approximation of piecewise smooth functions using deep ReLU neural networks

Author(s): Philipp Petersen, Felix Voigtlaender
Published in: Neural Networks, Issue 108, 2018, Page(s) 296-330, ISSN 0893-6080
DOI: 10.1016/j.neunet.2018.08.019

Constraint matrix factorization for space variant PSFs field restoration

Author(s): F Ngolè, J-L Starck, K Okumura, J Amiaux, P Hudelot
Published in: Inverse Problems, Issue 32/12, 2016, Page(s) 124001, ISSN 0266-5611
DOI: 10.1088/0266-5611/32/12/124001

Breaking degeneracies in modified gravity with higher (than 2nd) order weak-lensing statistics

Author(s): Austin Peel, Valeria Pettorino, Carlo Giocoli, Jean-Luc Starck, Marco Baldi
Published in: Astronomy & Astrophysics, Issue 619, 2018, Page(s) A38, ISSN 0004-6361
DOI: 10.1051/0004-6361/201833481

Cosmological constraints with weak-lensing peak counts and second-order statistics in a large-field survey

Author(s): Austin Peel, Chieh-An Lin, François Lanusse, Adrienne Leonard, Jean-Luc Starck, Martin Kilbinger
Published in: Astronomy & Astrophysics, Issue 599, 2017, Page(s) A79, ISSN 0004-6361
DOI: 10.1051/0004-6361/201629928

Degradation analysis in the estimation of photometric redshifts from non-representative training sets

Author(s): J D Rivera, B Moraes, A I Merson, S Jouvel, F B Abdalla, M C B Abdalla
Published in: Monthly Notices of the Royal Astronomical Society, Issue 477/4, 2018, Page(s) 4330-4347, ISSN 0035-8711
DOI: 10.1093/mnras/sty880

Improving weak lensing mass map reconstructions using Gaussian and sparsity priors: application to DES SV

Author(s): N Jeffrey, F B Abdalla, O Lahav, F Lanusse, J-L Starck, A Leonard, D Kirk, C Chang, E Baxter, T Kacprzak, S Seitz, V Vikram, L Whiteway, T M C Abbott, S Allam, S Avila, E Bertin, D Brooks, A Carnero Rosell, M Carrasco Kind, J Carretero, F J Castander, M Crocce, C E Cunha, C B D’Andrea, L N da Costa, C Davis, J De Vicente, S Desai, P Doel, T F Eifler, A E Evrard, B Flaugher, P Fosalba, J Frie
Published in: Monthly Notices of the Royal Astronomical Society, Issue 479/3, 2018, Page(s) 2871-2888, ISSN 0035-8711
DOI: 10.1093/mnras/sty1252

Multi-band morpho-Spectral Component Analysis Deblending Tool (MuSCADeT): Deblending colourful objects

Author(s): R. Joseph, F. Courbin, J.-L. Starck
Published in: Astronomy & Astrophysics, Issue 589, 2016, Page(s) A2, ISSN 0004-6361
DOI: 10.1051/0004-6361/201527923

A Mathematical Framework for Feature Selection from Real-World Data with Non-Linear Observations

Author(s): Genzel, Martin; Kutyniok, Gitta
Published in: Issue 25, 2016

Optimal Approximation with Sparsely Connected Deep Neural Networks

Author(s): Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen
Published in: 2017

Robust 1-Bit Compressed Sensing via Hinge Loss Minimization

Author(s): Martin Genzel, Alexander Stollenwerk
Published in: 2018

Recovering Structured Data From Superimposed Non-Linear Measurements

Author(s): Martin Genzel, Peter Jung
Published in: 2017

Compressed Sensing for Analog Signals

Author(s): Bernard G. Bodmann, Axel Flinth, Gitta Kutyniok
Published in: 2018

Anisotropic Multiscale Systems on Bounded Domains

Author(s): Grohs, Philipp; Kutyniok, Gitta; Ma, Jackie; Petersen, Philipp; Raslan, Mones
Published in: Issue 33, 2015

ℓ1-Analysis Minimization and Generalized (Co-)Sparsity: When Does Recovery Succeed?

Author(s): Martin Genzel, Gitta Kutyniok, Maximilian März
Published in: 2017

The Mismatch Principle: Statistical Learning Under Large Model Uncertainties

Author(s): Martin Genzel, Gitta Kutyniok
Published in: 2018

Structured, compactly supported Banach frame decompositions of decomposition spaces

Author(s): Voigtlaender, Felix
Published in: Issue 21, 2016

Learning sparse representations on the sphere

Author(s): Florent Sureau, Felix Voigtlaender, Malte Wust, Jean-Luc Starck, Gitta Kutyniok
Published in: 2018

A Distributed Learning Architecture for Scientific Imaging Problems

Author(s): A. Panousopoulou, S. Farrens, K. Fotiadou, A. Woiselle, G. Tsagkatakis, , J.-L. Starck, P. Tsakalides
Published in: 2018

Parameter inference and model comparison using theoretical predictions from noisy simulations

Author(s): Niall Jeffrey, Filipe B. Abdalla
Published in: 2018

Convolutional Neural Networks for Spectroscopic Redshift Estimation on Euclid Data

Author(s): Radamanthys Stivaktakis, Grigorios Tsagkatakis, Bruno Moraes, Filipe Abdalla, Jean-Luc Starck, Panagiotis Tsakalides
Published in: 2018

ZXCorr: Cosmological Measurements from Angular Power Spectra Analysis of BOSS DR12 Tomography

Author(s): Arthur Loureiro, Bruno Moraes, Filipe B. Abdalla, Andrei Cuceu, Michael McLeod, Lorne Whiteway, Sreekumar T. Balan, Aurélien Benoit-Lévy, Ofer Lahav, Marc Manera, Richard Rollins, Henrique S. Xavier
Published in: 2018

Analysis vs. synthesis sparsity for α-shearlets

Author(s): Felix Voigtlaender, Anne Pein
Published in: 2017

A distributed learning architecture for big imaging problems in astrophysics

Author(s): Athanasia Panousopoulou, Sammuel Farrens, Yannis Mastorakis, Jean-Luck Starck, Panagiotis Tsakailides
Published in: 2017 25th European Signal Processing Conference (EUSIPCO), 2017, Page(s) 1440-1444
DOI: 10.23919/eusipco.2017.8081447