Generative models, parameter learning and sparsity

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Workshop theme

A key issue in image reconstruction, and in inverse problems as a whole, is the correct choice of image priors (or regularisation functionals) and data models (or fidelity terms) in a variational or Bayesian reconstruction model. Depending on the setup of the model, very different qualitative image reconstruction results are obtained. A setup of a variational imaging approach is influenced by the type of image one aims to reconstruct, as well as the way the image or data is acquired. The knowledge of the image properties -- such as the regularity of the image or present scales of image structures -- and the capability of modelling them, are crucial for an accurate setup of the image prior and as such for faithfully reconstructing the image contents. The image prior can have various forms, such as a regularisation term or a basis in which the image should be expanded. Sparsity plays a central role here. Sparsity promoting regularization is a widespread and very popular approach to solve inverse problems. Standard SPR methods like total variation (TV) or l1 regularization have been shown to be powerful tools to recover inverse problems solutions from a reduced amount of noisy measurements. Nevertheless, despite their ability of capturing important features such as discontinuities, these model-based regularizations are also well known to produce artefacts, such as the staircasing effect, if the measured data does not fit the corresponding model. An ideal SPR for a given application should be tailor-made, and reconstruct solutions one would expect rather than to create best fits to a standardized model.
The mechanism of the data acquisition process embodies the data model. This model explains how the data is related to the underlying image, containing information about the noise distribution, the amount of under-sampling and the physics of the image acquisition technique. Several strategies for deriving an optimal choice for an image enhancement approach have been considered in the literature. More heuristic approaches derive the model setup from the physics behind the acquisition process. Statistically grounded approaches are more data driven in the sense that they estimate or learn the noise and structure from the data itself. Adaptive regularisation approaches for instance are capable of adjusting the parameter values locally taking into account the noise level and the local scale of structures in the image. Moreover, machine learning methods, e.g. dictionary learning, are very powerful techniques to determine the correct basis in which an image should be reconstructed. Recent approaches in the community also propose to learn the imaging model by bilevel optimisation techniques. For gaining more insight into the reconstruction abilities of regularisers their analysis via singular vectors has also proven valuable in some recent works in the community.

Timetable

Monday 30th October 2017
09:00 to 09:40	Registration	No Room Required
09:40 to 09:50	Welcome from Christie Marr (INI Deputy Director)	No Room Required
09:50 to 10:40	James Nagy Emory University Spectral Computed Tomography	Room 1
10:40 to 11:10	Morning Coffee	No Room Required
11:10 to 12:00	Eldad Haber University of British Columbia tba	Room 1
12:00 to 12:50	Christoph Brune Universiteit Twente Cancer ID - From Spectral Segmentation to Deep Learning	Room 1
12:50 to 14:00	Lunch @ Wolfson Court	No Room Required
14:00 to 14:50	Lars Ruthotto Emory University PDE-based Algorithms for Convolution Neural Network	Room 1
14:50 to 15:40	Gitta Kutyniok Technische Universität Berlin Optimal Approximation with Sparsely Connected Deep Neural Networks	Room 1
15:40 to 16:00	Eva-Maria Brinkmann Westfalische Wilhelms-Universitat Munster Enhancing fMRI Reconstruction by Means of the ICBTV-Regularisation Combined with Suitable Subsampling Strategies and Temporal Smoothing	Room 1
16:00 to 16:30	Afternoon Tea	No Room Required
16:30 to 17:20	Joan Bruna New York University; University of California, Berkeley Geometry and Topology of Neural Network Optimization	Room 1
17:20 to 18:10	Justin Romberg Georgia Institute of Technology Structured solutions to nonlinear systems of equations	Room 1
18:10 to 19:10	Poster Session & Welcome Wine Reception at INI	No Room Required

Tuesday 31st October 2017
09:00 to 09:50	Stacey Levine Duquesne University Denoising Geometric Image Features	Room 1
09:50 to 10:40	Ozan Öktem KTH - Royal Institute of Technology; Karolinska Institute Task Oriented Reconstruction using Deep Learning	Room 1
10:40 to 11:10	Morning Coffee	No Room Required
11:10 to 12:00	Lior Horesh IBM Research Accelerated Free-Form Model Discovery of Interpretable Models using Small Data	Room 1
12:00 to 12:50	Martin Benning University of Cambridge Nonlinear Eigenanalysis of sparsity-promoting regularisation operators	Room 1
12:50 to 14:00	Lunch @ Wolfson Court	No Room Required
14:00 to 14:50	Alfred Hero University of Michigan The tensor graphical lasso (Teralasso)	Room 1
14:50 to 15:40	Francis Bach INRIA Paris - Rocquencourt; ENS - Paris Breaking the Curse of Dimensionality with Convex Neural Networks	Room 1
15:40 to 16:00	Jonas Adler KTH - Royal Institute of Technology Learned forward operators: Variational regularization for black-box models	Room 1
16:00 to 16:30	Afternoon Tea	No Room Required
16:30 to 17:20	Julianne Chung Virginia Polytechnic Institute and State University Advancements in Hybrid Iterative Methods for Inverse Problems	Room 1
17:20 to 18:10	Andreas Hauptmann University College London Learning iterative reconstruction for high resolution photoacoustic tomography	Room 1

