Research
What is nonlinear signal processing?
Signal processing is concerned largely with the development of efficient algorithms for manipulating signals. Signals are typically represented by a sequence of numbers, such as obtained by sampling the output of sensors. For example, the outputs of three microphones in a noisy lecture theatre can be sampled over a short interval of time to generate three sequences corresponding to the audio signals impinging on each of the microphones. A signal processing task might be to develop an algorithm which takes these sequences as input and filters out the background noise, producing an output signal which ideally corresponds exactly with what the lecturer said in that short interval of time.
Developing signal processing algorithms is an iterative process, involving the modelling of the physical problem to be solved, the derivation of perhaps an optimal algorithm for solving the problem based on the model, followed by attempts to reduce the computational complexity of the algorithm to make it a viable solution in practice, often at the expense of optimality. This reduction in complexity may come about by making linear approximations to reduce the problem or sub-problem to one for which efficient algorithms are known.
We propose to study several nonlinear problems which occur frequently as sub-problems in signal processing tasks. We will develop a framework for deriving efficient numerical algorithms for implementing these tasks. This framework will not involve any approximations but rather will use the power of “nonlinear mathematics”, by which we mean differential geometry, to implement the task exactly.
Current Projects
We have the following projects avaliable: