Melbourne School of Engineering
Nonlinear Signal Processing Laboratory

POSTGRADUATE PROJECTS

The following PhD projects are currently available for students wishing to pursue postgraduate studies at NSP Lab. This list is not exhaustive but reflects ongoing research activity and interests. Students having a strong background in mathematics and with their own research proposal are particularly encouraged to contact NSP Lab to discuss postgraduate opportunities.

 

Information theory for signals

Markov Chain Sequential Monte Carlo

Information theory for signals

Information theory, having arisen from the systematic study of communication, is today known to have deep connections with many fields, most famous are statistical physics and probability theory. In statistical signal processing, information theory characterises a priori the performance of inference techniques. It does so by giving a, surprisingly elegant and succinct, quantification of the compressibility of data arising from a given statistical model. In many parts of system theory, information theory leads to valuable insights into complex random systems. The most promising recent applications are to neuronal networks.

Most usually, information theory appears in signal processing in static or stationary contexts. It then relates to data where time evolution plays no important role and applies to point estimation techniques. Stationarity assumptions do not survive even the mildest nonlinearity. It appears that for information theory to be applied to nonlinear signal processing, it needs to be extended from random variables to stochastic processes, i.e. to signals. While mathematicians have paid attention to this possibility, it remains somewhat obscure to engineers, statisticians, or neuroscientists.

Students working on this project will be asked to understand and adapt, for the needs of engineering problems, the techniques of information theory for signals. This involves, in particular, characterising their potential applications and using them to solve choice concrete problems. This will be an opportunity to learn, through supervised research, about statistical inference, information theory and some more advanced aspects of stochastic analysis. It will also lead to a better grasp of current target applications, e.g. nonlinear signal processing, neuroscience, mathematical finance. Information theory is a prominent topic within NSP Lab and students will profit from close interaction with NSP Lab researchers to gain specific expertise highly useful for future work.

Preliminary references

Contact - Dr. Salem Said

 

Markov Chain Sequential Monte Carlo

Monte Carlo methods date back to the 1940s and the Manhattan project. They refer to the use of generated random numbers in carrying out integrals or solutions of differential equations, ordinary or partial. Since they are now accessible to personal computers, they have become widely popular. In addition to their importance as numerical methods, they provide a complete paradigm for "computer probability". In fact, practical knowledge of Monte Carlo methods is sufficient for engineers to solve very advanced probabilistic problems.

Monte Carlo methods may be divided into, roughly speaking, sequential and serial. The first consist mainly of particle filtering techniques, the second of Markov chain Monte Carlo (MCMC). Particle filters require a considerable computational effort. While MCMC does not suffer from this problem, its convergence may be hard to ensure. For a long time, an important challenge has been to successfully bring together these two approaches.

Students with prior experience in using Monte Carlo methods for real problems are invited to discover recent works combining particle filtering with MCMC. Such works have extended Bayesian inference to a large new class of statistical models. Learning these cutting edge techniques will place the student in a great position to pursue research in nonlinear signal processing, especially in relation to filtering and nonparametric estimation. Applications span many problems in engineering and mathematical finance. We also propose to explore applications in neuroscience.

Preliminary reference

Contact - Dr. Salem Said