Jonathan H. Manton

• Executive Director, Mathematics, Information and Communication Sciences, Australian Research Council
• Professor and Queen Elizabeth II Fellow, Department of Information Engineering, The Australian National University, Australia
• Honorary Professorial Fellow, Department of Electrical and Electronic Engineering, The University of Melbourne, Australia
• Associate Editor, IEEE Transactions on Signal Processing
• Committee Member, IEEE Signal Processing for Communications (SPCOM) Technical Committee
• Committee Member, Mathematics Panel, ACT Board of Senior Secondary Studies

Professor Manton was born in April 1973. He received his Bachelor of Science (mathematics) and Bachelor of Engineering (electrical) degrees in 1995 and his Ph.D. degree in 1998, all from the University of Melbourne, Australia. From 1998 to 2004, he was with the Department of Electrical and Electronic Engineering at the University of Melbourne. During that time, he held a Postdoctoral Research Fellowship then subsequently a Queen Elizabeth II Fellowship, both from the Australian Research Council. In 2005 he became a full Professor in the Department of Information Engineering, Research School of Information Sciences and Engineering (RSISE) at the Australian National University. Since July 2006, he is on secondment to the Australian Research Council as Executive Director, Mathematics, Information and Communication Sciences. He was an Associate Editor for the conference editorial board, IEEE Control and Systems Society and currently is an Associate Editor for the IEEE Transactions on Signal Processing. He is also on the IEEE Signal Processing for Communications technical committee. His research interests range from pure mathematics (e.g. commutative algebra, algebraic geometry, differential geometry) to engineering (e.g. signal processing, wireless communications).

Students, researchers and academics with interests in the general areas of signal processing, wireless communications, systems and control, and mathematics are most welcome to contact me. (Legitimate email is occasionally filtered out; please try again if you have not received a reply within a few days.)

Some idea of my research interests can be gained from my Research Page. I'm always open and keen to investigate new areas.

Note that the Australian National University (ANU) is a world class university, as confirmed by the Times Higher Education Supplement ranking ANU 16th in the world and the Shanghai Jiao Tong University ranking ANU 3rd in the Asia Pacific region behind only Tokyo and Kyoto universities. (Results taken from the 2004 surveys.)

Masters and PhD Students

If you are a motivated student with a first class honours degree from a top university wishing to pursue a Masters or PhD degree by research in an area potentially related to mine, please make contact.

Suggestions for a research topic include:

• Optimal Designs in Wireless Communications: In a wireless communications system (e.g. mobile telephone, wireless internet), the received signal is a very distorted version of the transmitted signal. Decades of research has gone into the design of transmission and reception schemes (e.g. waveform design, error correcting codes) endeavouring to allow the receiver to determine correctly what was sent. This project will investigate a new method for designing optimal transmission/reception strategies. The method relies on using stochastic optimization algorithms for tuning the design.
• Super-Imposed Training for Time-Varying Channels: Recently, the idea of using a super-imposed stream of pilot symbols to facilitate the estimation of the channel has become popular. (Rather than transmit a training sequence followed by the data symbols, a known sequence is arithmetically added to the data sequence prior to transmission. Roughly speaking, the receiver can then filter out the effects of the data sequence and then estimate the channel as if the known sequence was a training sequence.) However, many issues are currently unanswered, including how best to estimate the channel, under what conditions is this method preferable to a training sequence method, and so forth.
• Automated Construction of Low Complexity Estimators: Much of digital signal processing is concerned with designing algorithms which take a stream of noisy data as input and return an estimate of some parameter, such as a radar system which attempts to estimate the location of the target or a mobile telephone which attempts to determine what the transmitted message was. From a mathematical perspective, often at the heart of such a computation is the need to compute a non-linear projection. This project will investigate systematic methods for designing low complexity approximations to various non-linear projection operators.
• Numerical Solution of Polynomial Equations: Although there is a formula for computing the roots of a quadratic equation, Galois proved that there is no closed form expression (at least representable in terms of radicals) for general polynomials of degree five and higher. Nevertheless, computing roots of polynomials is a fundamental operation and numerical algorithms exist for doing so. This project will consider new methods for solving polynomial equations, the requirement being that the algorithms must have a guaranteed running time and accuracy.
• Optimization on Manifolds: An example of a manifold is a smooth surface such as a sphere or torus, but seemingly more complicated sets such as the set of all two dimensional planes in five dimensional space can be made into a manifold too (in this example, the (5,2)-Grassmann manifold). In fact, there are many problems in signal processing (weighted low rank approximation, subspace tracking etc) which can be naturally reformulated as finding the minimum of a cost function defined on a manifold. This area of optimization on manifolds is a current hot topic with much room remaining for further innovations.
• Estimation and Filtering on Manifolds: The logical extension to Optimization on Manifolds is to consider the statistical problem of filtering on manifolds. As an example, an ant might be walking on the surface of a sphere and periodic measurements made of the approximate location of the ant. Given these measurements, it is required to estimate the current position of the ant. Another example is subspace tracking, which can be reformulated as a filtering problem on a Grassmann manifold. Results in this area may prove to be very useful to the signal processing community.
• Low Noise Linear Amplifier Design: The transistor is not a linear amplifier, rather the collector current is approximately an exponential function of the voltage drop across the base and emitter. Negative feedback is commonly used to make non-linear amplifiers behave approximately linearly. However, other methods have also been proposed. This project will analyse and compare existing techniques as well as investigate new ways of designing linear amplifiers out of non-linear devices. As an added challenge, the effect of thermal noise on the performance of each design will be studied.
• Sound Restoration: Restoring sound archived on old records (vinyl or shellac) is a challenging problem. Deterioration of the grooves in a record leads to audible "clicks". Once these clicks have been detected, they need to be removed by replacing them with an estimate of what the original signal might have been. Since clicks obliterate portions of the original signal, it is necessary to use clean samples on either side of the click to build up a stochastic model for what the original signal is and then draw samples from this model to fill in the parts obliterated by the clicks. This project will investigate new audio restoration techniques, and is offered in collaboration with Brian Davies.

Visiting Academics

If you would like to visit The Australian National University for several days and give a seminar, or spend a sabbatical here, please contact me. We endeavour to have a steady stream of international visitors through our doors.

Professor Jonathan Manton
Department of Information Engineering
The Research School of Information Sciences and Engineering
The Australian National University
Canberra ACT 0200
Australia

Tel: +61 2 6125 1531
Fax: +61 2 6125 8651

Email: j.manton AT ieee.org