Applications to inverse problems and machine learning tasks in biomedical imaging, e.g. 3D X-ray imaging, PET, ultrasound imaging, MRI, or multi-photon microscopy, are the major outcomes of this research project. Emphasis is put on optimization methods able to tackle data with both a large sample-size (“big N “) and/or many measurements (“big P “).
The explored methodologies are grounded on nonsmooth functional analysis, fixed point theory, parallel/distributed strategies, and neural networks. The new optimization tools that are developed are set in the general framework of graph signal processing, encompassing both regular graphs (e.g., images) and non-regular graphs (e.g., gene regulatory networks).
1. Proposition of new algorithms for solving high-dimensional continuous optimization problems. Particular attention is paid to the development of methods offering convergence guarantees while leading to efficient parallel implementations. Because of the versatility of the proposed approaches, a wide range of applications in image restoration and reconstruction are considered. These include parallel MRI, breast tomosynthesis, coronary disease assessment, and two-photon microscopy.
2. Design of optimization methods for solving signal processing problems and data mining problems over graphs. In terms of applications, the proposed methods for data mining and learning over graphs are employed in the analysis of biological networks.
3. Design of new strategies for deep learning, benefiting from robustness guarantees and faster training, and taking into account prior information. Proposing new neural network models is of crucial importance in the context of the diagnosis or prognosis of diseases from medical images. These correspond to critical application areas, where making the right decisions may save lives and must be explainable. The use of deep learning techniques in such context is difficult due to the various encountered limitations, such as the reduced number of available data, the lack of pertaining textural information or relevant features, as well as the very large size of medical data. Optimal methods are investigated to allow deep learning architectures to address these challenges successfully.