Transient Tomography for Defect Detection

The ability to locate, estimate the size and shape, along with the properties of a hidden defect concealed in an exterior enclosure is of importance to the sectors of Security (landmine detection or detecting explosive material or illicit substances in vehicles stationary or in motion), Energy (detecting underground pipe blockages or, monitoring the structural integrity of a reactor while reducing human exposure in harmful and hostile environments), Health (detecting anomalies/ tumours/viruses), etc.

Unlike similar tomographic techniques, e.g., electrical impedance/resistive/ capacitance tomography, which are stationary methods, time-dependent tomography uses transient data information to detect hidden defects which may be static or moving in time. In comparison with its stationary boundary potential + current flux formulation, the transient boundary temperature + heat flux formulation provides more temporal information to retrieve the unknown physical properties of the defect that is imaged. As such, the proposed research enhances non-destructively monitoring the integrity of structures, and practically it can be used to detect foreign obstacles concealed inside other objects.

Any tomography technique has at its heart a difficult inverse problem that needs to be solved, hence the mathematical analysis on the well- or ill-posedness of the model is necessary to be undertaken for scientific justification, as well as to be able to improve it. Difficulties arise due to the non-existence, non-uniqueness or the instability of solution, and establishing the degree of ill-posedness of the operator that needs inverting, is non-trivial.

Moreover, concerning the actual inversion, to detect buried/hidden objects based on the transient approach one has to solve a difficult nonlinear and ill-posed moving boundary problem, which leads to a non-convex multi-dimensional optimization that needs to be further regularized to achieve stable results.

The thermographic principle of taking surface temperature measurements as we dynamically heat or cool an object offers an interesting transformative idea, but the approach is yet to be tested in an uncontrolled environment, and current understanding of the applicability of the technique to industrial scenarios is yet to be apprehended. Therefore, this mathematical modelling project using thermal-waves will provide a solid platform on which improved instrumentation for imaging can be built. The adventure of the research is to verify and validate the appropriateness of the new model by inverting both numerically simulated and experimental data in order to ultimately become available for real life application.


The thermal-wave tomography modelling presented in this proposal serves as a proof-of-concept idea that can be improved in future studies to lead to new and non-invasive medical modalities for cancer detection and imaging. In particular, it may lead to a follow-up standard proposal for constructing the world’s first thermal breast tomography system that could revolutionise the way women are scanned for breast cancer.

The medical side of breast cancer detection constitutes, in the first instance, the main field of immediate practical application, but the potential of the technique to material characterization, e.g. landmine detection or security screening, is much broader. As the proposed tomography method can be used to control/monitor the temperature and for defect detection within materials, it would be of relevance to the EPSRC Core Programmes in engineering, materials, mathematical sciences, medical physics and geophysics, and to their Strategic Programmes in basic technology, security, energy, health, environment and life sciences interface.

For example, our research would fit the remit of funding opportunity from the call “Technology Touching Life” and/or the EPSRC Healthcare Technologies: Call for Investigator-lead Research Project. It can also be relevant to the United Nations Sustainable Development Goal 9: Industry, Innovation and Infrastructure and Goal 3: Good Health (e.g. low-cost diagnostics).