# Whats New

## Total-Variation – Fast Gradient Flow and Relations to Koopman Theory

Ido Cohen, Tom Berkov,  arXiv preprint  Code Abstract The space-discrete Total Variation (TV) flow is analyzed using several mode decomposition techniques. In the one-dimensional case, we provide analytic formulations to Dynamic Mode Decomposition (DMD) and to Koopman Mode Decomposition (KMD) of the TV-flow and compare the obtained modes to TV spectral decomposition. We propose a […]

## A Pseudo-Inverse for Nonlinear Operators

Eyal Gofer, Guy Gilboa,  arXiv preprint    Abstract The Moore-Penrose inverse is widely used in physics, statistics and various fields of engineering. Among other characteristics, it captures well the notion of inversion of linear operators in the case of overcomplete data. In data science, nonlinear operators are extensively used. In this paper we define and […]

## PhIT-Net: Photo-consistent Image Transform for Robust Illumination Invariant Matching

The 32nd British Machine Vision Conference (BMVC), Nov. 2021. Damian Kaliroff and Guy Gilboa BMVC link to paper, video and code Abstract We propose a new and completely data-driven approach for generating a photo- consistent image transform. We show that simple classical algorithms which operate in the transform domain become extremely resilient to illumination changes. […]

## Adaptive LiDAR Sampling and Depth Completion using Ensemble Variance

Accepted to IEEE Trans. Image Processing, 2021.   Eyal Gofer, Shachar Praisler, Guy Gilboa,  arXiv  Project details Abstract This work considers the problem of depth completion, with or without image data, where an algorithm may measure the depth of a prescribed limited number of pixels. The algorithmic challenge is to choose pixel positions strategically and […]

## Examining the Limitations of Dynamic Mode Decomposition through Koopman Theory Analysis

Ido Cohen, Guy Gilboa, arXiv preprint 2107.07456, 2021   Abstract This work binds the existence of Koopman Eigenfunctions (KEF’s), the geometric of the dynamics, and the validity of Dynamic Mode Decomposition (DMD) to one coherent theory. Viewing the dynamic as a curve in the state-space allows us to formulate an existence condition of KEF’s and […]

## Total-Variation Mode Decomposition

Ido Cohen, Tom Berkov, Guy Gilboa, “Total-Variation Mode Decomposition”,  Proc. SSVM 2021, pp. 52-64 Abstract In this work we analyze the Total Variation (TV) flow applied to one dimensional signals. We formulate a relation between Dynamic Mode Decomposition (DMD), a dimensionality reduction method based on the Koopman operator, and the spectral TV decomposition. DMD is adapted by time rescaling […]

## Nonlinear Spectral Processing of Shapes via Zero-homogeneous Flows

Jonathan Brokman, Guy Gilboa, Proc. SSVM, “Nonlinear Spectral Processing of Shapes via Zero-homogeneous Flows”, pp. 40-51, 2021 Abstract In this work we extend the spectral total-variation framework, and use it to analyze and process 2D manifolds embedded in 3D. Analysis is performed in the embedding space – thus “spectral arithmetics” manipulate the shape directly. This […]

## Nonlinear Power Method for Computing Eigenvectors of Proximal Operators and Neural Networks

Accepted to SIAM J. on Imaging Scienes, 2021 Leon Bungert,  Ester Hait-Fraenkel , Nicolas Papadakis and Guy Gilboa, arXiv Neural networks have revolutionized the field of data science, yielding remarkable solutions in a data-driven manner.  For instance, in the field of mathematical imaging, they have surpassed traditional methods based on convex regularization. However, a fundamental […]

## Modes of Homogeneous Gradient Flows

Accepted to SIAM J. on Imaging Sciences, 2021   Ido Cohen, Omri Azencot, Pavel Lifshitz, Guy Gilboa, arXiv, July 2020   Finding latent structures in data is drawing increasing attention in broad and diverse fields such as fluid dynamics, signal processing, and machine learning. In this work, we formulate Dynamic Mode Decomposition (DMD) for two types […]

## Revealing stable and unstable modes of denoisers through nonlinear eigenvalue analysis

Ester Hait-Fraenkel, Guy Gilboa, Revealing stable and unstable modes of denoisers through nonlinear eigenvalue analysis. J. Vis. Commun. Image Represent. 75: 103041 (2021) Ester Hait-Fraenkel, Guy Gilboa, arXiv In this paper, we propose to analyze stable and unstable modes of generic image denoisers through nonlinear eigenvalue analysis. We attempt to find input images for which […]

