Signal Processing Laboratory

The increasing availability of digital music media has created a need for machine-readable representations of musical data for archiving, searching, education and performance. A large number of tasks involved in this, such as music transcription, score alignment, audio synchronization and live `music minus one' accompaniment, can be set in a hidden Markov model (HMM) probabilistic framework, where the hidden state represents a position within the musical score. This talk will describe one such framework, together with an accompanying observation model describing how the spectrogram representation of audio is produced from a set of signal sources.

The material is based on the following links:

1. C. Raphael, "A Hybrid Graphical Model for Aligning Polyphonic Audio with Musical Scores", International Conference on Music Information Retrieval (ISMIR), 2004
2. N. Whiteley, A. T. Cemgil and Simon Godsill, "Bayesian Modelling of Temporal Structure in Musical Audio", 7th International Conference on Music Information Retrieval (ISMIR), 2006.
3. L. Grubb and R. B. Dannenberg, "A Stochastic Method of Tracking a Vocal Performer" in Proceedings of the International Computer Music Conference, San Francisco: International Computer Music Association, (1997), pp 301-308.

The area of image searching has become more important in recent years owing to the large growth of digital image libraries. The dual-tree discrete wavelet transform is able to achieve the properties of approximate shift invariance and good directional selectivity, together with multi-scale analysis. This talk gives an introduction to improve the efficiency of searching the image with the Dual-Tree Complex Wavelet Transform (DTCWT), and comparing it with the several other methods.

The material is based on the following links:

1. J.P. Lewis, "Fast Normalized Cross-Correlation"
2. Nick Kingsbury, "Complex Wavelets for Shift Invariant Analysis and Filtering of Signals", Journal of Applied and Computational Harmonic Analysis, vol 10, no 3, May 2001, pp. 234-253.

A short introduction to Recurrence Quantification Analysis (RQA), a nonlinear method for quantifying phase space trajectories, will be used to preview several novel methodologies that leverage RQA metrics for finding recurrent frequency and phase nonlinearities in EEG. Preliminary results will be highlighted that delineate the onset of cognitive processes in the cortex and repeatable neurological phenomenon. Clinical implications include assessing the depth of anesthesia, establishing metrics for comatose and persistent vegetative patients, surveying brain trauma, epilepsy, and quantification of other neurological and psychological responses. (This talk will continue from the earlier one on 28/02/2007.)

The material is based on the following links:

1. RECURRENCE PLOTS AND CROSS RECURRENCE PLOTS
2. N. Marwan: Encounters With Neighbours - Current Developments Of Concepts Based On Recurrence Plots And Their Applications, Ph.D. Thesis, University of Potsdam, ISBN 3-00-012347

Ultrasound can be used as a cheap, safe and non-invasive form of imaging in a medical context. There are, however, inherent resolution problems relating to the current generation of ultrasound imaging. This talk gives an introduction to the current imaging technique, its problems, and an algorithm based on Expectation Maximisation is described to enhance the images post-capture.

The material is based on the following links:

1. Restoration of Medical Pulse-Echo Ultrasound Images, James Kee Huat Ng
2. Wavelet Restoration of Medical Pulse-Echo Ultrasound Images in an EM Framework, J K H Ng, R W Prager, N G Kingsbury, G M Treece, A H Gee

This talk will introduce human visual signal processing. The brain extracts local cues or features and then assembles these to detect coherent and meaningful patterns. I will discuss how information is processed as it progresses through the visual pathway and then talk about Form perception, while trying to find out how the brain is a very 'efficient' coder and how the brain balances cost vs accuracy in visual analysis.

The material is based on the following links:

1. Introduction to human vision, "Eye, Brain, and Vision", David H. Hubel
2. Primary Visual cortex, "Eye, Brain, and Vision", David H. Hubel
3. Impulses Synapses and circuits, "Eye, Brain, and Vision", David H. Hubel
4. The eye, "Eye, Brain, and Vision", David H. Hubel

A short introduction to Recurrence Quantification Analysis (RQA), a nonlinear method for quantifying phase space trajectories, will be used to preview several novel methodologies that leverage RQA metrics for finding recurrent frequency and phase nonlinearities in EEG. Preliminary results will be highlighted that delineate the onset of cognitive processes in the cortex and repeatable neurological phenomenon. Clinical implications include assessing the depth of anesthesia, establishing metrics for comatose and persistent vegetative patients, surveying brain trauma, epilepsy, and quantification of other neurological and psychological responses.

