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Redundancy in Non-Orthogonal Transforms

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On the Density of Coprime Tuples of the Form (n, ⌊f1(n)⌋, …, ⌊fk(n)⌋), Where f_1, …, f_k Are Functions from a Hardy Field

Florian Karl Richter

Let k∈Nk∈Nk \in \mathbb{N} and let f1, …, f k belong to a Hardy field. We prove that under some natural conditions on the k-tuple ( f1, …, f k ) the density of the set {n∈N:gcd(n,⌊f1(n)⌋,…,⌊fk(n)⌋)=1}{n∈N:gcd(n,⌊f1(n)⌋,…,⌊fk(n)⌋)=1}\displaystyle{\big{n \i ...

Springer International Publishing2017

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

Multi-Graph Learning of Spectral Graph Dictionaries

Pascal Frossard

We study the problem of learning constitutive features for the effective representation of graph signals, which can be considered as observations collected on different graph topologies. We propose to learn graph atoms and build graph dictionaries that pro ...

2015

Dictionary Learning Over Distributed Models

Ali H. Sayed

In this paper, we consider learning dictionary models over a network of agents, where each agent is only in charge of a portion of the dictionary elements. This formulation is relevant in Big Data scenarios where large dictionary models may be spread over ...

IEEE2015

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

Online dictionary learning over distributed models

Ali H. Sayed

In this paper, we consider learning dictionary models over a network of agents, where each agent is only in charge of a portion of the dictionary elements. This formulation is relevant in big data scenarios where multiple large dictionary models may be spr ...

IEEE2014

LAYOUT ASSESSMENT METHOD AND SYSTEM

Frank Grégoire Jean de Morsier, Virginia Estellers Casas, Nathalie Casati, Maria Gabrani

Candidate layout patterns can be assessed using a sparse pattern dictionary of known design layout patterns by determining sparse coefficients for each candidate pattern, reconstructing the respective candidate pattern, and determining reconstruction error ...

U.S. Patent and Trademark Office; U.S. DEPARTMENT OF COMMERCE2013

Sparse Approximation Using M-Term Pursuit and Application in Image and Video Coding

Pascal Frossard, Pierre Vandergheynst, Adel Rahmoune

This paper introduces a novel algorithm for sparse approximation in redundant dictionaries called the M-term pursuit (MTP). This algorithm decomposes a signal into a linear combination of atoms that are selected in order to represent the main signal compon ...

Institute of Electrical and Electronics Engineers2012

Greedy Dictionary Selection for Sparse Representation

Volkan Cevher, Andreas Krause

We develop an efficient learning framework to construct signal dictionaries for sparse representation by selecting the dictionary columns from multiple candidate bases. By sparse, we mean that only a few dictionary elements, compared to the ambient signal ...

2011

Dictionary learning in stereo imaging

Pascal Frossard, Ivana Tosic

This paper presents a new method for learning overcomplete dictionaries adapted to efficient joint representation of stereo images. We first formulate a sparse stereo image model where the multi-view correlation is described by local geometric transforms o ...

Institute of Electrical and Electronics Engineers2011