Parameter Estimation -in sparsity we trust

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 ...

Swärd, Johan — Lund University


Group-Sparse Regression - With Applications in Spectral Analysis and Audio Signal Processing

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 ...

Kronvall, Ted — Lund University


Robust Network Topology Inference and Processing of Graph Signals

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 ...

Rey, Samuel — King Juan Carlos University


Sparse Modeling Heuristics for Parameter Estimation - Applications in Statistical Signal Processing

This thesis examines sparse statistical modeling on a range of applications in audio modeling, audio localizations, DNA sequencing, and spectroscopy. In the examined cases, the resulting estimation problems are computationally cumbersome, both as one often suffers from a lack of model order knowledge for this form of problems, but also due to the high dimensionality of the parameter spaces, which typically also yield optimization problems with numerous local minima. In this thesis, these problems are treated using sparse modeling heuristics, with the resulting criteria being solved using convex relaxations, inspired from disciplined convex programming ideas, to maintain tractability. The contributions to audio modeling and estimation focus on the estimation of the fundamental frequency of harmonically related sinusoidal signals, which is commonly used model for, e.g., voiced speech or tonal audio. We examine both the problems of estimating multiple audio sources ...

Adalbjörnsson, Stefan Ingi — Lund University


Sparse Sensing for Statistical Inference: Theory, Algorithms, and Applications

In today's society, we are flooded with massive volumes of data in the order of a billion gigabytes on a daily basis from pervasive sensors. It is becoming increasingly challenging to locally store and transport the acquired data to a central location for signal/data processing (i.e., for inference). To alleviate these problems, it is evident that there is an urgent need to significantly reduce the sensing cost (i.e., the number of expensive sensors) as well as the related memory and bandwidth requirements by developing unconventional sensing mechanisms to extract as much information as possible yet collecting fewer data. The first aim of this thesis is to develop theory and algorithms for data reduction. We develop a data reduction tool called sparse sensing, which consists of a deterministic and structured sensing function (guided by a sparse vector) that is optimally designed ...

Chepuri, Sundeep Prabhakar — Delft University of Technology


Direction Finding In The Presence of Array Imperfections, Model Mismatches and Multipath

In direction finding (DF) applications, there are several factors affecting the estimation accuracy of the direction-of-arrivals (DOA) of unknown source locations. The major distortions in the estimation process are due to the array imperfections, model mismatches and multipath. The array imperfections usually exist in practical applications due to the nonidealities in the antenna array such as mutual coupling (MC) and gain/phase uncertainties. The model mismatches usually occur when the model of the received signal differs from the signal model used in the processing stage of the DF system. Another distortion is due to multipath signals. In the multipath scenario, the antenna array receives the transmitted signal from more than one path with different directions and the array covariance matrix is rank-deficient. In this thesis, three new methods are proposed for the problems in DF applications in the presence of array ...

Elbir, Ahmet M. — Middle East Technical Univresity


Robust Adaptive Machine Learning Algorithms for Distributed Signal Processing

Distributed networks comprising a large number of nodes, e.g., Wireless Sensor Networks, Personal Computers (PC’s), laptops, smart phones, etc., which cooperate with each other in order to reach a common goal, constitute a promising technology for several applications. Typical examples include: distributed environmental monitoring, acoustic source localization, power spectrum estimation, etc. Sophisticated cooperation mechanisms can significantly benefit the learning process, through which the nodes achieve their common objective. In this dissertation, the problem of adaptive learning in distributed networks is studied, focusing on the task of distributed estimation. A set of nodes sense information related to certain parameters and the estimation of these parameters constitutes the goal. Towards this direction, nodes exploit locally sensed measurements as well as information springing from interactions with other nodes of the network. Throughout this dissertation, the cooperation among the nodes follows the diffusion optimization ...

Chouvardas, Symeon — National and Kapodistrian University of Athens


Learning from structured EEG and fMRI data supporting the diagnosis of epilepsy

Epilepsy is a neurological condition that manifests in epileptic seizures as a result of an abnormal, synchronous activity of a large group of neurons. Depending on the affected brain regions, seizures produce various severe clinical symptoms. Epilepsy cannot be cured and in many cases is not controlled by medication either. Surgical resection of the region responsible for generating the epileptic seizures might offer remedy for these patients. Electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) measure the changes of brain activity in time over different locations of the brain. As such, they provide valuable information on the nature, the timing and the spatial origin of the epileptic activity. Unfortunately, both techniques record activity of different brain and artefact sources as well. Hence, EEG and fMRI signals are characterised by low signal to noise ratio. Data quality and the vast amount ...

Hunyadi, Borbála — KU Leuven


Distributed Stochastic Optimization in Non-Differentiable and Non-Convex Environments

The first part of this dissertation considers distributed learning problems over networked agents. The general objective of distributed adaptation and learning is the solution of global, stochastic optimization problems through localized interactions and without information about the statistical properties of the data. Regularization is a useful technique to encourage or enforce structural properties on the resulting solution, such as sparsity or constraints. A substantial number of regularizers are inherently non-smooth, while many cost functions are differentiable. We propose distributed and adaptive strategies that are able to minimize aggregate sums of objectives. In doing so, we exploit the structure of the individual objectives as sums of differentiable costs and non-differentiable regularizers. The resulting algorithms are adaptive in nature and able to continuously track drifts in the problem; their recursions, however, are subject to persistent perturbations arising from the stochastic nature of ...