The material is based on the following links:

1. RECURRENCE PLOTS AND CROSS RECURRENCE PLOTS
2. N. Marwan: Encounters With Neighbours - Current Developments Of Concepts Based On Recurrence Plots And Their Applications, Ph.D. Thesis, University of Potsdam, ISBN 3-00-012347

This talk will be an introduction to Sequential Monte Carlo methods for filtering and smoothing in time series models. After reviewing the basic concepts such as importance sampling, resampling, Rao-Blackwellization, I will illustrate how those ideas can be applied for inference in switching state space models (using the mixture Kalman filter) and changepoint models (where exact inference is possible).

The material is based on the following papers:

1. A. Doucet, S. Godsill, and C. Andrieu, "On sequential Monte Carlo sampling methods for Bayesian filtering," Statistics and Computing, vol. 10, no. 3, pp. 197-208, 2000.
2. R. Chen and J. S. Liu, "Mixture Kalman filters," J. R. Statist. Soc., vol. 10, 2000.
3. P. Fearnhead, "Exact and efficient bayesian inference for multiple changepoint problems," Tech. Rep., Dept. of Math. and Stat., Lancaster University, 2003.

The nonlinear Bayesian filtering problem is addressed, using Sequential Monte Carlo techniques, or particle filters, for an approximate solution. The basic theory is briefly discussed and some methods such as the marginalized particle filter or Rao-Blackwellized particle filter is discussed in detail, in particular elaborating on the computational complexity of the algorithm. Several applications mainly in positioning and tracking are described, and compared to traditional approaches. Particularly, the use of external database information to enhance estimation performance is discussed for GPS free underwater and surface navigation. In parallel, fundamental limits are derived analytically or numerically using the Cramer-Rao lower bound, and the result from estimation studies is compared to the corresponding lower bound. Finally, some ongoing working in the positioning and tracking field within the particle filter framework is discussed briefly.

All following materials can be downloaded from here:

1. R. Karlsson. Particle Filtering for Positioning and Tracking Applications. Dissertations. No. 924, Linköping University, Linköping, Sweden, March 2005.
2. R. Karlsson and F. Gustafsson. Surface and underwater navigation using particle filters. IEEE Trans. Signal Processing, 54(11):4204--4213, 2006
3. R. Karlsson, T. Schön, and F. Gustafsson. Complexity analysis of the marginalized particle filter. IEEE Trans. Signal Processing, 53(11), November 2005

With shameless self-involvement, I will present some work that I've been involved in during my PhD on trying to develop methods through which functional relationships between genes may be inferred. We'll look at the problem from both ends, the causes (transcription factor binding) and the effect (mixtures of mRNA concentration functions) of functional relationships, and in each case present an algorithm for performing inference in that domain. It should be fun.

The relevant materials can be download from here.

1. A Sequential Monte Carlo EM Approach to the Transcription Factor Binding Site Identification Problem
2. BAYESIAN UNSUPERVISED SIGNAL CLASSIFICATION BY DIRICHLET PROCESS MIXTURES OF GAUSSIAN PROCESSES

Motion capture is the richest source of data on human motion for computer animation. The positions of markers attached to the subject are captured at high frequency rate enabling us to reconstruct the details of human motion. Motion capture data always contains large number of frames which makes post-processing difficult. The file size is also an issue, since a few hundred megabytes are required to store a motion as short as a few minutes.

This presentation will first give a brief introduction for 3D human motion and motion capture systems, followed by our proposed 3D human motion compression scheme, a framework based on multiresolution Wavelet decomposition. Given a set of motion capture data and a global error constraint, our system finds the optimal combination of the decomposition levels for the joints that minimizes the number of frames stored. We model this problem as a discrete dynamic optimization problem, then use dynamic programming technique to find the optimal solution. A non-linear reconstruction algorithm is then adopted as the refinement process to further improve the visual quality of the compressed motion. Our approach can achieve a 200 to 1 compression ratio in the reconstruction without noticeable perceptual artifacts. Future works and demonstrations are then presented to conclude the talk.

The relevant materials can be download from here.

1. multiresolution wavelet decomposition
2. some background about dynamic programming

The study of detection and tracking of targets has a long history. The basic problem has remained the same since the invention of Radar and other long range sensors. Numerous approaches have been proposed over the years to tackle this problem, ranging from Kalman filter and its non-linear extensions to JPDAF trackers. More significantly, the detection and tracking are treated as two separate processes. This is partly due to the limitations of computation powers and as well as lack of feasible computational framework for optimal non-linear filter.

