Publications related to Nondyadic and nonlinear multiresolution image approximations

Eigendecomposition-Free Training of Deep Networks for Linear Least-Square Problems

Pascal Fua, Mathieu Salzmann, Zheng Dang, Kwang Moo Yi, Fei Wang, Yinlin Hu

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector corresponding to the smal ...

IEEE COMPUTER SOC2021

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Nicolas Henri Bernard Flammarion, Aditya Vardhan Varre, Loucas Pillaud-Vivien

Motivated by the recent successes of neural networks that have the ability to fit the data perfectly \emph{and} generalize well, we study the noiseless model in the fundamental least-squares setup. We assume that an optimum predictor fits perfectly inputs ...

2021

Frequency-Domain Diffusion Adaptation Over Networks

Ali H. Sayed, Ricardo Merched, Shuo Zhang

This paper analyzes the implementation of least-mean-squares (LMS)-based, adaptive diffusion algorithms over networks in the frequency-domain (FD). We focus on a scenario of noisy links and include a moving-average step for denoising after self-learning to ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Superluminal Motion-Assisted Four-Dimensional Light-in-Flight Imaging

Edoardo Charbon, Andrei Ardelean, Ming-Lo Wu, Kazuhiro Morimoto

Advances in high-speed imaging techniques have opened new possibilities for capturing ultrafast phenomena such as light propagation in air or through media. Capturing light in flight in three-dimensional xyt space has been reported based on various types o ...

AMER PHYSICAL SOC2021

Shortest-support multi-spline bases for generalized sampling

Michaël Unser, Alexis Marie Frederic Goujon, Shayan Aziznejad, Alireza Naderi

Generalized sampling consists in the recovery of a function f, from the samples of the responses of a collection of linear shift-invariant systems to the input f . The reconstructed function is typically a member of a finitely generated integer-shift invar ...

2021

Convergence of adaptive algorithms for constrained weakly convex optimization

Volkan Cevher, Ahmet Alacaoglu, Yurii Malitskyi

We analyze the adaptive first order algorithm AMSGrad, for solving a constrained stochastic optimization problem with a weakly convex objective. We prove the

\tilde O(t^{-1/2})

rate of convergence for the squared norm of the gradient of Moreau envelope, ...

2021

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...

EPFL2020

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

Michaël Unser, Pakshal Narendra Bohra

We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Convergences of Regularized Algorithms and Stochastic Gradient Methods with Random Projections

Volkan Cevher, Junhong Lin

We study the least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space as a special case. We rst investigate regularized algorithms adapted to a projection operator on a closed subspace ...

2020

Coordinate Difference Matrices

Martin Vetterli, Gilles Baechler, Miranda Krekovic, Golnooshsadat Elhami

In many problems such as phase retrieval, molecular biology, source localization, and sensor array calibration, one can measure vector differences between pairs of points and attempt to recover the position of these points; this class of problems is called ...

SIAM PUBLICATIONS2020

Nondyadic and nonlinear multiresolution image approximations

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Eigendecomposition-Free Training of Deep Networks for Linear Least-Square Problems

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Frequency-Domain Diffusion Adaptation Over Networks

Superluminal Motion-Assisted Four-Dimensional Light-in-Flight Imaging

Shortest-support multi-spline bases for generalized sampling

Convergence of adaptive algorithms for constrained weakly convex optimization

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

Convergences of Regularized Algorithms and Stochastic Gradient Methods with Random Projections

Coordinate Difference Matrices

Eigendecomposition-Free Training of Deep Networks for Linear Least-Square Problems

Superluminal Motion-Assisted Four-Dimensional Light-in-Flight Imaging

Frequency-Domain Diffusion Adaptation Over Networks

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Convergences of Regularized Algorithms and Stochastic Gradient Methods with Random Projections

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Coordinate Difference Matrices

Convergence of adaptive algorithms for constrained weakly convex optimization

Shortest-support multi-spline bases for generalized sampling