Matching Pursuit With Block Incoherent Dictionaries

Peotta, Lorenzo

doi:10.1109/tsp.2007.896022

Cited by 17 publications

(13 citation statements)

References 20 publications

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“…We present extensions of the BP, the matching pursuit (MP), and the OMP algorithms to the block-sparse case and prove corresponding performance guarantees. We point out that the term block-coherence was used previously in [31] in the context of quantifying the recovery performance of the MP algorithm in block-incoherent dictionaries. Our definition pertains to block-versions of the MP and the OMP algorithm and is different from that used in [31].…”

Section: Introductionmentioning

confidence: 99%

Block-Sparse Signals: Uncertainty Relations and Efficient Recovery

Eldar

Kuppinger

Bölcskei

2010

IEEE Trans. Signal Process.

1,187

1,015

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Abstract-We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. An uncertainty relation for block-sparse signals is derived, based on a block-coherence measure, which we introduce. We then show that a block-version of the orthogonal matching pursuit algorithm recovers block k-sparse signals in no more than k steps if the block-coherence is sufficiently small. The same condition on block-coherence is shown to guarantee successful recovery through a mixed 2/ 1-optimization approach. This complements previous recovery results for the block-sparse case which relied on small block-restricted isometry constants. The significance of the results presented in this paper lies in the fact that making explicit use of block-sparsity can provably yield better reconstruction properties than treating the signal as being sparse in the conventional sense, thereby ignoring the additional structure in the problem.

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Section: Introductionmentioning

confidence: 99%

Block-Sparse Signals: Uncertainty Relations and Efficient Recovery

Eldar

Kuppinger

Bölcskei

2010

IEEE Trans. Signal Process.

1,187

1,015

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“…The parameter ρ thus controls the degree of regressor coherence, 0 ≤ ρ ≤ 1. Figure 1 verifies the stationary performance of the proposed method in comparison with the non-recursive group-SPICE, the standard SPICE, the group-LASSO with an oracle choice of hyperparameter, as well as the (greedy) block matching pursuit [28] and block orthogonal matching pursuit [29]. The results are based on 500 Monte-Carlo (MC) simulations of N = 100 samples with…”

Section: Numerical Resultsmentioning

confidence: 72%

Online group-sparse estimation using the covariance fitting criterion

Kronvall

Adalbjörnsson

Nadig

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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In this paper, we present a time-recursive implementation of a recent hyperparameter-free group-sparse estimation technique. This is achieved by reformulating the original method, termed group-SPICE, as a square-root group-LASSO with a suitable regularization level, for which a time-recursive implementation is derived. Using a proximal gradient step for lowering the computational cost, the proposed method may effectively cope with data sequences consisting of both stationary and non-stationary signals, such as transients, and/or amplitude modulated signals. Numerical examples illustrates the efficacy of the proposed method for both coherent Gaussian dictionaries and for the multi-pitch estimation problem.

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“…In [22], the authors provide a new analysis of Matching Pursuit, when the dictionary is built from an incoherent union of possibly coherent subdictionaries. A sufficient condition that guarantees the selection of atoms from the correct subdictionaries is shown.…”

Section: Recovery Condition For Bc-ompmentioning

confidence: 99%

Multitask Additive Models With Shared Transfer Functions Based on Dictionary Learning

Fawzi

Sinn

Frossard

2017

IEEE Trans. Signal Process.

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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 their interpretability: the transfer functions provide visual means for inspecting the models and identifying domain-specific relations between inputs and outputs. However, in large-scale problems involving the prediction of many related tasks, learning independently additive models results in a loss of model interpretability, and can cause overfitting when training data is scarce. We introduce a novel multi-task learning approach which provides a corpus of accurate and interpretable additive models for a large number of related forecasting tasks. Our key idea is to share transfer functions across models in order to reduce the model complexity and ease the exploration of the corpus. We establish a connection with sparse dictionary learning and propose a new efficient fitting algorithm which alternates between sparse coding and transfer function updates. The former step is solved via an extension of Orthogonal Matching Pursuit, whose properties are analyzed using a novel recovery condition which extends existing results in the literature. The latter step is addressed using a traditional dictionary update rule. Experiments on realworld data demonstrate that our approach compares favorably to baseline methods while yielding an interpretable corpus of models, revealing structure among the individual tasks and being more robust when training data is scarce.Our framework therefore extends the well-known benefits of additive models to common regression settings possibly involving thousands of tasks. Index TermsAdditive models, nonparametric regression, dictionary learning, sparse representations, multi-task learning.

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Matching Pursuit With Block Incoherent Dictionaries

Abstract: Abstract-

Cited by 17 publications

References 20 publications

Block-Sparse Signals: Uncertainty Relations and Efficient Recovery

Block-Sparse Signals: Uncertainty Relations and Efficient Recovery

Online group-sparse estimation using the covariance fitting criterion

Multitask Additive Models With Shared Transfer Functions Based on Dictionary Learning

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