This thesis is based on nine papers, all concerned with parameter estimation. The thesis aims at solving problems related to real-world applications such as spectroscopy, DNA sequencing, and audio processing, using sparse modeling heuristics. For the problems considered in this thesis, one is not only concerned with finding the parameters in the signal model, but also to determine the number of signal components present in the measurements. In recent years, developments in sparse modeling have allowed for methods that jointly estimate the parameters in the model and the model order. Based on these achievements, the approach often taken in this thesis is as follows. First, a parametric model of the considered signal is derived, containing different parameters that capture the important characteristics of the signal. When the signal model has been determined, an optimization problem is formed aimed at finding ...

The topic of this thesis is speech enhancement with a focus on models of voiced speech. Speech is divided into two subcategories dependent on the characteristics of the signal. One part is the voiced speech, the other is the unvoiced. In this thesis, we primarily focus on the voiced speech parts and utilise the structure of the signal in relation to speech enhancement. The basis for the models is the harmonic model which is a very often used model for voiced speech because it describes periodic signals perfectly. First, we consider the problem of non-stationarity in the speech signal. The speech signal changes its characteristics continuously over time whereas most speech analysis and enhancement methods assume stationarity within 20-30 ms. We propose to change the model to allow the fundamental frequency to vary linearly over time by introducing a chirp ...

This thesis deals with the modeling of structured signals under different sparsity constraints. Many phenomena exhibit an inherent structure that may be exploited when setting up models, examples include audio waves, radar, sonar, and image objects. These structures allow us to model, identify, and classify the processes, enabling parameter estimation for, e.g., identification, localisation, and tracking. In this work, such structures are exploited, with the goal to achieve efficient localisation and tracking of a structured source signal. Specifically, two scenarios are considered. In papers A and B, the aim is to find a sparse subset of a structured signal such that the signal parameters and source locations may be estimated in an optimal way. For the sparse subset selection, a combinatorial optimization problem is approximately solved by means of convex relaxation, with the results of allowing for different types of ...

Music is built from sound, ultimately resulting from an elaborate interaction between the sound-generating properties of physical objects (i.e. music instruments) and the sound perception abilities of the human auditory system. Humans, even without any kind of formal music training, are typically able to ex- tract, almost unconsciously, a great amount of relevant information from a musical signal. Features such as the beat of a musical piece, the main melody of a complex musical ar- rangement, the sound sources and events occurring in a complex musical mixture, the song structure (e.g. verse, chorus, bridge) and the musical genre of a piece, are just some examples of the level of knowledge that a naive listener is commonly able to extract just from listening to a musical piece. In order to do so, the human auditory system uses a variety of cues ...

This doctorate thesis focuses on sparse regression, a statistical modeling tool for selecting valuable predictors in underdetermined linear models. By imposing different constraints on the structure of the variable vector in the regression problem, one obtains estimates which have sparse supports, i.e., where only a few of the elements in the response variable have non-zero values. The thesis collects six papers which, to a varying extent, deals with the applications, implementations, modifications, translations, and other analysis of such problems. Sparse regression is often used to approximate additive models with intricate, non-linear, non-smooth or otherwise problematic functions, by creating an underdetermined model consisting of candidate values for these functions, and linear response variables which selects among the candidates. Sparse regression is therefore a widely used tool in applications such as, e.g., image processing, audio processing, seismological and biomedical modeling, but is ...

Audio systems receive the speech signals of interest usually in the presence of noise. The noise has profound impacts on the quality and intelligibility of the speech signals, and it is therefore clear that the noisy signals must be cleaned up before being played back, stored, or analyzed. We can estimate the speech signal of interest from the noisy signals using a priori knowledge about it. A human speech signal is broadband and consists of both voiced and unvoiced parts. The voiced part is quasi-periodic with a time-varying fundamental frequency (or pitch as it is commonly referred to). We consider the periodic signals basically as the sum of harmonics. Therefore, we can pass the noisy signals through bandpass filters centered at the frequencies of the harmonics to enhance the signal. In addition, although the frequencies of the harmonics are the ...

Sound source separation refers to the task of estimating the signals produced by individual sound sources from a complex acoustic mixture. It has several applications, since monophonic signals can be processed more efficiently and flexibly than polyphonic mixtures. This thesis deals with the separation of monaural, or, one-channel music recordings. We concentrate on separation methods, where the sources to be separated are not known beforehand. Instead, the separation is enabled by utilizing the common properties of real-world sound sources, which are their continuity, sparseness, and repetition in time and frequency, and their harmonic spectral structures. One of the separation approaches taken here use unsupervised learning and the other uses model-based inference based on sinusoidal modeling. Most of the existing unsupervised separation algorithms are based on a linear instantaneous signal model, where each frame of the input mixture signal is modeled ...

It is increasingly more common that an occasion is recorded by multiple individuals with the proliferation of recording devices such as smart phones. When properly aligned, these recordings may provide several audio and visual perspectives to a scene which leads to several applications in restoring, remastering and remixing frameworks in various fields. In this study, we interpret the problem of aligning multiple unsynchronized audio sequences in a probabilistic framework. In this manner, we propose a novel, model based approach where we define a template generative model. We define 6 different generative models using this template covering basically all kinds of features (real valued, positive, binary and categorical). Proper scoring functions that evaluates the quality of an alignment are derived from each model where we are able to penalize non-overlapping alignments and alignment of a single sequence against a pre-aligned sequences. ...

