The main objective of this proposal is to explore and develop new methods and optimized algorithms
for the analysis of
high-dimensional data under the assumption of structured sparsity and
low-rank conditions. Special attention will be paid to the impact of
the numerical methods in statistical
applications, especially in the domain of variable selection. We will investigate the
benefits
of structured sparse and low-rank models and their algorithms in relation to multiscale sparse
decompositions, the
regularization of inverse problems and in medical imaging.
By linking these concepts to convex optimization problems, the planned research
also contributes
to turning these theoretical concepts into practical and efficient techniques for the solution
of large scale
inverse problems.