# Research

The main objective of the project is the definition of new numerical methods, together with the improvement of existing ones, in order to obtain accurate reconstructions and classifications of images with a low computational cost in terms of resources and CPU time.

In addition, specific applications may lead to new structured linear algebra problems whose solution could be of interest also for other applications not included in this project.

The main applications considered in this project are:

A.1) Image deblurring and denoising.

A.2) X-ray and microwave image restoration.

A.3) Analysis and classification of biomedical data.

In several of the aforementioned applications, the noise is not negligible and usually discrete ill-posed problems are obtained that require regularization. Indeed, the data are provided as matrices or tensors and the above discrete problems can be considered as a discretization of ill-posed problems. Moreover, for some applications it is useful to combine structured linear algebra tools with optimization or approximation techniques.

The numerical methods that we will investigate are mainly of three kinds:

B.1) Iterative regularization methods and acceleration techniques.

B.2) Numerical methods for nonlinear regularization models.

B.3) Non-negative factorizations and subdivision schemes.

The project is structured as a single research unit since it is focused on topics that are largely common to all the participants. This organization can take advantage of the synergies and maximize the collaboration among the members of the project. The potential of the project is actually based on the interaction and the exchange of experiences of participants with different backgrounds, some more related to the study of structured matrices in the field of numerical linear algebra, and others more related to the solution of real biomedical or astrophysical problems.

The organization into a single unit will not undermine the principle of collaboration among different research institutions, which is guaranteed by the fact that all the participants belong to different research centers located in different areas of Italy:

- University of Insubria (UNINSUBRIA)

- University of Genova (UNIGE)

- University of Milano-Bicocca (UNIMIB)

- University of Modena and Reggio Emilia (UNIMORE)

- University of Trieste (UNITS)

- IC-CNR of Bari (CNR)

- IAC-CNR of Bari (IAC).