+publisher:"University of New South Wales" +contributor:("Solo, Victor, Electrical Engineering & Telecommunications, Faculty of Engineering, UNSW")

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University of New South Wales

1. Marjanovic, Goran. lq sparse signal estimation with applications.

Degree: Electrical Engineering & Telecommunications, 2012, University of New South Wales

URL: http://handle.unsw.edu.au/1959.4/52400 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11073/SOURCE01?view=true

► The use of sparsity has emerged in the last fifteen years as an important tool for solving many problems in the areas of signal processing… (more)

▼ The use of sparsity has emerged in the last fifteen years as an important tool for solving many problems in the areas of signal processing and statisticalinference. In this dissertation we pursue three significant applications of sparsity; sparse linear regression, low rank matrix completion and sparseinverse covariance selection. In the first and third topic, sparsity refers to having a small number of nonzero vector and matrix entries respectively,while in the second topic it is associated with low matrix rank.A penalized approach is considered involving optimization of an objective function with two terms. One of the terms measures the goodness of fit i.e.the error between the observed data and the estimated solution, while the other is a penalty responsible for inducing sparse solutions, hence the namepenalized problem.It is well understood that the natural way of inducing sparsity is through the l0 ``norm'' i.e. the counting function or the discrete metric. Since the l0function is non convex, a large volume of literature has instead resorted to using the convex l1 norm as the penalty. Therefore, the failure to consider thel0 penalized problem is a point of departure for this dissertation. In order to bridge the gap between the l0 and l1 penalties, the focus becomes thedevelopment of non convex optimization methods for the lq (0<q<1) penalized problem.Chapters 1 and 2 provide and describe the motivation and technical background respectively.Chapter 3 considers the topic of sparse linear regression, where we develop a nonlinear conjugate gradient algorithm for optimizing a smoothed lqpenalized least squares problem. The algorithm is applicable to any q>0 but the emphasis is on 0<q<1. Imposing basic assumptions, we prove that theiterates converge to a stationary point, and if this point is a local minimizer then it is also proved that the convergence is R-linear. Simulations are giventhat illustrate the potential of considering the use of our algorithm.Chapter 4 considers the topic of low rank matrix completion, where we develop an algorithm for optimizing an lq (rank) penalized least squares problemwith 0<q<1. In the development process we solve a non-trivial one dimensional lq optimization problem that is fundamental to our work. Additionally, ageneral algorithm convergence (fixed point) result with a non-trivial proof is given for 0≤q<1. We illustrate with data analysis examples, comparing thereconstruction quality of three matrix singular value penalties: l0, l1 and lq, 0<q<1.Chapter 5 considers the topic of sparse inverse covariance estimation, where we develop an algorithm for optimizing an lq penalized log-likelihoodproblem with 0≤q<1. The development requires the solutions of the one dimensional lq optimization problem from Chapter 4. These are additionallyused to prove some algorithm properties as well as some fixed point results. We illustrate with simulations and a real world application example.Reconstruction comparisons are given using four penalties: l0, l1, lq with 0<q<1, and SCAD.Both,… Advisors/Committee Members: Solo, Victor, Electrical Engineering & Telecommunications, Faculty of Engineering, UNSW.

Subjects/Keywords: Inverse problems; Sparse; Non convex; Matrix completion; Inverse covariance; Linear regression; Penalized problem

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APA (6^th Edition):

Marjanovic, G. (2012). lq sparse signal estimation with applications. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/52400 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11073/SOURCE01?view=true

Chicago Manual of Style (16^th Edition):

Marjanovic, Goran. “lq sparse signal estimation with applications.” 2012. Doctoral Dissertation, University of New South Wales. Accessed April 15, 2021. http://handle.unsw.edu.au/1959.4/52400 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11073/SOURCE01?view=true.

MLA Handbook (7^th Edition):

Marjanovic, Goran. “lq sparse signal estimation with applications.” 2012. Web. 15 Apr 2021.

Vancouver:

Marjanovic G. lq sparse signal estimation with applications. [Internet] [Doctoral dissertation]. University of New South Wales; 2012. [cited 2021 Apr 15]. Available from: http://handle.unsw.edu.au/1959.4/52400 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11073/SOURCE01?view=true.