Vlaski, Stefan — University of California, Los Angeles


Solving inverse problems in room acoustics using physical models, sparse regularization and numerical optimization

Reverberation consists of a complex acoustic phenomenon that occurs inside rooms. Many audio signal processing methods, addressing source localization, signal enhancement and other tasks, often assume absence of reverberation. Consequently, reverberant environments are considered challenging as state-ofthe-art methods can perform poorly. The acoustics of a room can be described using a variety of mathematical models, among which, physical models are the most complete and accurate. The use of physical models in audio signal processing methods is often non-trivial since it can lead to ill-posed inverse problems. These inverse problems require proper regularization to achieve meaningful results and involve the solution of computationally intensive large-scale optimization problems. Recently, however, sparse regularization has been applied successfully to inverse problems arising in different scientific areas. The increased computational power of modern computers and the development of new efficient optimization algorithms makes it possible ...

Antonello, Niccolò — KU Leuven


A Geometric Deep Learning Approach to Sound Source Localization and Tracking

The localization and tracking of sound sources using microphone arrays is a problem that, even if it has attracted attention from the signal processing research community for decades, remains open. In recent years, deep learning models have surpassed the state-of-the-art that had been established by classic signal processing techniques, but these models still struggle with handling rooms with strong reverberations or tracking multiple sources that dynamically appear and disappear, especially when we cannot apply any criteria to classify or order them. In this thesis, we follow the ideas of the Geometric Deep Learning framework to propose new models and techniques that mean an advance of the state-of-the-art in the aforementioned scenarios. As the input of our models, we use acoustic power maps computed using the SRP-PHAT algorithm, a classic signal processing technique that allows us to estimate the acoustic energy ...

Diaz-Guerra, David — University of Zaragoza


Auditory Inspired Methods for Multiple Speaker Localization and Tracking Using a Circular Microphone Array

This thesis presents a new approach to the problem of localizing and tracking multiple acoustic sources using a microphone array. The use of microphone arrays offers enhancements of speech signals recorded in meeting rooms and office spaces. A common solution for speech enhancement in realistic environments with ambient noise and multi-path propagation is the application of so-called beamforming techniques, that enhance signals at the desired angle, using constructive interference, while attenuating signals coming from other directions, by destructive interference. Such beamforming algorithms require as prior knowledge the source location. Therefore, source localization and tracking algorithms are an integral part of such a system. However, conventional localization algorithms deteriorate in realistic scenarios with multiple concurrent speakers. In contrast to conventional localization algorithms, the localization algorithm presented in this thesis makes use of fundamental frequency or pitch information of speech signals in ...

Habib, Tania — Signal Processing and Speech Communication Laboratory, Graz University of Technology, Austria


Exploiting Prior Information in Parametric Estimation Problems for Multi-Channel Signal Processing Applications

This thesis addresses a number of problems all related to parameter estimation in sensor array processing. The unifying theme is that some of these parameters are known before the measurements are acquired. We thus study how to improve the estimation of the unknown parameters by incorporating the knowledge of the known parameters; exploiting this knowledge successfully has the potential to dramatically improve the accuracy of the estimates. For covariance matrix estimation, we exploit that the true covariance matrix is Kronecker and Toeplitz structured. We then devise a method to ascertain that the estimates possess this structure. Additionally, we can show that our proposed estimator has better performance than the state-of-art when the number of samples is low, and that it is also efficient in the sense that the estimates have Cramér-Rao lower Bound (CRB) equivalent variance. In the direction of ...

Wirfält, Petter — KTH Royal Institute of Technology


Stochastic Schemes for Dynamic Network Resource Allocation

Wireless networks and power distribution grids are experiencing increasing demands on their efficiency and reliability. Judicious methods for allocating scarce resources such as power and bandwidth are of paramount importance. As a result, nonlinear optimization and signal processing tools have been incorporated into the design of contemporary networks. This thesis develops schemes for efficient resource allocation (RA) in such dynamic networks, with an emphasis in stochasticity, which is accounted for in the problem formulation as well as in the algorithms and schemes to solve those problems. Stochastic optimization and decomposition techniques are investigated to develop low-complexity algorithms with specific applications in cross-layer design of wireless communications, cognitive radio (CR) networks and smart power distribution systems. The costs and constraints on the availability of network resources, together with diverse quality of service (QoS) requirements, render network design, management, and operation challenging ...

Lopez Ramos, Luis Miguel — King Juan Carlos University


Compressed sensing approaches to large-scale tensor decompositions

Today’s society is characterized by an abundance of data that is generated at an unprecedented velocity. However, much of this data is immediately thrown away by compression or information extraction. In a compressed sensing (CS) setting the inherent sparsity in many datasets is exploited by avoiding the acquisition of superfluous data in the first place. We combine this technique with tensors, or multiway arrays of numerical values, which are higher-order generalizations of vectors and matrices. As the number of entries scales exponentially in the order, tensor problems are often large-scale. We show that the combination of simple, low-rank tensor decompositions with CS effectively alleviates or even breaks the so-called curse of dimensionality. After discussing the larger data fusion optimization framework for coupled and constrained tensor decompositions, we investigate three categories of CS type algorithms to deal with large-scale problems. First, ...

Vervliet, Nico — KU Leuven

The current layout is optimized for mobile phones. Page previews, thumbnails, and full abstracts will remain hidden until the browser window grows in width.

The current layout is optimized for tablet devices. Page previews and some thumbnails will remain hidden until the browser window grows in width.