# Tutorials

SSP2014 will feature tutorials on topics of current and emerging interest related to statistical signal processing and its applications.

## Selected tutorials

### Network signal processing: A topological approach

#### Presented by Prof Hamid Krim, North Carolina State University

##### Abstract

The tutorial focuses on the exploration and exploitation of network for processing sensor data. We will lay down the basic graph theoretic concepts that will be used throughout the lecture, and will show how they can be used for modeling sensor networks. Algorithms to determine topological properties of graphs will be mapped onto decentralized protocols that can be used to capture the network state. We will also discuss ways of adapting these techniques to time-varying networks, and will build on this background to provide solutions to so-called big data problems with dimension reduction techniques with provable guarantees to preserve topology.

The specific list of topics covered is given in the following list:

- Graphs and their simplicial generalizations (adjacency, incidence …)
- Laplacians on graphs L = D − A and and graph intrinsic properties (connectivity etc.) and connection to continuous Laplacian
- Laplace-Beltrami operators on graphs, and their generalizations (so-called Hodge Laplacians) and their intrinsice properties (connectivity and other topological characteristics)
- Topology of graphs/simplicial complexes, and its algebraic formulation
- Basic operators and their implied Homology and co-homology interpretations
- Graph construction from a deployed sensor network
- Algebraic topology view of common sensor problems
- Distributed detection of sensor failures
- Distributed Localization of sensor failures
- Mitigation of sensor failures
- Dynamic failures and persistent tracking of sensor network state

##### Biography of the presenter

Hamid Krim received his degrees in Electrical Engineering. As a member of technical staff at AT&T Bell Labs, he has worked in the area of telephony and digital communication systems/subsystems. In 1991 he became a NSF Post-doctoral scholar at Foreign Centers of Excellence (LSS Supelec/Univ. of Orsay, Paris, France). He subsequently joined the Laboratory for Information and Decision Systems, MIT, Cambridge, MA, as a Research Scientist performing/supervising research in his area of interest, and later as a faculty in the ECE dept. at North Car. State Univ. in Raleigh, N.C. in 1998. He is an original contributor and now an affiliate of the Center for Imaging Science sponsored by the Army. He also is a recipient of the NSF Career Young Investigator award. He is a Fellow of IEEE and was on the editorial board of the IEEE Trans. on SP and regularly contributes to the society in a variety of ways. He is a member of SIAM and of Sigma Xi. His research interests are in statistical Signal Processing and mathematical modeling with a keen emphasis on applications.

##### References

1. Harish Chintakunta and Hamid Krim, “Topological Fidelity in Sensor Networks”, 2011. Manuscript. arXiv:1106.6069v1 (to appear in SP Trans.)

2. Harish Chintakunta and Hamid Krim, “Divide and Conquer: Localizing Coverage Holes in Sensor Networks”, 2010. Proceedings of IEEE SECON

3. Tahbaz-Salehi,A and Jadbabaie, A., “Distributed Coverage Verification in Sensor Networks Without Location Information”, IEEE Transactions Automatic Control, 2010.

4. Vin De Silva , Robert Ghrist, “Homological sensor networks”, Notices of the American Mathematical Society, 2007.

### Point Process, Random Finite Sets and Multi-Object Estimation

#### Presented by Prof Ba-Ngu Vo, Curtin University

##### Abstract

Multi-object systems are systems in which the number of objects and their states are unknown and stochastically vary with time. Multi-object systems arise in a host of applications areas, including aerospace, defense, computer vision, robotic and biomedical research. The last decade has witnessed exciting developments in multi-object state estimation with the introduction of random finite set to the field. The history of random set traces back to the problem of Buffon’s needle and has long been used by statisticians in many diverse applications including astronomy, atomic physics, biology, sampling theory, stereology, etc. Since 2003, Mahler’s seminal work on the random finite set approach to multi-object system, which culminated in the probability hypothesis density (PHD) filter, has continued to attract substantial interests from academia and industry alike.

This tutorial is an introduction to the random finite set paradigm to dynamic state estimation and outlines recent developments beyond the PHD filters. The session will present participants with the latest advances in multi-object dynamic state estimation methodology. It provides a unified perspective of multi-object filtering in a very intuitive manner by drawing direct parallels with the simpler problem of single-object filtering. Random finite sets are used as a tool for modeling multi-object systems and formulating the multi-object estimation problem in the Bayesian framework. Latest state-of-the-arts algorithms, including the PHD filters are presented. These techniques are illustrated in a number of applications areas including, radar/sonar, computer vision, and robotics. It is envisaged that participants will come away with sufficient know-how to apply these algorithms.