Council of Science Editors:

Marjanovic G. lq sparse signal estimation with applications. [Doctoral Dissertation]. University of New South Wales; 2012. Available from: http://handle.unsw.edu.au/1959.4/52400 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11073/SOURCE01?view=true

University of New South Wales

2. Seneviratne, Seneviratne. l0 Sparse signal processing and model selection with applications.

Degree: Electrical Engineering & Telecommunications, 2012, University of New South Wales

URL: http://handle.unsw.edu.au/1959.4/52431 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11104/SOURCE01?view=true

► Sparse signal processing has far-reaching applications including compressed sensing, media compression/denoising/deblurring, microarray analysis and medical imaging. The main reason for its popularity is that many… (more)

▼ Sparse signal processing has far-reaching applications including compressed sensing, media compression/denoising/deblurring, microarray analysis and medical imaging. The main reason for its popularity is that many signals have a sparse representation given that the basis is suitably selected. However the difficulty lies in developing an efficient method of recovering such a representation. To this aim, two efficient sparse signal recovery algorithms are developed in the first part of this thesis. The first method is based on direct minimization of the l0 norm via cyclic descent, which is called the L0LS-CD (l0 penalized least squares via cyclic descent) algorithm. The other method minimizes smooth approximations of sparsity measures including those of the l0 norm via the majorization minimization (MM) technique, which is called the QC (quadratic concave) algorithm. The L0LS-CD algorithm is developed further by extending it to its multivariate (V-L0LS-CD (vector L0LS-CD)) and group (gL0LS-CD (group L0LS-CD)) regression variants. Computational speed-ups to the basic cyclic descent algorithm are discussed and a greedy version of L0LS-CD is developed. Stability of these algorithms is analyzed and the impact of the penalty parameter and proper initialization on the algorithm performance are highlighted. A suitable method for performance comparison of sparse approximating algorithms in the presence of noise is established. Simulations compare L0LS-CD and V-L0LS-CD with a range of alternatives on under-determined as well as over-determined systems. The QC algorithm is applicable to a class of penalties that are neither convex nor concave but have what we call the quadratic concave property. Convergence proofs of this algorithm are presented and it is compared with the Newton algorithm, concave convex (CC) procedure, as well as with the class of proximity algorithms. Simulations focus on the smooth approximations of the l0 norm and compare them with other l0 denoising algorithms. Next, two applications of sparse modeling are considered. In the first application the L0LS-CD algorithm is extended to recover a sparse transfer function in the presence of coloured noise. The second uses gL0LS-CD to recover the topology of a sparsely connected network of dynamic systems. Both applications use Laguerre basis functions for model expansion. The role of model selection in sparse signal processing is widely neglected in literature. The tuning/penalty parameter of a sparse approximating problem should be selected using a model selection criterion which minimizes a desired discrepancy measure. Compared to the commonly used model selection methods, the SURE (Stein's unbiased risk estimator) estimator stands out as one which does not suffer from the limitations of other methods. Most model selection criterion are developed based on signal or prediction mean squared error. The last section of this thesis develops an SURE criterion instead for parameter mean square error and applies this result to… Advisors/Committee Members: Solo, Victor, Electrical Engineering & Telecommunications, Faculty of Engineering, UNSW.

Subjects/Keywords: l0 Norm; Sparse Signal Processing; Model Selection

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APA (6^th Edition):

Seneviratne, S. (2012). l0 Sparse signal processing and model selection with applications. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/52431 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11104/SOURCE01?view=true

Chicago Manual of Style (16^th Edition):

Seneviratne, Seneviratne. “l0 Sparse signal processing and model selection with applications.” 2012. Doctoral Dissertation, University of New South Wales. Accessed April 15, 2021. http://handle.unsw.edu.au/1959.4/52431 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11104/SOURCE01?view=true.

MLA Handbook (7^th Edition):

Seneviratne, Seneviratne. “l0 Sparse signal processing and model selection with applications.” 2012. Web. 15 Apr 2021.

