Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Machine Learning
Adaptive signal models: theory, algorithms, and audio applications
Adaptive signal models: theory, algorithms, and audio applications
Convex Optimization
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Matching pursuit and atomic signal models based on recursive filterbanks
IEEE Transactions on Signal Processing
Fast orthogonal least squares algorithm for efficient subset modelselection
IEEE Transactions on Signal Processing
Stochastic time-frequency dictionaries for matching pursuit
IEEE Transactions on Signal Processing
Dark Energy in Sparse Atomic Estimations
IEEE Transactions on Audio, Speech, and Language Processing
Sparse and structured decompositions of signals with the molecular matching pursuit
IEEE Transactions on Audio, Speech, and Language Processing
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Matching Pursuits with random sequential subdictionaries
Signal Processing
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In the pursuit of a sparse signal model, mismatches between the signal and the dictionary, as well as atoms poorly selected by the decomposition process, can diminish the efficiency and meaningfulness of the resulting representation. These problems increase the number of atoms needed to model a signal for a given error, and they obscure the relationships between signal content and the elements of the model. To increase the efficiency and meaningfulness of a signal model built by an iterative descent pursuit, such as matching pursuit (MP), we propose integrating into its atom selection criterion a measure of interference between an atom and the model. We define interference and illustrate how it describes the contribution of an atom to modeling a signal. We show that for any nontrivial signal, the convergent model created by MP must have as much destructive as constructive interference, i.e., MP cannot avoid correction in the signal model. This is not necessarily a shortcoming of orthogonal variants of MP, such as orthogonal MP (OMP). We derive interference-adaptive iterative descent pursuits and show how these can build signal models that better fit the signal locally, and reduce the corrections made in a signal model. Compared with MP and its orthogonal variants, our experimental results not only show an increase in model efficiency, but also a clearer correspondence between the signal and the atoms of a representation.