Dynamic state estimation is a significant component of statistical signal processing. This tutor presents important theoretical and algorithmic advances in dynamic multi-object estimation. This is an emerging area of research in statistical signal processing with a wide range of applications, which will enrich the statistical signal processing literature.

##### Biography of the presenter

Ba-Ngu Vo received his Bachelor degrees jointly in Science and Electrical Engineering with first class honors in 1994, and PhD in 1997. He had held various research positions at various institutions including CUHK. In 2010, he joined the University of Western Australia as Winthrop Professor and Chair of Signal Processing. Currently he is Professor and Chair of Signals and Systems in the Department of Electrical and Computer Engineering at Curtin University. Prof Vo is a recipient of the Australian Research Council’s inaugural Future Fellowship and the 2010 Australian Museum Eureka Prize for Outstanding Science in support of Defense or National Security. He is an associate editor of the IEEE Transaction on Aerospace and Electronic System. He is best known as a pioneer in the random set approach to multi-object filtering. His research interests are signal processing, systems theory and stochastic geometry with emphasis on target tracking, space situational awareness, robotics and computer vision.

##### References

- B.-N. Vo S. Singh and A. Doucet, “Sequential Monte Carlo methods for Bayesian Multi-target filtering with Random Finite Sets,” IEEE Trans. Aerospace and Electronic Systems, Vol. 41, No. 4, pp. 1224–1245, 2005.
- B.-N. Vo, and W. K. Ma, “The Gaussian mixture Probability Hypothesis Density filter,” IEEE Trans. Signal Processing, Vol. 54, No. 11, pp. 4091–4104, 2006.
- B.-T. Vo, B.-N. Vo, and A. Cantoni, “Analytic implementations of the Cardinalised Probability Hypothesis Density Filter,” IEEE Trans. Signal Processing, Vol. 55, No. 7, Part 2, pp. 3553–3567, 2007.
- D. Schuhmacher, B.-T. Vo, and B.-N. Vo, “A consistent metric for performance evaluation in multi-object filtering,” IEEE Trans. Signal Processing, Vol. 56, No. 8 Part 1, pp. 3447– 3457, 2008.
- B.-T. Vo, B.-N. Vo, and A. Cantoni, “The Cardinality Balanced multi-Bernoulli multi-target filter and its implementations” IEEE Trans. Signal Processing, vol. 57, no. 2, pp. 409–423, 2009.

**Download presentation slides** Point Process, Random Finite Sets and Multi-Object Estimation *2.83mb*

### Cyclostationary Signal Processing and its Generalizations

#### Presented by Prof Antonio Napolitano, University of Napoli, “Parthenope”

##### Abstract

In this tutorial, a review of cyclostationarity-based signal processing techniques for weak-signal detection, source location, and modulation classification will be presented [1]. Application to radar/sonar and cognitive radio will be considered. New classes of processes that generalize the cyclostationary model will be also reviewed [4], [5]. For these classes, the basic problems of probabilistic characterization, statistical function estimation, and sampling will be addressed [2], [3], [4], [5]. It will be shown how the new models allow one to remove constraints imposed by the so-called narrow-band condition [4, Sec. 7.5.1] which is necessary for cyclostationarity-based algorithms. With respect to cyclostationarity-based algorithms, the new models will allow one to consider scenarios with wider bandwidths, larger relative radial speeds between transmitter and receiver, larger data-record lengths, and lower values of SNR and SIR [5]. Cyclostationary signal processing, cognitive radio and radar, and wide-band mobile communications are hot topics for the signal processing community. A tutorial on consolidated and emerging results in these topics is of interest for attendees of SSP 2014.

##### Biography of the presenter

Antonio Napolitano (M’95, SM’07) was born in Napoli, Italy, in 1964. He received the Ph.D. degree in electronic and computer engineering in 1994, from the University of Napoli Federico II. Since 2005 he is Full Professor of Telecommunications at the University of Napoli ”Parthenope”. In 1995 was recipient of the EURASIP Best Paper Award for an article on higher order cyclostationarity and in 2006 for an article on the functional approach for signal analysis. In 2008 received form Elsevier the Most Cited Paper Award for the review article on cyclostationarity [1]. He is Associate Editor of the IEEE Transactions on Signal Processing and in the Editorial Board of Signal Processing (Elsevier). Since 2008 he is Elected Member of the Signal Processing Theory and Method Technical Committee (SPTM-TC) of the IEEE Signal Processing Society.