Vancouver:

Seneviratne S. l0 Sparse signal processing and model selection with applications. [Internet] [Doctoral dissertation]. University of New South Wales; 2012. [cited 2021 Apr 15]. Available from: http://handle.unsw.edu.au/1959.4/52431 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11104/SOURCE01?view=true.

Council of Science Editors:

Seneviratne S. l0 Sparse signal processing and model selection with applications. [Doctoral Dissertation]. University of New South Wales; 2012. Available from: http://handle.unsw.edu.au/1959.4/52431 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11104/SOURCE01?view=true

University of New South Wales

3. Piggott, Marc. Stochastic Algorithms in Riemannian Manifolds and Adaptive Networks.

Degree: Electrical Engineering & Telecommunications, 2016, University of New South Wales

URL: http://handle.unsw.edu.au/1959.4/57040 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42307/SOURCE02?view=true

► The combination of adaptive network algorithms and stochastic geometric dynamics has the potential to make a large impact in distributed control and signal processing applications.… (more)

▼ The combination of adaptive network algorithms and stochastic geometric dynamics has the potential to make a large impact in distributed control and signal processing applications. However, both literatures contain fundamental unsolved problems. The thesis is thus in two main parts.In part I, we consider stochastic differential equations (SDEs) evolving in a matrix Lie group. To undertake any kind of statistical signal processing or control task in this setting requires the simulation of such geometric SDEs. This foundational issue has barely been addressed previously.Chapter 1 contains background and motivation. Chapter 2 develops numerical schemes for simulating SDEs that evolve in SO(n) and SE(n). We propose novel, reliable, efficient schemes based on diagonal Padé approximants, where each trajectory lies in the respective manifold. We prove first order convergence in mean uniform squared error using a new proof technique. Simulations for SDEs in SO(50) are provided. In part II, we study adaptive networks. These are collections of individual agents (nodes) that cooperate to solve estimation, detection, learning and adaptation problems in real time from streaming data, without a fusion center. We study general diffusion LMS algorithms - including real time consensus - for distributed MMSE parameter estimation. This choice is motivated by two major flaws in the literature. First, all analyses assume the regressors are white noise, whereas in practice serial correlation is pervasive. Dealing with it however is much harder than the white noise case. Secondly, since the algorithms operate in real time, we must consider realization-wise behavior. There are no such results. To remedy these flaws, we uncover the mixed time scale structure of the algorithms. We then perform a novel mixed time scale stochastic averaging analysis.Chapter 3 contains background and motivation. Realization-wise stability (chapter 4) and performance including network MSD, EMSE and realization-wise fluctuations (chapter 5) are then studied. We develop results in the difficult but realistic case of serial correlation. We observe that the popular ATC, CTA and real time consensus algorithms are remarkably similar in terms of stability and performance for small constant step sizes.Parts III and IV contain conclusions and future work. Advisors/Committee Members: Solo, Victor, Electrical Engineering & Telecommunications, Faculty of Engineering, UNSW.

Subjects/Keywords: convergence; strong mixing; correlation; distributed learning; stochastic averaging; Lie groups; distributed learning; LMS; convergence; strong mixing

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Piggott, M. (2016). Stochastic Algorithms in Riemannian Manifolds and Adaptive Networks. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/57040 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42307/SOURCE02?view=true

Chicago Manual of Style (16^th Edition):

Piggott, Marc. “Stochastic Algorithms in Riemannian Manifolds and Adaptive Networks.” 2016. Doctoral Dissertation, University of New South Wales. Accessed April 15, 2021. http://handle.unsw.edu.au/1959.4/57040 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42307/SOURCE02?view=true.

MLA Handbook (7^th Edition):

Piggott, Marc. “Stochastic Algorithms in Riemannian Manifolds and Adaptive Networks.” 2016. Web. 15 Apr 2021.

Vancouver:

Piggott M. Stochastic Algorithms in Riemannian Manifolds and Adaptive Networks. [Internet] [Doctoral dissertation]. University of New South Wales; 2016. [cited 2021 Apr 15]. Available from: http://handle.unsw.edu.au/1959.4/57040 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42307/SOURCE02?view=true.