## Experts with Lower-Bounded Loss Feedback: A Unifying Framework

Eyal Gofer, Guy Gilboa,  arxiv preprint The most prominent feedback models for the best expert problem are the full information and bandit models. In this work we consider a simple feedback model that generalizes both, where on every round, in addition to a bandit feedback, the adversary provides a lower bound on the loss of […]

## New Book

Many thanks to the whole group for contributing, commenting and proof-reading the new book. The online version can be downloaded at the Springer site

## Horizon 2020 RISE grant started March 2018

A 4 year grant NoMADS,  Nonlocal Methods for Arbitrary Data Sources, as part of the RISE program, started on March 2018. Includes Collaboration between universities (Munster, Cambridge, UCLA, Bordeaux, Carnegie Mellon, Technion and more..) and industry.

## Paper of Raz & Guy accepted

The paper, based on the master thesis of Raz Nossek is now accepted (Sept 2017): R. Nossek & G. Gilboa, “Flows generating nonlinear eigenfunctions”, Journal of Scientific Computing. (a pdf of the accepted version will be published soon, see arXiv version)

## TIP Paper of Ety

Ety’s paper in IEEE Trans. on Image Processing is published, “Blind Facial Image Quality Enhancement Using Non-Rigid Semantic Patches “.

## Workshop in Cambridge Sept 2017

Tal and Guy participated in a workshop in Cambridge (Newton Institute) on Variational methods, new optimisation techniques and new fast numerical algorithms. Tal presented a poster on Spectral TV Hashing. Guy presented a talk: Nonlinear spectral analysis – beyond the convex case

## Workshop at Oberwolfach Math Institute, Germany, Jan 2016

Participating in a workshop on Mathematical Imaging and Surface Processing at the Oberwolfach Math Institute, Germany, January 2016.

## Postdoc position

Requirements Strong mathemetical and theoretical background. Knowledge in PDE’s, variational methods and convex analysis. PhD from departments of Applied Math/EE/CS. Solid publication record. Creativity. Knowledge in image processing – an advantage (not a must). Knowledge in Matlab – an advantage (not a must). English – high writing and speaking skills. Description of Position Performing research […]

## SIAM Conf on Imaging Sciences, Albuquerque, USA, May 2016

Giving 2 talks (and being a co-author in 3 others) in SIAM Conf on Imaging Sciences.

## Talk at Cambridge (Oct 2015)

Talk at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, at the Applied and Computational Analysis Seminar on “Processing Textures in the Spectral Total-Variation Domain”, Oct. 2015.

## Talk at the International Applied Math Congress, ICIAM (Aug. 2015)

The International Congress on Industrial and Applied Mathematics (ICIAM) is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics. From August 10 to 14, 2015, mathematicians from around the world will gather in Beijing, China for the 8th […]

## SSVM 2015 presentations (June 2015)

Presenting papers in Scale Space and Variational Methods in Computer Vision (SSVM) in Lège Cap Ferret, France (June 2015).

## Matlab Code Section

Matlab code of some articles is given in a new Code section.

## Talk at the Applied Math Seminar, Technion (Nov. 2014)

See more details.

## Talk at RICAM, Linz (Oct. 2014)

I will be giving a talk at RICAM (Radon Institute for Computational and Applied Mathematics) in October. This is part of the Special Semester on New Trends in Calculus of Variations and is within the second workshop on Variational Methods in Imaging.

## 3D Lab Now Open

The renovation of the 3D Lab is finished! (July 2014) New projects concerning 3D video processing and analysis are planned to be conducted in the lab. It is located on the 6th floor of Meyer Bldg (room 661) and is part of the VISL lab.   The 3D animation is thanks to Jason Hise.

## TCE talk

See more on the Technion TCE confernce . Abstract of the talk Peeling Images – A Structured Layer Representation Using the TV Transform

## SIAM Imaging Science Conference

The talk is given in Hong-Kong on May at SIAM-IS 2014 on texture analysis of color images using the TV transform (within the minisymposium on Color Perception and Image Enhancement, see program) .