Wednesday 1st November 2017
09:00 to 09:50	Mila Nikolova CNRS (Centre national de la recherche scientifique); ENS de Cachan Below the Surface of the Non-Local Bayesian Image Denoising Method	Room 1
09:50 to 10:40	Xavier Bresson Nanyang Technological University Convolutional Neural Networks on Graphs	Room 1
10:40 to 11:10	Morning Coffee	No Room Required
11:10 to 12:00	Julie Delon Université Paris Descartes High-Dimensional Mixture Models For Unsupervised Image Denoising (HDMI)	Room 1
12:00 to 12:50	Bangti Jin University College London Sparse Recovery by l0 Penalty	Room 1
12:50 to 14:00	Lunch @ Wolfson Court	No Room Required
14:00 to 17:00	Free Afternoon	No Room Required

Thursday 2nd November 2017
09:00 to 09:50	Silvia Gazzola University of Bath Krylov Subspace Methods for Sparse Reconstruction	Room 1
09:50 to 10:40	Pierre Weiss Université de Toulouse Generating sampling patterns in MRI	Room 1
10:40 to 11:10	Morning Coffee	No Room Required
11:10 to 12:00	Anders Hansen University of Cambridge On computational barriers in data science and the paradoxes of deep learning	Room 1
12:00 to 12:50	Josiane Zerubia INRIA Sophia Antipolis Stochastic geometry for automatic object detection and tracking	Room 1
12:50 to 14:00	Lunch @ Wolfson Court	No Room Required
14:00 to 14:50	Mario Figueiredo Universidade de Lisboa Divide and Conquer: Patch-based Image Denoising, Restoration, and Beyond	Room 1
14:50 to 15:40	Marcelo Pereyra Heriot-Watt University Bayesian analysis and computation for convex inverse problems: theory, methods, and algorithms	Room 1
15:40 to 16:00	Pol del Aguila Pla KTH - Royal Institute of Technology Cell detection by functional inverse diffusion and group sparsity	Room 1
16:00 to 16:30	Afternoon Tea	No Room Required
16:30 to 17:20	Claire Boyer Université Pierre et Marie Curie Paris Structured compressed sensing and recent theoretical advances on optimal sampling	Room 1
17:20 to 18:10	Tuomo Valkonen University of Liverpool What do regularisers do?	Room 1
19:30 to 22:00	Formal Dinner at Corpus Christi College	No Room Required

Friday 3rd November 2017
09:00 to 09:50	Irene Waldspurger Université Paris-Dauphine Alternating projections for phase retrieval with random sensing vectors	Room 1
09:50 to 10:40	Martin Holler University of Graz Analysis and applications of structural-prior-based total variation regularization for inverse problems	Room 1
10:40 to 11:10	Morning Coffee	No Room Required
11:10 to 12:00	Raymond Chan Chinese University of Hong Kong A Nuclear-norm Model for Multi-Frame Super-resolution Reconstruction	Room 1
12:00 to 12:50	Mihaela Pricop-jeckstadt Technische Universität Dresden From spatial learning to machine learning: an unsupervised approach with applications to behavioral science	Room 1
12:50 to 14:00	Lunch @ Wolfson Court	No Room Required
14:00 to 14:50	Robert Plemmons Wake Forest University Sparse Recovery Algorithms for 3D Imaging using Point Spread Function Engineering	Room 1
14:50 to 15:40	Jeff Calder University of Minnesota The weighted p-Laplacian and semi-supervised learning	Room 1
15:40 to 16:10	Afternoon Tea	No Room Required

Variational methods and effective algorithms for imaging and vision

Generative models, parameter learning and sparsity

Speakers

Jonas Adler KTH - Royal Institute of Technology
Francis Bach INRIA Paris - Rocquencourt; ENS - Paris
Martin Benning University of Cambridge
Claire Boyer Université Pierre et Marie Curie Paris
Xavier Bresson Nanyang Technological University
Eva-Maria Brinkmann Westfalische Wilhelms-Universitat Munster
Joan Bruna New York University; University of California, Berkeley
Christoph Brune Universiteit Twente
Jeff Calder University of Minnesota
Raymond Chan Chinese University of Hong Kong
Julianne Chung Virginia Polytechnic Institute and State University
Pol del Aguila Pla KTH - Royal Institute of Technology
Julie Delon Université Paris Descartes
Mario Figueiredo Universidade de Lisboa
Silvia Gazzola University of Bath
Eldad Haber University of British Columbia
Anders Hansen University of Cambridge
Andreas Hauptmann University College London
Alfred Hero University of Michigan
Martin Holler University of Graz
Lior Horesh IBM Research
Bangti Jin University College London
Gitta Kutyniok Technische Universität Berlin
Stacey Levine Duquesne University
James Nagy Emory University
Mila Nikolova CNRS (Centre national de la recherche scientifique); ENS de Cachan
Marcelo Pereyra Heriot-Watt University
Robert Plemmons Wake Forest University
Mihaela Pricop-jeckstadt Technische Universität Dresden
Justin Romberg Georgia Institute of Technology
Lars Ruthotto Emory University
Tuomo Valkonen University of Liverpool
Irene Waldspurger Université Paris-Dauphine
Pierre Weiss Université de Toulouse
Josiane Zerubia INRIA Sophia Antipolis
Ozan Öktem KTH - Royal Institute of Technology; Karolinska Institute

