Publications associées à Matrix unit

Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

Nicolas Macris, Jean François Emmanuel Barbier

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...

AMER PHYSICAL SOC2022

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Daniel Kuhn, Tobias Sutter, Wouter Jongeneel

We propose a principled method for projecting an arbitrary square matrix to the non- convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and ...

2023

Fast recovery and approximation of hidden Cauchy structure

Robert Gerhard Jérôme Luce

We derive an algorithm of optimal complexity which determines whether a given matrix is a Cauchy matrix, and which exactly recovers the Cauchy points defining a Cauchy matrix from the matrix entries. Moreover, we study how to approximate a given matrix by ...

Elsevier Science Inc2016

Design of Steerable Wavelets to Detect Multifold Junctions

Michaël Unser, Cédric René Jean Vonesch, Zsuzsanna Püspöki, Virginie Sophie Uhlmann

We propose a framework for the detection of junctions in images. Although the detection of edges and key points is a well examined and described area, the multiscale detection of junction centers, especially for odd orders, poses a challenge in pattern ana ...

IEEE2015

Randomized Extended Kaczmarz For Solving Least Squares

Nikolaos Freris

We present a randomized iterative algorithm that exponentially converges in the mean square to the minimum l(2)-norm least squares solution of a given linear system of equations. The expected number of arithmetic operations required to obtain an estimate o ...

Society for Industrial and Applied Mathematics2013

Multi-Way Compressed Sensing for Sparse Low-Rank Tensors

Anastasios Kyrillidis

For linear models, compressed sensing theory and methods enable recovery of sparse signals of interest from few measurements-in the order of the number of nonzero entries as opposed to the length of the signal of interest. Results of similar flavor have mo ...

IEEE Institute of Electrical and Electronics Engineers2012

Average case analysis of sparse recovery with Thresholding: New bounds based on average dictionary coherence

Pierre Vandergheynst, Mohammad Golbabaee

This paper analyzes the performance of the simple thresholding algorithm for sparse signal representations. In particular, in order to be more realistic we introduce a new probabilistic signal model which assumes randomness for both the amplitude and also ...

2008