Publications

List of papers ordered by popularity Papers and Citation info

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 […]

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 […]

Multiscale Texture Orientation Analysis using Spectral Total-Variation Decomposition

D. Horesh, G. Gilboa, “Multiscale orientation detection using the total variation transform”, Proc. Scale Space and Variational Methods in Computer Vision (SSVM), 2015. Abstract: Multi-level texture separation can considerably improve texture analysis, a significant component in many computer vision tasks. This paper aims at obtaining precise local texture orientations of images in a multiscale manner, […]

Fundamentals of Non-local Total Variation Spectral Theory

J.-F. Aujol, G. Gilboa, N. Papadakis, “Non local total variation spectral framework”, Proc. Scale Space and Variational Methods in Computer Vision (SSVM), 2015. Abstract: Eigenvalue analysis based on linear operators has been extensively used in signal and image processing to solve a variety of problems such as segmentation, dimensionality reduction and more. Recently, nonlinear spectral […]

A Total Variation Spectral Framework for Scale and Texture Analysis

G. Gilboa, “A Total Variation Spectral Framework for Scale and Texture Analysis”, SIAM Journal on Imaging Sciences, Vol. 7, No. 4, pp. 1937–1961, 2014. Abstract: A new total variation (TV) spectral framework is presented. A TV transform is proposed which can be interpreted as a spectral domain, where elementary TV features, like disks, approach impulses. A […]

Nonlinear Band-Pass Filtering Using the TV Transform

G. Gilboa, “Nonlinear Band-Pass Filtering Using the TV Transform”, Proc. European Signal Processing Conference (EUSIPCO-2014), Lisbon, pp. 1696 – 1700, 2014. Abstract: A distinct family of nonlinear filters is presented. It is based on a new formalism, defining a nonlinear transform based on the TV-functional. Scales in this sense are related to the size of the object and […]

Report on the Total Variation Spectral Framework

G. Gilboa, “A Total Variation Spectral Framework for Scale and Texture Analysis”, CCIT Report 833, 2013. Abstract: A new total variation (TV) spectral framework is presented. A TV transform is proposed which can be interpreted as a spectral domain, where elementary TV features, like disks, approach impulses. A reconstruction formula from the pectral to the spatial […]

A Spectral Approach to Total Variation

G. Gilboa, “A spectral approach to total variation”, Scale-Space and Variational Methods, SSVM 2013, LNCS 7893, p. 36-47, 2013. Abstract: The total variation (TV) functional is explored from a spectral perspective. We formulate a TV transform based on the second time derivative of the total variation flow, scaled by time. In the transformation domain disks yield impulse […]

Expert regularizers for task specific processing

G. Gilboa, “Expert regularizers for task specific processing”, Scale-Space and Variational Methods, SSVM 2013, LNCS 7893, p. 24-35, 2013 Abstract: This study is concerned with constructing expert regularizers for specific tasks. We discuss the general problem of what is desired from a regularizer, when one knows the type of images to be processed. The aim is to improve […]

Nonlocal linear image regularization and supervised segmentation

G. Gilboa, S. Osher, “Nonlocal linear image regularization and supervised segmentation”, SIAM Multiscale Mod. Simul. (MMS), Vol. 6, No. 2, pp. 595-630, 2007. Abstract A nonlocal quadratic functional of weighted differences is examined. The weights are based on image features and represent the affinity between different pixels in the image. By prescribing different formulas for the weights, one […]

Nonlinear Scale Space with Spatially Varying Stopping Time

G. Gilboa, “Nonlinear Scale Space with Spatially Varying Stopping Time”, PAMI, Vol. 30, No. 12, pp. 2175-2187, 2008. Abstract: A general scale space algorithm is presented for denoising signals and images with spatially varying dominant scales. The process is formulated as a partial differential equation with spatially varying time. The proposed adaptivity is semi-local and is in conjunction with the […]

Estimation of optimal PDE-based denoising in the SNR sense

G. Gilboa, N. Sochen, Y.Y. Zeevi, “Estimation of optimal PDE-based denoising in the SNR sense”, IEEE Trans. on Image Processing Vol. 15, No. 8, pp. 2269-2280, 2006. Abstract: This paper is concerned with finding the best PDE-based denoising process, out of a set of possible ones. We focus either on finding the proper weight of the fidelity term […]

Nonlocal Convex Functionals for Image Regularization

G. Gilboa, J. Darbon, S. Osher and T. Chan, Nonlocal Convex Functionals for Image Regularization. UCLA CAM Report 06-57 Abstract: We examine weighted nonlocal convex functionals. The weights determine the affinities between different regions in the image and are computed according to image features. The L1 energy of this type can be viewed as a nonlocal extension of […]

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