Funded by GDR ISIS Dates : September 2021 – September 2023
This project focuses on large scale optimization problems in signal processing and imaging. A natural way to tackle them is to exploit their underlying structure, and to represent them at different resolution levels. The use of multiresolution schemes, such as wavelets transforms, is not new in imaging and is widely used to define regularization strategies. However, such techniques could be used to a wider extent, in order to accelerate the optimization algorithms used for their solution and to tackle large datasets. Techniques based on such ideas are usually called multilevel optimization methods and are well-known and widely used in the field of smooth optimization and especially in the solution of partial differential equations. Optimization problems arising in image reconstruction are however usually nonsmooth and thus solved by proximal methods. Such approaches are efficient for small-scale problems but still computationally demanding for problems with very high-dimensional data. The ambition of this project is thus to combine proximal methods and multiresolution analysis not only as a regularization, but as a solution to accelerate proximal algorithms.