##### References

- W. A. Gardner, A. Napolitano, and L. Paura, “Cyclostationarity: Half a century of research,” Signal Processing, vol. 86, no. 4, pp. 639–697, April 2006.
- A. Napolitano and M. Tesauro, “Almost-periodic higher-order statistic estimation,” IEEE Transactions on Information Theory, vol. 57, no. 1, pp. 514–533, January 2011.
- A. Napolitano, “Sampling of spectrally correlated processes,” IEEE Transactions on Signal Processing, vol. 59, no. 2, pp. 525–539, February 2011.
- A. Napolitano, Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications. John Wiley & Sons Ltd – IEEE Press, 2012.
- A. Napolitano, “Generalizations of cyclostationarity: A new paradigm for signal processing for mobile communications, radar, and sonar,” IEEE Signal Processing Magazine, vol. 30, no. 6, pp. 53–63, November 2013.

**Download presentation slides** Cyclostationary Signal Processing and its Generalizations *6.54mb*

### Compressive Parameter Estimation: The Good, The Bad, and The Ugly

#### Presented by Prof Yuejie Chi, Ohio State University & Prof Ali Pezeshki, Colorado State University

##### Abstract

In a great number of sensing and imaging applications, we are interested in resolving a sparse superposition of parameterized signals from noisy measurements collected at a sensor suite, and the unknown signal parameters typically lie in a continuous space. Compressed sensing has been recently recognized as an emerging tool to take advantage of the sparsity prior to discretizing the continuous parameter space into a fine grid; this, however, raises both theoretical and algorithmic issues. This tutorial will examine the history of parameter estimation algorithms, give a survey of compressed sensing, and discuss both benefits and drawbacks of compressed sensing approaches for parameter estimation. The tutorial will examine sensitivities of compressed sensing to model mismatch and gridding of the parameter space and will discuss the impact of compressive sensing on Fisher information and threshold effects in parameter estimation. It will also cover recently proposed convex optimization methods that aim to eliminate gridding issues while maintaining some of the benefits of compressed sensing.

##### Biographies of the Presenters

Yuejie Chi is an assistant professor in the Electrical and Computer Engineering Department at The Ohio State University, with a joint appointment in the Biomedical Informatics Department at the Wexner Medical School since September 2012. She received a M.A. and a Ph.D. in Electrical Engineering from Princeton University, and a B.Eng. in Electrical Engineering from Tsinghua University. She received a Roberto Padovani scholarship from Qualcomm Inc. in 2010, a Best Paper Award at ICASSP in 2012, and a Google Faculty Research Award in 2013. Her research interests include high-dimensional data analysis, statistical signal processing, machine learning and their applications in networks, active sensing, imaging and bioinformatics.

Ali Pezeshki is an assistant professor in the Department of Electrical and Computer Engineering at Colorado State University, with a joint appointment in the Department of Mathematics. He received the B.Sc. and M.Sc. degrees in electrical engineering from the University of Tehran, Tehran, Iran, in 1999 and 2001, respectively. He received his PhD degree in electrical engineering at Colorado State University in 2004. In 2005, he was a postdoctoral research associate with the Electrical and Computer Engineering Department at Colorado State University. From January 2006 to August 2008, he was a postdoctoral research associate with The Program in Applied and Computational Mathematics at Princeton University. His research interests are in statistical signal processing, coding theory, active/passive sensing, and bioimaging. He is currently serving as a member of the Editorial Board of IEEEAccess.

##### References

- Y. Chi, L.L. Scharf, A. Pezeshki, and R. Calderbank, “Sensitivity of Basis Mismatch to Compressed Sensing,” IEEE Trans. on Signal Processing, vol. 59, pp. 2182-2195, 2011.
- Y. Chen and Y. Chi, “Robust Spectral Compressed Sensing via Structured Matrix Completion,” IEEE Trans. on Information Theory, Apr. 2013, under review.
- P. Pakrooh, L.L. Scharf, A. Pezeshki, and Y. Chi, “Analysis of Fisher Information and the Cramer-Rao Bound for Nonlinear Parameter Estimation after Compressed Sensing,” in International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, Canada, May. 2013.
- Y. Chi and Y. Chen, “Compressive Recovery of 2-D O_-Grid Frequencies,” in Asilomar Conference on Signals, Systems, and Computers (Asilomar), Paci_c Grove, CA, Nov. 2013.
- P. Pakrooh, A. Pezeshki, and L. L. Scharf, “Threshold E_ects in Parameter Estimation from Compressed Data,” in 1st IEEE Global Conference on Signal and Information Processing, Austin, TX, Dec. 3-5, 2013.

