Sparse Modeling of Grouped Line Spectra
(2015) Abstract
 This licentiate thesis focuses on clustered parametric models for estimation of line spectra, when the spectral content of a signal source is assumed to exhibit some form of grouping. Different from previous parametric approaches, which generally require explicit knowledge of the model orders, this thesis exploits sparse modeling, where the orders are implicitly chosen. For line spectra, the nonlinear parametric model is approximated by a linear system, containing an overcomplete basis of candidate frequencies, called a dictionary, and a large set of linear response variables that selects and weights the components in the dictionary. Frequency estimates are obtained by solving a convex optimization program, where the sum of squared... (More)
 This licentiate thesis focuses on clustered parametric models for estimation of line spectra, when the spectral content of a signal source is assumed to exhibit some form of grouping. Different from previous parametric approaches, which generally require explicit knowledge of the model orders, this thesis exploits sparse modeling, where the orders are implicitly chosen. For line spectra, the nonlinear parametric model is approximated by a linear system, containing an overcomplete basis of candidate frequencies, called a dictionary, and a large set of linear response variables that selects and weights the components in the dictionary. Frequency estimates are obtained by solving a convex optimization program, where the sum of squared residuals is minimized. To discourage overfitting and to infer certain structure in the solution, different convex penalty functions are introduced into the optimization. The cost tradeoff between fit and penalty is set by some user parameters, as to approximate the true number of spectral lines in the signal, which implies that the response variable will be sparse, i.e., have few nonzero elements. Thus, instead of explicit model orders, the orders are implicitly set by this tradeoff. For grouped variables, the dictionary is customized, and appropriate convex penalties selected, so that the solution becomes group sparse, i.e., has few groups with nonzero variables. In an array of sensors, the specific timedelays and attenuations will depend on the source and sensor positions. By modeling this, one may estimate the location of a source. In this thesis, a novel joint location and grouped frequency estimator is proposed, which exploits sparse modeling for both spectral and spatial estimates, showing robustness against sources with overlapping frequency content. For audio signals, this thesis uses two different features for clustering. Pitch is a perceptual property of sound that may be described by the harmonic model, i.e., by a group of spectral lines at integer multiples of a fundamental frequency, which we estimate by exploiting a novel adaptive total variation penalty. The other feature, chroma, is a concept in musical theory, collecting pitches at powers of 2 from each other into groups. Using a chroma dictionary, together with appropriate group sparse penalties, we propose an automatic transcription of the chroma content of a signal. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8046494
 author
 Kronvall, Ted ^{LU}
 supervisor

 Andreas Jakobsson ^{LU}
 organization
 publishing date
 2015
 type
 Thesis
 publication status
 published
 subject
 keywords
 line spectra, parameter estimation, convex optimization, groupsparsity, blocksparsity, dictionary learning, ADMM, adaptive penalty, total variation, multipitch estimation, chroma, audio processing, TDOA, nearfield localization, amplitude modulation
 pages
 156 pages
 publisher
 Centre for Mathematical Sciences, Lund University
 external identifiers

 other:LUTFMS20172015
 language
 English
 LU publication?
 yes
 id
 1b3a7f94e86c4cdcbafdd36326d53417 (old id 8046494)
 date added to LUP
 20160401 14:03:41
 date last changed
 20181121 20:22:54
@misc{1b3a7f94e86c4cdcbafdd36326d53417, abstract = {{This licentiate thesis focuses on clustered parametric models for estimation of line spectra, when the spectral content of a signal source is assumed to exhibit some form of grouping. Different from previous parametric approaches, which generally require explicit knowledge of the model orders, this thesis exploits sparse modeling, where the orders are implicitly chosen. For line spectra, the nonlinear parametric model is approximated by a linear system, containing an overcomplete basis of candidate frequencies, called a dictionary, and a large set of linear response variables that selects and weights the components in the dictionary. Frequency estimates are obtained by solving a convex optimization program, where the sum of squared residuals is minimized. To discourage overfitting and to infer certain structure in the solution, different convex penalty functions are introduced into the optimization. The cost tradeoff between fit and penalty is set by some user parameters, as to approximate the true number of spectral lines in the signal, which implies that the response variable will be sparse, i.e., have few nonzero elements. Thus, instead of explicit model orders, the orders are implicitly set by this tradeoff. For grouped variables, the dictionary is customized, and appropriate convex penalties selected, so that the solution becomes group sparse, i.e., has few groups with nonzero variables. In an array of sensors, the specific timedelays and attenuations will depend on the source and sensor positions. By modeling this, one may estimate the location of a source. In this thesis, a novel joint location and grouped frequency estimator is proposed, which exploits sparse modeling for both spectral and spatial estimates, showing robustness against sources with overlapping frequency content. For audio signals, this thesis uses two different features for clustering. Pitch is a perceptual property of sound that may be described by the harmonic model, i.e., by a group of spectral lines at integer multiples of a fundamental frequency, which we estimate by exploiting a novel adaptive total variation penalty. The other feature, chroma, is a concept in musical theory, collecting pitches at powers of 2 from each other into groups. Using a chroma dictionary, together with appropriate group sparse penalties, we propose an automatic transcription of the chroma content of a signal.}}, author = {{Kronvall, Ted}}, keywords = {{line spectra; parameter estimation; convex optimization; groupsparsity; blocksparsity; dictionary learning; ADMM; adaptive penalty; total variation; multipitch estimation; chroma; audio processing; TDOA; nearfield localization; amplitude modulation}}, language = {{eng}}, note = {{Licentiate Thesis}}, publisher = {{Centre for Mathematical Sciences, Lund University}}, title = {{Sparse Modeling of Grouped Line Spectra}}, url = {{https://lup.lub.lu.se/search/files/3750309/8046497.pdf}}, year = {{2015}}, }