Council of Science Editors:

Piggott M. Stochastic Algorithms in Riemannian Manifolds and Adaptive Networks. [Doctoral Dissertation]. University of New South Wales; 2016. Available from: http://handle.unsw.edu.au/1959.4/57040 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42307/SOURCE02?view=true

University of New South Wales

4. Cassidy, Benjamin. Statistical signal processing methods for imaging brain activity.

Degree: Electrical Engineering & Telecommunications, 2014, University of New South Wales

URL: http://handle.unsw.edu.au/1959.4/53487 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12182/SOURCE02?view=true

► Functional neuroimaging involves the study of cognitive scientific questions by measuring and modelling brain activity, using techniques such as Functional Magnetic Resonance Imaging (fMRI) and… (more)

▼ Functional neuroimaging involves the study of cognitive scientific questions by measuring and modelling brain activity, using techniques such as Functional Magnetic Resonance Imaging (fMRI) and Magnetoencephalography (MEG). These non-invasive methods give indirect views into brain functioning: fMRI measures changes in relative blood oxygenation as a response to neural activation, and MEG externally samples the weak magnetic fields generated by neural activity. Additionally the data are corrupted by noise. So analysing the data from these modalities presents many challenges. This thesis presents four new statistical signal processing methods for improving the analysis of functional neuroimaging data.The thesis opens with a motivating chapter. Then chapter 2 makes the case for the significance of the topics tackled in the later chapters by reviewing pertinent literature.Chapter 3 develops a suite of formal statistical diagnostic tests to critique the model construction process, when analysing fMRI data from task-based experiments. The methods are developed in the Lagrange Multiplier testing framework (long popular in econometrics) as an approximation to likelihood ratio tests. In particular we develop three tests that examine the adequacy of assuming non-linearity, non-stationarity and the validity of the common Double Gamma specification for hemodynamic response in fMRI.Chapter 4 of this thesis develops a new system identification method, using T2* fMRI to construct a map of the direct effects of transcranial direct current stimulation (tDCS) on the brain. The method is developed in the framework of so-called time-series Intervention Analysis to quantitatively determine whether a single stimulus to a system has significant effect on its operation.In Chapter 5 we develop a new method for solving the MEG inverse problem. The method calculates maximally sparse estimates of brain activity via spatial L0 regularisation, while constraining the solution to be smooth throughout time. In Chapter 6 we develop a new approach to describe the fMRI based functional connectivity of the brain using a network model. The method measures Mutual Information between brain regions, and jointly accounts for spurious spatial correlations, temporal correlations, and sparsity of connections between brain regions, to construct a single estimate of activity interactions.We demonstrate the utility of all these methods by analysing simulated data and real experimental data. Advisors/Committee Members: Solo, Victor, Electrical Engineering & Telecommunications, Faculty of Engineering, UNSW, Rae, Caroline, Neuroscience Research Australia, Faculty of Medicine, UNSW.

Subjects/Keywords: Magnetoencephalography; Statistical signal processing; Brain imaging; FMRI

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Cassidy, B. (2014). Statistical signal processing methods for imaging brain activity. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/53487 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12182/SOURCE02?view=true

Chicago Manual of Style (16^th Edition):

Cassidy, Benjamin. “Statistical signal processing methods for imaging brain activity.” 2014. Doctoral Dissertation, University of New South Wales. Accessed April 15, 2021. http://handle.unsw.edu.au/1959.4/53487 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12182/SOURCE02?view=true.

MLA Handbook (7^th Edition):

Cassidy, Benjamin. “Statistical signal processing methods for imaging brain activity.” 2014. Web. 15 Apr 2021.

Vancouver:

Cassidy B. Statistical signal processing methods for imaging brain activity. [Internet] [Doctoral dissertation]. University of New South Wales; 2014. [cited 2021 Apr 15]. Available from: http://handle.unsw.edu.au/1959.4/53487 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12182/SOURCE02?view=true.

Council of Science Editors:

Cassidy B. Statistical signal processing methods for imaging brain activity. [Doctoral Dissertation]. University of New South Wales; 2014. Available from: http://handle.unsw.edu.au/1959.4/53487 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12182/SOURCE02?view=true

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