Weighted sparse signal decomposition

Babaie‐Zadeh, Massoud; Mehrdad, Behzad; Giannakis, Georgios B.

doi:10.1109/icassp.2012.6288652

Cited by 6 publications

(10 citation statements)

References 13 publications

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“…This problem is studied in [6] under the title "weighted sparse decomposition". It defines the weighted 0 -norm as…”

Section: Introductionmentioning

confidence: 99%

“…In [6] all the assigned weights are assumed to be positive. However, in some applications there might be a need to consider negative weights as well.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, assume that the p i = Pr (s i 0) has a Bernoulli distribution, and the probability of its activity, p i , is known a priori. As [6] shows, the MAP estimation for this problem can be achieved by solving a P 0,w problem with the weights…”

Section: Introductionmentioning

confidence: 99%

“…The paper is organized as follows: In the next section, we study the uniqueness condition of our problem and, using WSL0 algorithm [6], we will verify the condition numerically. In Section III, we provide an application example for our problem.…”

Section: Introductionmentioning

confidence: 99%

“…However, in some applications, one may want to assign different priorities to different atoms for being included in the decomposition. This results to the so called "weighted sparse decomposition" problem [Babaie-Zadeh et al 2012]. However, Babaie-Zadeh et al studied this problem only for positive weights; but in some applications (e.g.…”

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confidence: 99%

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A generalization of weighted sparse decomposition to negative weights

Delfi

Aziznejad

Amani

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Sparse solutions of underdetermined linear systems of equations are widely used in different fields of signal processing. This problem can also be seen as a sparse decomposition problem. Traditional sparse decomposition gives the same priority to all atoms for being included in the decomposition or not. However, in some applications, one may want to assign different priorities to different atoms for being included in the decomposition. This results to the so called "weighted sparse decomposition" problem [Babaie-Zadeh et al. 2012]. However, Babaie-Zadeh et al. studied this problem only for positive weights; but in some applications (e.g. classification) better performance can be obtained if some weights become negative. In this paper, we consider "weighted sparse decomposition" problem in its general form (positive and negative weights). A tight uniqueness condition and some applications for the general case will be presented.

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“…This problem is studied in [6] under the title "weighted sparse decomposition". It defines the weighted 0 -norm as…”

Section: Introductionmentioning

confidence: 99%

“…In [6] all the assigned weights are assumed to be positive. However, in some applications there might be a need to consider negative weights as well.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

A generalization of weighted sparse decomposition to negative weights

Delfi

Aziznejad

Amani

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

Self Cite

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Integrated Analysis of EEG and fMRI Using Sparsity of Spatial Maps

2016

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Integration of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) is an open problem, which has motivated many researches. The most important challenge in EEG-fMRI integration is the unknown relationship between these two modalities. In this paper, we extract the same features (spatial map of neural activity) from both modality. Therefore, the proposed integration method does not need any assumption about the relationship of EEG and fMRI. We present a source localization method from scalp EEG signal using jointly fMRI analysis results as prior spatial information and source separation for providing temporal courses of sources of interest. The performance of the proposed method is evaluated quantitatively along with multiple sparse priors method and sparse Bayesian learning with the fMRI results as prior information. Localization bias and source distribution index are used to measure the performance of different localization approaches with or without a variety of fMRI-EEG mismatches on simulated realistic data. The method is also applied to experimental data of face perception of 16 subjects. Simulation results show that the proposed method is significantly stable against the noise with low localization bias. Although the existence of an extra region in the fMRI data enlarges localization bias, the proposed method outperforms the other methods. Conversely, a missed region in the fMRI data does not affect the localization bias of the common sources in the EEG-fMRI data. Results on experimental data are congruent with previous studies and produce clusters in the fusiform and occipital face areas (FFA and OFA, respectively). Moreover, it shows high stability in source localization against variations in different subjects.

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