### Harmonic Analysis *on* and *of* Irregular Domains, Graphs, and Networks

#### Presented by Prof Naoki Saito, University of California, Davis,

##### Abstract

Traditional harmonic analytic tools such as Fourier and wavelet transforms have been the ‘crown jewels’ for a variety of fields involving regularly-sampled data such as data compression, image analysis, and statistical signal processing. On the other hand, there is an explosion of interest and demand to analyze data sampled on irregular grids, graphs, and networks, e.g., biological networks, sensor networks, social networks, etc. The conventional harmonic analysis tools originally developed for regular Euclidean spaces and regular lattices cannot directly handle such datasets. They are now being transferred to these more general settings to analyze data measured on them as well as their geometric and topological structures. In this process, the eigenvalues and eigenfunctions of the Laplace operator appropriately defined on those domains play a pivotal role. This can be easily recognized since the sine and cosine functions are the Laplacian eigenfunctions for the unit interval in R (with appropriate boundary conditions) after all. Together with the corresponding eigenvalues, the Laplacian eigenfunctions carry important topological and geometric information of the domains where the data are sampled. Moreover, they provide useful information to partition the domains into subdomains via the celebrated Courant nodal domain theorem, and hence serve as building blocks for constructing wavelet-like multiscale basis functions on such domains. In this tutorial, I plan to review this emerging field from the basics to cutting-edge applications, which I strongly believe will benefit the participants of this SSP workshop.

The topics covered in this tutorial are:

- Motivations
- Basics of Laplacian eigenvalue problems
- Laplacian eigenvalue problems on irregular domains; spectral geometry
- Laplacian eigenvalue problems on graphs and networks; building wavelet-like bases on graphs and networks
- Applications in signal processing on graphs and networks.

##### Biography of the presenter

Naoki Saito received the B.Eng. and the M.Eng. degrees in mathematical engineering from the University of Tokyo, Japan, in 1982 and 1984, respectively, and the Ph.D. in applied mathematics from Yale University in 1994. From 1984 to 1997, he worked for Schlumberger Ltd., first in Japan, and then in USA. In 1997, he joined the Department of Mathematics at the University of California, Davis, where he is currently a professor, and served as chair of the Graduate Group in Applied Mathematics from 2007 until 2012. Dr. Saito’s honors include: the Best Paper Award from SPIE for the wavelet applications in signal and image processing conference (1994); the Henri Doll Award (the highest honor for technical papers presented at the annual symposium within the Schlumberger organization) (1997); the ONR Young Investigator Award (2000); and the Presidential Early Career Award for Scientists and Engineers (2000). He has been serving on an editorial board of the two major journals: Applied and Computational Harmonic Analysis; Inverse Problems and Imaging. He is a senior member of IEEE as well as a member of IMS, JSIAM, and SIAM. In addition, he has also been serving as Vice Chair of the SIAM Activity Group on Imaging Science (SIAG/IS) and as Chair of the 2014 SIAG/IS Prize Selection Committee. He is also a frequent participant of the SSP workshops; he participated in the SSP in 2005, 2007, and 2009 (due to his schedule conflicts, he could not participate in the SSP in 2011 and 2012).

##### References

- N. Saito, “Data analysis and representation on a general domain using eigenfunctions of Laplacian,” Applied and Computational Harmonic Analysis, vol. 25, no. 1, pp. 68–97, 2008.
- N. Saito and E. Woei, “Analysis of neuronal dendrite patterns using eigenvalues of graph Laplacians,” Japan SIAM Letters, vol. 1, pp. 13–16, 2009. Invited Paper.
- L. Lieu and N. Saito, “Signal classification by matching node connectivities,” Proceedings of 15th IEEE Workshop on Statistical Signal Processing, pp. 81–84, 2009.
- L. Lieu and N. Saito, “Signal ensemble classification using low-dimensional embeddings and Earth Mover’s Distance,” in Wavelets and Multiscale Analysis: Theory and Applications (J. Cohen and A. I. Zayed, eds.), Chap. 11, pp.227–256, 2011, Birkhäuser.
- Y. Nakatsukasa, N. Saito, and E. Woei, “Mysteries around graph Laplacian eigenvalue 4,” Linear Algebra and Its Applications, vol. 438, no. 8, pp. 3231–3246, 2013.

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