Ever increasing demands of modern battlefield have placed an increasing strain on modern sensor systems. They need to be able to detect and track targets with lower and lower signature and in a hostile environment of high level of false alarm. Recent approaches to this difficult problem formulates the detection and tracking as a joint estimation process. Non-linear filter such as particle filter is well poised to tackle this in an optimal fashion.

This presentation will highlight two recent works in the area of particle filters in joint detection and tracking. The first is a paper by Kreucher et. al. on Particle Filtering for Multitarget Detection and Tracking. The second is by Zia Khan et. al. on MCMC-Based Particle Filtering for Tracking a Variable Number of Interacting Targets. The aim of the presentation is to introduce the interesting contributions of these papers, and briefly describe some results and possible extensions.

The presentation will initially deal with Geometric Algebra, a framework based on the algebras of Clifford and Grassmann, and will show how it can be used in analysing 3-dimensional transformations. This is not a system designed specifically for the task in hand, but rather a framework for all mathematical physics. Central to the power of this approach is the way in which the formalism deals with rotations; for example, if we have two arbitrary sets of vectors, known to be related via a 3-D rotation, the rotation is easily recoverable if the vectors are given. Extracting the rotation by conventional means is not straightforward. The calculus associated with geometric algebra is particularly powerful, enabling one, in a very natural way, to take derivatives with respect to any multivector (general element of the algebra). What this means in practice is that we can minimize with respect to rotors representing rotations, vectors representing translations, or any other relevant geometric quantity.

Any motion capture process starts with calibrating the cameras – i.e. determining their relative positions and orientations and the internal characteristics. In any practical system, we require this process to be easy to accomplish and the results to be accurate. This initial stage is the subject of the presentation, in particular the determination of the relative orientations and positions of any number of cameras given no special calibration object. Geometric algebra is used to develop the algorithms for calibration, which result in an iterative scheme which does not require any non-linear minimization stage.

Then I will present some results showing accuracy of the calibrations via simulations and tests on real data.

Finally a study on how to extend these algorithms to determine the internal calibration is briefly discussed.

The relevant materials can be download from here.

1. J. Lasenby, A. Stevenson, Using geometric algebra for optical motion capture. Geometric Algebra, with applications in science and engineering, eds. Bayro-Corrochano & Sobczyk, Birkhauser, pp. 147-169, 2000. Click here to download.
2. J. Lasenby, W.J. Fitzgerald, C.J.L. Doran and A.N. Lasenby, New Geometric Methods for Computer Vision. Int. J. Computer Vision, 26(3), pp. 191-213, 1998. Click here to download.

After a brief background discussion of model-based signal processing, we introduce the idea of the innovations approach. It is shown that this method of deriving the processor provides a large amount of insight into the development and eventual design of practical model-based schemes . By first starting with the batch minimum variance solution to the state estimation problem, we show that by reformulating the problem in terms of an orthogonal transformation leads naturally to the innovations sequence. With the batch solution in hand, we then show how it evolves to a recursive formulation and to the linear MBP or equivalently the Kalman filter in the linear Gaussian case.. We provide a brief overview of the entire filter derivation. Next we investigate properties of the innovations sequence and show how they provide insight to the optimal design of the MBP. Practical statistical tests are then presented and demonstrated on a simple example to illustrate the idea of the minimum variance design and analysis using the innovations approach.

The reference text: "Model-Based Signal Processing," Candy, Wiley, 2006. is available at the reference desk in the Engineering Library--people can use it. Other materials can be downloaded here.

In many signal processing applications it is required to estimate a latent or ‘hidden’ process (the ‘state’ of the system) from noisy, convolved or non-linearly distorted observations. Since data also arrive sequentially in many applications it is therefore desirable (or essential) to estimate the hidden process on-line, in order to avoid memory storage of huge datasets and to make inferences and decisions in real time. Some typical applications from the engineering perspective include:

• Tracking for radar and sonar applications
• Real-time enhancement of speech and audio signals
• Sequence and channel estimation in digital communications channels
• Medical monitoring of patient eeg/ecg signals
• Image sequence tracking

In this tutorial we will consider sequential estimation in such applications. Only when the system is linear and Gaussian can exact estimation be performed, using the classical Kalman filter. I will present a succinct derivation of the Kalman filter, based on Bayesian updating of probability models. In most applications, however, there are elements of non-Gaussianity and/or non-linearity which make analytical computations impossible. Here we must adopt numerical strategies. I will consider a powerful class of Monte Carlo filters, known generically as particle filters, which are well-adapted to general problems in this category. Worked examples will be given for several simple modelling scenarios.