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Participants

Jonas Adler KTH - Royal Institute of Technology
Lourdes Agapito University College London
Daniel Alexander University College London
Simon Arridge University College London
John Aston University of Cambridge
Angelica I. Aviles-Rivero University of Cambridge
Francis Bach INRIA Paris - Rocquencourt; ENS - Paris
Yousra Bekhti Télécom ParisTech
Martin Benning University of Cambridge
Yoeri Boink Universiteit Twente
Claire Boyer Université Pierre et Marie Curie Paris
Yuri Boykov University of Western Ontario
Xavier Bresson Nanyang Technological University
Eva-Maria Brinkmann Westfalische Wilhelms-Universitat Munster
Joan Bruna New York University; University of California, Berkeley
Christoph Brune Universiteit Twente
Martin Burger Universität Münster
Corentin Caillaud École Polytechnique
Jeff Calder University of Minnesota
Elsa Cazelles Institut de Mathématiques de Bordeaux
Antonin Chambolle CNRS (Centre national de la recherche scientifique); École Polytechnique
Raymond Chan Chinese University of Hong Kong
Ke Chen University of Liverpool
Julianne Chung Virginia Polytechnic Institute and State University
Veronica Corona University of Cambridge
Valentin Debarnot CNRS (Centre national de la recherche scientifique)
Noemie Debroux Université de Rouen
Pol del Aguila Pla KTH - Royal Institute of Technology
Julie Delon Université Paris Descartes
Matthias Ehrhardt University of Cambridge
Mario Figueiredo Universidade de Lisboa
Andrew Fitzgibbon Microsoft (UK)
Marion Foare ENS - Lyon
Silvia Gazzola University of Bath
Aude Genevay Université Paris-Dauphine; École Normale Supérieure
Joana Grah The Alan Turing Institute
Harshit Gupta EPFL - Ecole Polytechnique Fédérale de Lausanne
Stéphanie Guérit Université Catholique de Louvain
Eldad Haber University of British Columbia
Anders Hansen University of Cambridge
Andreas Hauptmann University College London
Alfred Hero University of Michigan
Michael Hintermüller Humboldt-Universität zu Berlin
Martin Holler University of Graz
Lior Horesh IBM Research
Ian Jermyn Durham University
Bangti Jin University College London
Yunho Kim Ulsan national institute of science and technology (UNIST)
Nick Kingsbury University of Cambridge
Meike Kinzel Universität Münster
Lisa Maria Kreusser University of Cambridge
Gitta Kutyniok Technische Universität Berlin
Lukas Lang University of Cambridge
Stacey Levine Duquesne University
Pan Liu Cambridge Centre for Analysis; Carnegie Mellon University
John Maccormick Dickinson College, Pennsylvania; University of East Anglia
James Nagy Emory University
Mila Nikolova CNRS (Centre national de la recherche scientifique); ENS de Cachan
George Papanikos University of Nottingham
Simone Parisotto Cambridge Centre for Analysis
Marcelo Pereyra Heriot-Watt University
Gabriel Peyre CNRS - Ecole Normale Superieure Paris
Robert Plemmons Wake Forest University
Joerg Polzehl Weierstraß-Institut für Angewandte Analysis und Stochastik
Mihaela Pricop-jeckstadt Technische Universität Dresden
Erlend Skaldehaug Riis University of Cambridge
Michael Roberts University of Liverpool
Justin Romberg Georgia Institute of Technology
Lars Ruthotto Emory University
Malena Sabaté University of Bath
Carola Schönlieb University of Cambridge
Ferdia Sherry University of Cambridge
Zuoqiang Shi Tsinghua University
Jack Spencer University of Liverpool
Karsten Tabelow Weierstraß-Institut für Angewandte Analysis und Stochastik
Xue-Cheng Tai Hong Kong Baptist University
Matthew Thorpe University of Cambridge
Tuomo Valkonen University of Liverpool
Pierre Vanergheynst EPFL - Ecole Polytechnique Fédérale de Lausanne
Olga Veksler University of Western Ontario
Irene Waldspurger Université Paris-Dauphine
Pierre Weiss Université de Toulouse
Evren Yarman WesternGeco (Schlumberger)
Joo Dong Yun None / Other
Josiane Zerubia INRIA Sophia Antipolis
Kewei Zhang University of Sussex
Ozan Öktem KTH - Royal Institute of Technology; Karolinska Institute