Robust Optimization For Medical Image Processing

An important problem in image processing research is quantifying the uncertainty of the image reconstruction process. For example, if we reconstruct, denoise, or inpaint (fill large, unobserved blocks of) an image, but do not have enough measurements from a given region, we want to express that our reconstructed image may be erroneous in that region. This problem is especially relevant in medical imaging. The main framework for expressing uncertainty in the above scenario is Bayesian (see for example [1]), where a prior is placed on the original image and is propagated through the reconstruction process via Bayesian inference.

In this project, we take an alternative approach by exploring how we can build robustness into the reconstruction process. The main tool will be robust optimization [2], [$6.3, 3]. The project will consist of reviewing the relevant literature and on trying out new ideas on medical images.


[1] J. M. Bardsley, "MCMC-Based Image Reconstruction With Uncertainty Quantification", SIAM J. Sci. Comput., Vol. 34, No. 3, pp. A1316-A1332, 2012 (

[2] D. Bertsimas, D. B. Brown, C. Caramanis, "Theory and Applications of Robust Optimization", SIAM Review, Vol. 53, No. 3, pp. 464-501, 2011 (

[3] S. Boyd, L. Vandenberghe, Convex Optimization. Cambridge University Press, 2004 (

Supervisor name: 
Dr. Joao Mota
Supervisor and Deputy email addresses:

Project Type: