Group-Sparse Regression : With Applications in Spectral Analysis and Audio Signal Processing
Author
Summary, in English
The first three papers in the thesis, A-C, concerns group-sparse regression for temporal identification and spatial localization, of different features in audio signal processing. In Paper A, we derive a model for audio signals recorded on an array of microphones, arbitrarily placed in a three-dimensional space. In a two-step group-sparse modeling procedure, we first identify and separate the recorded audio sources, and then localize their origins in space. In Paper B, we examine the multi-pitch model for tonal audio signals, such as, e.g., musical tones, tonal speech, or mechanical sounds from combustion engines. It typically models the signal-of-interest using a group of spectral lines, located at some integer multiple of a fundamental frequency. In this paper, we replace the regularizers used in previous works by a group-wise total variation function, promoting a smooth spectral envelope. The proposed combination of regularizers thereby avoids the common suboctave error, where the fundamental frequency is incorrectly classified using half of the fundamental frequency. In Paper C, we analyze the performance of group-sparse regression for classification by chroma, also known as pitch class, e.g., the musical note C, independent of the octave.
The last three papers, D-F, are less application-specific than the first three; attempting to develop the methodology of sparse regression more independently of the application. Specifically, these papers look at model order selection in group-sparse regression, which is implicitly controlled by choosing a hyperparameter, prioritizing between the regularizer and the fitting term in the optimization problem. In Papers D and E, we examine a metric from array processing, termed the covariance fitting criterion, which is seemingly hyperparameter-free, and has been shown to yield sparse estimates for underdetermined linear systems. In the paper, we propose a generalization of the covariance fitting criterion for group-sparsity, and show how it relates to the group-sparse regression problem. In Paper F, we derive a novel method for hyperparameter-selection in sparse and group-sparse regression problems. By analyzing how the noise propagates into the parameter estimates, and the corresponding decision rules for sparsity, we propose selecting it as a quantile from the distribution of the maximum noise component, which we sample from using the Monte Carlo method.
Department/s
- Mathematical Statistics
- Statistical Signal Processing Group
Publishing year
2017-09-22
Language
English
Full text
Document type
Dissertation
Publisher
Mathematical Statistics, Centre for Mathematical Sciences, Lund University
Topic
- Probability Theory and Statistics
- Signal Processing
Keywords
- sparse regression
- group-sparsity
- statistical modeling
- regularization
- hyperparameter-selection
- spectral analysis
- audio signal processing
- classification
- localization
- multi-pitch estimation
- chroma
- convex optimization
- ADMM
- cyclic coordinate descent
- proximal gradient
Status
Published
Research group
- Statistical Signal Processing Group
Supervisor
ISBN/ISSN/Other
- ISBN: 978-91-7753-418-1
- ISBN: 978-91-7753-417-4
Defence date
20 October 2017
Defence time
13:15
Defence place
Lecture hall MH:Riesz, Matematikcentrum, Sölvegatan 18, Lund University, Faculty of Engineering.
Opponent
- Richard Heusdens (Professor)