Real-Time Subsampled Analysis and Recovery for High-Resolution 3D Tomography

The project will be aligned with the EPSRC Centre for Doctoral Training CDT in Distributed Algorithms:The What, How and where of Next-Generation Data Science.

The student will benefit from the cohort-based training associated with the CDT as well as access to the CDT’s dedicated supercomputing facilities at the University of Liverpool.

The CDT is part of the wider Signal Processing Group where the student will benefit from collaborating with experts in Bayesian computational methodology, autonomy, decision support, data fusion, tracking, image processing, radar processing, acoustic analysis, text analytics, machine learning, behavioural analytics, simulation and energy-efficient hardware implementation.

Description: 3D Imaging, commonly referred to as tomography, is used in many state-of-the-art imaging and characterisation methods, critical to both the medical and engineering sciences. There are several mechanisms used to obtain experimental data, that range from imaging multiple identical structures naturally oriented in different directions, to tilting either the object or illumination and acquiring images of the same structure from multiple different directions.

In all cases, the quality of the final 3D reconstruction is determined by the total number of different projections and the signal to noise of each individual image. This requirement creates numerous experimental challenges; it takes time to acquire each projection, and to achieve high signal/noise each projection requires a high flux of potentially damaging radiation (X-rays, electron, protons, light etc). 

Recently SenseAI has developed a suite of 2D and hyperspectral imaging tools that use compressive sensing and sparse-coding based methods to reduce image acquisition time and inpaint missing information (www.youtube.com/@SenseAI_Innovations). 

Expanding the current 2D methodology into 3D imaging at a speed, resolution and sensitivity that can lead to practical applications will require several innovative approaches to be developed. For example, new considerations arise when determining the form and shape of the data subregions used for patch-based inpainting methods. While there are often cases where each axis may be treated identically (such as 3D imaging where the third axis represents an additional spatial dimension), this assumption is not universally valid. In the case of rotational volumetric imaging, where the third dimension represents a given angle, adjacent voxels along the 3^rd axis no longer represent a linear translation in real-space, and thus, previous assumptions made about similar 2-dimensional data do not hold, requiring the development of a novel sensing model. Additionally, while the current (GPU parallelised) implementation for 2D signals relies on the vectorisation of each subregion, previous research has shown that for larger 3D volumes, tensor-based dictionary learning, such the representation of each signal as a sparse sum of Kruskal decompositions, can lead to an improvement in both signal recovery and time-to-solution.

The goal of this PhD is therefore to evaluate the different approaches to sparse sampling, signal modelling and recovery in 3 dimensions to develop a practical methodology that will allow optimised real-time subsampled analysis of 3D signals for a range of imaging applications.

Every project aligned to the CDT is offered in collaboration with an industrial partner who as well as providing co-supervision will also offer the unique opportunity for students to access state of the art computing platforms, work on real world problems, benchmarking, and data. Our graduates will gain unparalleled experiences working across academic disciplines in highly sought-after topic areas, answering industry need.

The project is suited to a candidate with an undergraduate or master’s degree in a numerate subject, with an interest in next generation data science, computing, and working with partners to solve real-world problems.

The successful student will be based at the University of Liverpool and be aligned to the CDT and Signal Processing Group .

This studentship is open to British and EU nationals.

Apply now: https://www.liverpool.ac.uk/distributed-algorithms-cdt/apply/

Applicants please note: You must not submit a research proposal. The PhD project is defined. You must provide a supporting statement (no more than 700 words) that explains why you are interested in undertaking a PhD, this specific topic and joining the research group. More application guidance can be found on the apply link above.