Blind Source Separation by Sparse Decomposition in a Signal Dictionary

By Michael Zibulevsky, Barak A. Pearlmutter. 2001

859 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Signal Processing

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In Signal Processing

Citations in the corpus

The Sound of Pixels (2018, background): “While auditory scene analysis [1] is widely studied in the fields of environmental sound recognition [2,3] and source separation [4,5,6,7,8,9], the natural synchronization between vision and sound can provide a rich supervisory signal for grounding sounds in vision [10,11,12].”
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images (2009, background): “Can we separate the two sources? Such source separation problems are fundamental in the processing of acoustic signals, for example, in the separation of speech from impulsive noise by independent component analysis (ICA) algorithms [94, 164, 109].”
On the Identifiability of Overcomplete Dictionaries via the Minimisation Principle Underlying K-SVD (2013, background): “In [2] the authors themselves state that the algorithm is only of theoretical interest and also the (cid:96) 1 -minimisation principle, suggested in [35], [24] and studied in [17], [14], [18], is not suitable for very high-dimensional data.”
Learning Sparsifying Transforms (2013, background): “However, the transform learning Problem (P3) performs poorly in signal processing applications in the absence of the crucial penalty, which as discussed earlier, helps overcome the scale ambiguity and control the condition number.”
Task-Driven Dictionary Learning (2010, background): “…dictionary instead of a pre-deﬁned one—based on wavelets [1] for example—has recently led to state-of-the-art results in numerous low-level signal processing tasks such as image denoising [2], [3], [4], audio processing [5], [6], as well as classiﬁcation tasks [7], [8], [9], [10], [11], [12].”
Independent component analysis: recent advances (2013, methodology): “Related methods with non-Gaussian models for the atoms were developed by Zibulevsky and Pearlmutter (2001), and adaptation of the time-frequency decomposition was considered by Pham and Cardoso (2003); Kisilev et al. (2003); see (Gribonval and Zibulevsky, 2010) for a review.”
Blind Haze Separation (2006, methodology): “This prior of image statistics can be exploited for the entropy estimation needed in the optimization [1, 35].”
A Block Coordinate Descent Method for Regularized Multiconvex Optimization with Applications to Nonnegative Tensor Factorization and Completion (2013, background): “Assuming s 1 , · · · , s n are sparse under some dictionary B ∈ R T × p , namely, s i = y i B and y i ∈ R 1 × T is sparse for i = 1 , . . . , n , [12,79] use the sparse BSS model min where for a certain covariance matrix C .”
A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed $\ell ^{0}$ Norm (2008, background): “The second step requires that for each sample ( t0) the sparse solution of the USLE x(t0) = As(t0) be found [1], [2], [22], [23].”
Learning to Separate Object Sounds by Watching Unlabeled Video (2018, methodology): “Popular approaches include Independent Component Analysis (ICA) [36], sparse decomposition [78], Computational Auditory Scene Analysis (CASA) [21], non-negative matrix factorization (NMF) [23,24,46,69], probabilistic latent variable models [34,61], and deep learning [32,35].”
Upper Limits on the 21 cm Epoch of Reionization Power Spectrum from One Night with LOFAR (2017, methodology): “…modes from the data-cubes in Stokes I and any remaining instrumental polarization leakage in Stokes V. GMCA is a blind source separation technique introduced by Zibulevsky & Pearlmutter (2001), which uses as few assumptions about the data as possible in order to form a model of the foregrounds.”