The electric conductivity of a human chest might reveal certain attributes standing out; a beating heart, two lungs filled with air, or perhaps a small malignant breast lump. Breast cancer is a leading cause of death in the world and to successfully act based on screening, one must be certain of the existence of the lump, but also its size and position in its early stages. Many, falsely diagnosed with breast cancer by mammographic screening, experience psychological distress, and uncertainty for years [1]. Mammographic imaging based on x-ray may give you an estimate of the inside of a breast, but give no account of the uncertainty in the same estimate due to measurement noise among other things.
Hybrid imaging techniques pose a possible different way of seeing the physical properties of the inside of an object while measuring only the outside of the object. An example is acousto-electric tomography (AET) in which current and voltage surface measurements give information on the conductive properties of an object. The object may be slightly deformed when subject to acoustic waves, and so its conductive properties change. This allows for more surface measurements by emitting different waves into the object, and in some sense, this gives more information on the interior of the object. Reconstructing the conductivity from the surface measurements is a hybrid inverse problem, and such reconstructions have shown to enjoy promising contrast and resolution. Malignant tissue has significantly higher electrical conductivity than healthy surrounding tissue making AET a candidate method for early detection of malignant tumors.
When solving hybrid inverse problems, in theory, specific choices are made regarding the model, e.g. with which speed a wave travels through the object. The reconstructions are very much sensitive to these choices. When solving these problems in practice, however, we should take into consideration the uncertainty in the model and the measured data, and quantify the impact in the obtained results. How to do this in a computationally efficient manner is the goal of this project. In the future when you get a scan at the hospital, you might receive two pictures - the best reconstruction and a corresponding chart of the certainty of each pixel. Knowing the certainty of the reconstruction and its features make decision-making easier.
This project is part of the research initiative CUQI (Computational Uncertainty Quantification for Inverse problems) funded by Villum Fonden https://www.compute.dtu.dk/english/cuqi. The goal of CUQI is to make uncertainty quantification (UQ) for inverse problems readily available for non-experts.