This thesis addresses the development of a system for pitch-informed solo and accompaniment separation capable of separating main instruments from music accompaniment regardless of the musical genre of the track, or type of music accompaniment. For the solo instrument, only pitched monophonic instruments were considered in a single-channel scenario where no panning or spatial location information is available. In the proposed method, pitch information is used as an initial stage of a sinusoidal modeling approach that attempts to estimate the spectral information of the solo instrument from a given audio mixture. Instead of estimating the solo instrument on a frame by frame basis, the proposed method gathers information of tone objects to perform separation. Tone-based processing allowed the inclusion of novel processing stages for attack re nement, transient interference reduction, common amplitude modulation (CAM) of tone objects, and for better ...

This thesis develops new mathematical theory and presents novel recovery algorithms for discrete linear dynamical systems (LDS) with sparsity constraints on either control inputs or initial state. The recovery problems in this framework manifest as the problem of reconstructing one or more sparse signals from a set of noisy underdetermined linear measurements. The goal of our work is to design algorithms for sparse signal recovery which can exploit the underlying structure in the measurement matrix and the unknown sparse vectors, and to analyze the impact of these structures on the efficacy of the recovery. We answer three fundamental and interconnected questions on sparse signal recovery problems that arise in the context of LDS. First, what are necessary and sufficient conditions for the existence of a sparse solution? Second, given that a sparse solution exists, what are good low-complexity algorithms that ...

It takes more time to think of a silent scene, action or event than finding one that emanates sound. Not only speaking or playing music but almost everything that happens is accompanied with or results in one or more sounds mixed together. This makes acoustic event detection (AED) one of the most researched topics in audio signal processing nowadays and it will probably not see a decline anywhere in the near future. This is due to the thirst for understanding and digitally abstracting more and more events in life via the enormous amount of recorded audio through thousands of applications in our daily routine. But it is also a result of two intrinsic properties of audio: it doesn’t need a direct sight to be perceived and is less intrusive to record when compared to image or video. Many applications such ...

This dissertation is concerned with the development of Markov chain Monte Carlo (MCMC) methods for the Bayesian restoration of degraded audio signals. First, the Bayesian approach to time series modelling is reviewed, then established MCMC methods are introduced. The first problem to be addressed is that of model order uncertainty. A reversible-jump sampler is proposed which can move between models of different order. It is shown that faster convergence can be achieved by exploiting the analytic structure of the time series model. This approach to model order uncertainty is applied to the problem of noise reduction using the simulation smoother. The effects of incorrect autoregressive (AR) model orders are demonstrated, and a mixed model order MCMC noise reduction scheme is developed. Nonlinear time series models are surveyed, and the advantages of linear-in- the-parameters models explained. A nonlinear AR (NAR) model, ...

In the thesis, various aspects of deconvolution of ultrasonic pulse-echo signals in nondestructive testing are treated. The deconvolution problem is formulated as estimation of a reflection sequence which is the impulse characteristic of the inspected object and the estimation is performed using either maximum a posteriori (MAP) or linear minimum mean square error (MMSE) estimators. A multivariable model is proposed for a certain multiple transducer setup allowing for frequency diversity, thereby improving the estimation accuracy. Using the MAP estimator three different material types were treated, with varying amount of sparsity in the reflection sequences. The Gaussian distribution is used for modelling materials containing a large number of small scatters. The Bernoulli--Gaussian distribution is used for sparse data obtained from layered structures and a genetic algorithm approach is proposed for optimizing the corresponding MAP criterion. Sequences with intermediate sparsity suitable of ...

The abundance of large and heterogeneous systems is rendering contemporary data more pervasive, intricate, and with a non-regular structure. With classical techniques facing troubles to deal with the irregular (non-Euclidean) domain where the signals are defined, a popular approach at the heart of graph signal processing (GSP) is to: (i) represent the underlying support via a graph and (ii) exploit the topology of this graph to process the signals at hand. In addition to the irregular structure of the signals, another critical limitation is that the observed data is prone to the presence of perturbations, which, in the context of GSP, may affect not only the observed signals but also the topology of the supporting graph. Ignoring the presence of perturbations, along with the couplings between the errors in the signal and the errors in their support, can drastically hinder ...

This PhD thesis considers the problem of locating some target nodes in different wireless infrastructures such as wireless cellular radio networks and wireless sensor networks. To be as realistic as possible, mixed line-of-sight and non-line-of-sight (LOS/NLOS) localization environment is introduced. Both the conventional non-cooperative localization and the new emerging cooperative localization have been studied thoroughly. Owing to the random nature of the measurements, probabilistic methods are more advanced as compared to the old-fashioned geometric methods. The gist behind the probabilistic methods is to infer the unknown positions of the target nodes in an estimation process, given a set of noisy position related measurements, a probabilistic measurement model, and a few known reference positions. In contrast to the majority of the existing methods, harsh but practical constraints are taken into account: neither offline calibration nor non-line-of-sight state identification is equipped in ...