WP1.1 Scalable solutions for probabilistic modelling and uncertainty quantification
WP1.1 Summary presentation slides
This work package will investigate Bayesian uncertainty quantification tools for linear inverse problems across a range of scales. In the first instance this research will be primarily illustrated by imaging applications involving data under-sampling, high (non-standard) noise sources and observed phenomena which are non-stationary. While most existing uncertainty quantification tools simply measure image quality, it is often unclear how such measures translate into uncertainty about the information of interest, e.g., the presence or movement of an object or anomaly, as intended in this work.  
Typical application scenarios include hyperspectral imaging, low-photon imaging/ranging (single-photon Lidar) and radiation monitoring (nuclear safety).     

WP1.2 Summary presentation slides
WP1.2 Scalable dynamic and distributed inference
WP1.2 will develop novel message passing (MP) algorithms for inference in distributed and modular sensor networks (e.g. Dstl’s SAPIENT system). Bayesian graphical models provide a powerful framework for representing structure in distributions over many heterogeneous variables. Scalable solutions focus on approximate inference, utilising: bespoke approximations, Gaussian-mixture Belief Propagation (BP), particle BP, kernel BP, expectation particle BP, and approximate MPs. This WP will investigate: (1) trade-offs between accuracy, complexity, convergence, and communication-bandwidth for resource-constrained scenarios and high-volumes of data (linked to WP2.1/2.2); (2) improving efficiency in settings with mixed-integer/non-Gaussian continuous variables.  
Exemplar applications include the on-line detection of fleeting non-stationary signals, and tracking an unknown number of targets from multiple-heterogeneous sensors.

• "Adaptive Kernel Kalman Filter Multi-Sensor Fusion." 2021 IEEE 24th International Conference on Information Fusion (FUSION). IEEE, 2021 - View video
• Adaptive Kernel Kalman Filter M. W. Sun, M. E. Davies, I. Proudler, J.R. Hopgood - View video

WP1.3 Techniques for high-dimensional, and non-traditional signals
WP1.3 will develop signal processing techniques for high-dimensional, heterogeneous and non-traditional data. We will consider dimensionality reduction, where techniques such as tensor factorisation or polynomial matrix decomposition approaches are potential candidates to lead to low rank or subspace approximations. Robustness to high data volumes and limited reliability of sensors will be key. For scenarios that included heterogeneous and in parts non-traditional sensor data, graph signal processing techniques will be explored to capture complex correlations within and between data streams.
Exemplar applications include data acquired by e.g. large sonar arrays, and irregular, heterogeneous data that draws some inputs form non-traditional sources such as social networks or intelligence reports.

• Polynomial Procrustes Problem: Paraunitary Approximation of Matrices of Analytic Functions - View video
• EURASIP webinar - Formulating and Solving Broadband Multichannel Problems Using Matrices of Functions - View video