Publications associées à Fast orthogonal sparse approximation algorithms over local dictionaries

A Structured Dictionary Perspective on Implicit Neural Representations

Pascal Frossard, Beril Besbinar, Guillermo Ortiz Jimenez, Gizem Yüce

Implicit neural representations (INRs) have recently emerged as a promising alternative to classical discretized representations of signals. Nevertheless, despite their practical success, we still do not understand how INRs represent signals. We propose a ...

IEEE COMPUTER SOC2022

Dictionary Learning for Two-Dimensional Kendall Shapes

Michaël Unser, Virginie Sophie Uhlmann, Julien René Pierre Fageot, Anna You-Lai Song

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between algorithmic simplici ...

SIAM PUBLICATIONS2020

Fourier Sampling in Signal Processing and Numerical Linear Algebra

Amir Zandieh

This thesis focuses on developing efficient algorithmic tools for processing large datasets. In many modern data analysis tasks, the sheer volume of available datasets far outstrips our abilities to process them. This scenario commonly arises in tasks incl ...

EPFL2020

MATHICSE Technical Report : Frequency-domain non-intrusive greedy Model Order Reduction based on minimal rational approximation

Fabio Nobile, Davide Pradovera

We present a technique for Model Order Reduction (MOR) of frequency-domain problems relying on rational interpolation of vector-valued functions. The selection of the sample points is carried out adaptively according to a greedy procedure. We describe seve ...

MATHICSE2020

Deep Micro-Dictionary Learning and Coding Network

Yan Yan, Wei Wang, Wei Xiao

In this paper, we propose a novel Deep Micro-Dictionary Learning and Coding Network (DDLCN). DDLCN has most of the standard deep learning layers (pooling, fully, connected, input/output, etc.) but the main difference is that the fundamental convolutional l ...

IEEE2019

A Universal Sampling Method for Reconstructing Signals with Simple Fourier Transforms

Mikhail Kapralov, Amir Zandieh

Reconstructing continuous signals based on a small number of discrete samples is a fundamental problem across science and engineering. We are often interested in signals with "simple" Fourier structure - e.g., those involving frequencies within a bounded r ...

ASSOC COMPUTING MACHINERY2019

On Matching Pursuit and Coordinate Descent

Sai Praneeth Reddy Karimireddy, Martin Jaggi, Sebastian Urban Stich, Anant Raj

Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers ...

2018

Low Frequency Sound Field Reconstruction in Non-rectangular Room: A Numerical Validation

Hervé Lissek, Etienne Thierry Jean-Luc Rivet, Vu Thach Pham

Characterization of sound fields in rooms has always been a challenging task. A faithful reconstruction of sound fields in rooms generally would require an impractically high number of microphones. At low frequencies, where sound field can be modeled as a ...

2018

Landmark-Based Shape Encoding and Sparse-Dictionary Learning in the Continuous Domain

Michaël Unser, Daniel Andreas Schmitter

We provide a generic framework to learn shape dictionaries of landmark-based curves that are defined in the continuous domain. We first present an unbiased alignment method that involves the construction of a mean shape as well as training sets whose eleme ...

2018

Fast hierarchical solvers for symmetric eigenvalue problems

Ana Susnjara

In this thesis we address the computation of a spectral decomposition for symmetric banded matrices. In light of dealing with large-scale matrices, where classical dense linear algebra routines are not applicable, it is essential to design alternative tech ...

EPFL2018

Super Resolution Phase Retrieval for Sparse Signals

Martin Vetterli, Amina Chebira, Gilles Baechler, Juri Ranieri, Miranda Krekovic

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the magnitude of its Fo ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2018

Multi-task additive models with shared transfer functions based on dictionary learning

Pascal Frossard, Alhussein Fawzi

Additive models form a widely popular class of regression models which represent the relation between covariates and response variables as the sum of low-dimensional transfer functions. Besides flexibility and accuracy, a key benefit of these models is the ...

Institute of Electrical and Electronics Engineers2017

An Adaptive Sublinear-Time Block Sparse Fourier Transform

Mikhail Kapralov, Volkan Cevher, Jonathan Mark Scarlett, Amir Zandieh

The problem of approximately computing the

k

dominant Fourier coefficients of a vector

X

quickly, and using few samples in time domain, is known as the Sparse Fourier Transform (sparse FFT) problem. A long line of work on the sparse FFT has resulted in ...

2017

Graph learning under sparsity priors

Pascal Frossard, Ntorina Thanou, Hermina Petric Maretic

Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the application domain. ...

Ieee2017

Dictionary Learning Based on Sparse Distribution Tomography

Michaël Unser, Pedram Pad

We propose a new statistical dictionary learning algorithm for sparse signals that is based on an α-stable innovation model. The parameters of the underlying model—that is, the atoms of the dictionary, the sparsity index α and the dispersion of the transfo ...

P. Pad2017

Fast Computation Of Spectral Projectors Of Banded Matrices

Daniel Kressner, Ana Susnjara

We consider the approximate computation of spectral projectors for symmetric banded matrices. While this problem has received considerable attention, especially in the context of linear scaling electronic structure methods, the presence of small relative s ...

Siam Publications2017

Dictionary learning for fast classification based on soft-thresholding

Pascal Frossard, Alhussein Fawzi

Classifiers based on sparse representations have recently been shown to provide excellent results in many visual recognition and classification tasks. However, the high cost of computing sparse representations at test time is a major obstacle that limits t ...

Springer2015

A Fast Hadamard Transform for Signals with Sub-linear Sparsity in the Transform Domain

Martin Vetterli, Robin Scheibler, Saeid Haghighatshoar

In this paper, we design a new iterative low-complexity algorithm for computing the Walsh-Hadamard transform (WHT) of an N dimensional signal with a K-sparse WHT. We suppose that N is a power of two and K = O(N^α), scales sub-linearly in N for some α ∈ (0, ...

Institute of Electrical and Electronics Engineers2015

Transformation-Invariant Dictionary Learning for Classification with 1-Sparse Representations

Pascal Frossard, Elif Vural, Ahmet Caner Yüzügüler

Sparse representations of images in well-designed dictionaries can be used for effective classification. Meanwhile, training data available in most realistic settings are likely to be exposed to geometric transformations, which poses a challenge for the de ...

2014

Jump-Sparse and Sparse Recovery Using Potts Functionals

Martin Kurt Storath

We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals. We obtain analytical results (existence of minimizers, complexity) on inverse Potts functionals and pr ...

Ieee-Inst Electrical Electronics Engineers Inc2014