Other materials can be downloaded here.

The slides can be downloaded here.

In many signal processing applications it is required to estimate a latent or ‘hidden’ process (the ‘state’ of the system) from noisy, convolved or non-linearly distorted observations. Since data also arrive sequentially in many applications it is therefore desirable (or essential) to estimate the hidden process on-line, in order to avoid memory storage of huge datasets and to make inferences and decisions in real time. Some typical applications from the engineering perspective include:

• Tracking for radar and sonar applications
• Real-time enhancement of speech and audio signals
• Sequence and channel estimation in digital communications channels
• Medical monitoring of patient eeg/ecg signals
• Image sequence tracking

In this tutorial we will consider sequential estimation in such applications. Only when the system is linear and Gaussian can exact estimation be performed, using the classical Kalman filter. I will present a succinct derivation of the Kalman filter, based on Bayesian updating of probability models. In most applications, however, there are elements of non-Gaussianity and/or non-linearity which make analytical computations impossible. Here we must adopt numerical strategies. I will consider a powerful class of Monte Carlo filters, known generically as particle filters, which are well-adapted to general problems in this category. Worked examples will be given for several simple modelling scenarios.

Other materials can be downloaded here.

This presentation will give an introduction to Audio Speaker Localisation and Tracking. It will focus on Darren Ward et al. (see attached paper). This paper reviews particle filtering algorithms applied to the tracking of a human being in a room.

Tracking is based on differing spatial delays between microphone pairs which are used to provide a bearing angle for the speaker. Multiple bearings are then triangulated to obtain an estimate of the speaker’s position. This estimated is then tracked using Particle Filters.

Current issues and possible extensions of this algorithm will be discussed and include:

• Dealing with periods of silence using dynamics and voice activity detection
• Incorporation of fixed lag smoothing to correct for erroneous predictions
• Extension to multiple speakers and the echoic environment
• Spacing of microphones close enough to each other to allow for all pairings to be used (and for incorporation into a portable mobile device)
• Use of amplitude and time delays parameters for very closely spaced microphones as a different data steam, as introduced in Yilmaz and Rickard (see attached paper) in a Blind Source Separation environment
• Extension to use this tracking information for room shape identification and reverberation cancellation

This presentation will give an introduction to the Particle Swarm Optimization (PSO) algorithm, which is a recently stochastic optimization method proposed by J. Kennedy and R. C. Eberhart in 1995 (see attached paper). It is inspired by the behaviour of a bird flock or insect swarm, and can be seen as a distributed algorithm for multidimensional search. According to PSO mechanism, each individual adjusts its flying speed and direction to fly through a hyperspace based on the information from the best local or global individual and its past experience. Therefore, by observing the behaviour of the flock and memorizing individual flying history, all the individuals in the swarm can quickly converge to near-optimal geographical positions.

A great deal of improvement strategies have been proposed, in which the “Kalman Swarm” (see attached paper) embodies quite promising performance compared with other methods. Kalman Swarm method will be investigated in this presentation, and a more general optimization method will be proposed under the framework of Bayesian filtering technique. At last some (potential) applications of these PSO methods will be addressed.

This presentation will deal with the global optimization procedure engineered by Peter Muller (see attached paper), termed model augmentation. The goal of optimization in an uncertain environment, is concerned with the maximization of the expected utility surface with respect to some choice variable. In this procedure, the choice variable over which the optimization is achieved is seen as a random variable. A new joint probability model over the data, parameters, and artificial choice variable is defined in such a way that the marginal distribution over this new artificial choice random variable is set to be proportional to the expected utility function. This means that the problem of optimization is artificially recast in the domain of estimation, and samples from the marginal over the choice variable will be representative of the expected utility function. The direct implication is that more interesting regions of the utility surface will be sampled with high probability.

