Paul is a researcher in the development of algorithms and techniques of machine learning and signal processing, and the application of these techniques in nuclear magnetic resonance, audio, communications and biomedical devices.

The specific techniques he uses include:
◾ Machine Learning for solutions of inverse problems.
◾ Convex analysis.
◾ Blind Source Separation (BSS) methods such as Independent Component Analysis (ICA).
◾ Bayesian methods.

Areas of application include:
◾ Image reconstruction (e.g., medical imaging, radio astronomy).
◾ Magnetic resonance (imaging, spectroscopy and relaxometry).
◾ Modelling of human physiology (e.g., cerebral haemodynamics).
◾ Modelling of the human cochlea.

Other areas Paul has worked on in the past include:
◾ Holographic sound recording and reproduction.
◾ Sonar signal processing.
◾ Acoustic source localisation and tracking (including bioacoustics).
◾ Passive detection of foetal heartbeat.
◾ Seizure detection in neonatal electroencephalogram (EEG).
◾ Self-calibration of microphone arrays.
◾ Load-bar signal analysis.
◾ Real time prediction of wireless channels.

Since 2006, he has been awarded over three million dollars of research funding including Marsden (NZ) and MBIE (NZ) and ERC (European Commission) grants.