The above approach opens the door for a whole collection of sampling based methods to be applied to a wide variety of difficult optimization problems. In his paper, Muller uses a MCMC based method to sample from the artificial distribution. In addition where the expected utility surface is very flat, annealing methods may be used to sharpen the peaks. Future research will focus on the application of the particle filter methods in the above framework to challenging time varying stochastic optimization problems. This may lead to application to diverse fields such as (non-linear) adaptive filtering, control problems, radar tracking, perceptual audio restoration and financial objectives.

Other materials can be downloaded here.

This paper introduces a method by which intuitive feature entities can be created from ILP coefficients. The ILP transform is a pyramid of decimated complex-valued coefficients at multiple scales, derived from dual-tree complex wavelets, whose phases indicate the presence of different feature types (edges and ridges). We use an Expectation-Maximization algorithm to cluster large ILP coefficients that are spatially adjacent and similar in phase. We then demonstrate the relationship that these clusters possess with respect to observable image content.

The ILP coefficients it refers to are developed in this support paper:

COARSE-LEVEL OBJECT RECOGNITION USING INTERLEVEL PRODUCTS OF COMPLEX WAVELETS This paper introduces the Interlevel Product (ILP) which is a transform based upon the Dual-Tree ComplexWavelet. Coefficients of the ILP have complex values whose magnitudes indicate the amplitude of multilevel features, and whose phases indicate the nature of these features (e.g. ridges vs. edges). In particular, the ILP coefficients are invariant to small shifts in the original images. We accordingly introduce this transform as a solution to coarse scale template matching, where alignment concerns between decimation of a target and decimation of a larger search image can be mitigated, and computational efficiency can be maintained. Furthermore, template matching with ILP coefficients can provide several intuitive “near-matches” that may be of interest in image retrieval applications.

And finally, the original complex wavelet paper upon which it is all based can be found here.

Other materials can be downloaded here: paper 1 and paper 2.

Psychoacoustics can be defined simply as the psychological study of hearing. The initial aim of psychoacoustics research is to find out how hearing works. Recently, psychoacoustics models became very popular and initiated numerous breakthroughs in high bandwidth audio applications; for example, Mpeg one layer 3 audio. The presentation will introduce basic concepts of psychoacoustics and elaborate on perceptually motivated approaches to statistical music restoration.

The materials can be downloaded here: paper.

Research into the reproduction of sound is an extremely active area due to the direct consumer applications and the ability for instant feedback during development. In this presentation I will give an overview of the work that I completed as an undergraduate at the Australian National University and as a Research Engineering at National ICT Australia. This work was based around using spherical harmonics to generate an accurate model of sound within a 3D region of space. Within this frame work we where able to establish a relationship between the number of loudspeakers used in the reproduction, the size of the reproduction region (sweet-spot), the maximum frequency component within the sound field and a measure of 'reproduction accuracy'.

The materials can be downloaded here: paper and thesis.

In order to obtain better result in NMR, chemistry people need higher dimensional NMR processing. But, it is time consuming process so that a few chemists have been trying to reduce dimensions using GFT and RT-NMR, I will give a presentation about methodologies to support such a system (speically, RT-NMR) with statistical approaches such as Markov Random Field.

The materials can be downloaded here: paper 1, paper 2, and paper 3.

In this Reading Group session we will discuss the following paper:
M. Zibulevsky, B. A. Pearlmutter, P. Bofill, and P. Kisilev, "Blind Source Separation by Sparse Decomposition", chapter in the book: S. J. Roberts, and R.M. Everson eds., Independent Component Analysis: Principles and Practice, Cambridge, 2001.
The paper addresses the source separation problem by means of sparsity.

The link with the Independent Component Analysis approach presented in the following seminal paper will be shown:
Bell A.J. and Sejnowski T.J. 1995. An information maximisation approach to blind separation and blind deconvolution, Neural Computation, 7, 6, 1129-1159.

J-F Cardoso showed that the information maximisation method presented in the latter paper is equivalent to standard maximum likelihood estimation. The following paper might be helpful to understand the information maximisation approach:
Jean-François Cardoso, Infomax and maximum likelihood for source separation, IEEE Letters on Signal Processing, vol. 4, no. 4, pp. 112-114, April, 1997.

The reader might like to read the too latter papers to understand the links between sparsity based methods and ICA methods. However the Reading Group session will mainly focus on the Zibulevsky and al paper only.

The materials can be downloaded here, and the slides in Powerpoint can be downloaded here.

The materials can be downloaded here, and the slides in Powerpoint can be downloaded here.

The slides can be downloaded here.