Summer School on
Recent Advancements in
Computational and Learning Methods for
INVERSE PROBLEMS

July 11-15, 2022
Mathematics and Computer Science Department, Cagliari, Italy

About The Event

The summer school on "Recend Advancements in Computational and Learning Methods for Inverse Problems" will be held at the Mathematics and Computer Science Department of the University of Cagliari (Sardinia, Italy) on July 11-15, 2022.
The summer school consist of one longer course that will provide background in Numerical Linear Algebra and give an overview of classical and new solution methods for both small and large-scale inverse ill-posed problems. In addition, there will be 5 short courses on specific topics.

An Overview of Ill-Posed Inverse Problems

Many questions in Applied Mathematics, Science, and Engineering lead to Inverse Problems. These problems often arise when one is interested in determining the cause of an observed effect in
  • inverse helioseismology, where one seeks to determine the structure of the sun by measurements from earth or space,
  • medical imaging, e.g., electrocardiographic imaging, computerized tomography,
  • image restoration, where one is interested in determining an unavailable exact image from an available contaminated version,
  • adaptive optics, where one is interested in determining the shape of mirrors that provide high resolution of a contaminated image.
Many inverse problems are said to be ill-posed, because they either might not have a solution, the solution might not be unique, or small perturbations in the available data can give rise to very large perturbations in the computed solution. The data generally is obtained by measurement and, therefore, is typically contaminated by an error due to measurement inaccuracies. One is faced with the problem of determining a meaningful solution to the inverse ill-posed problem in the presence of error in the data.

The difficulties in solving ill-posed problems can be reduced by replacing the given problem by a nearby problem, whose solution is less sensitive to errors in the data. This replacement is referred to as regularization. The most commonly used regularization technique is due to Tikhonov. It replaces the original problem by a penalized least squares problem. Many other regularization techniques have been developed. All regularization techniques require the determination of a regularization parameter that determines how much the original problem is modified. It is important to choose both a suitable regularization method and an appropriate value of the regularization parameter to obtain accurate solutions of inverse ill-posed problems.

Techniques of Numerical Linear Algebra can be used to investigate the problems to be solved and to devise regularization methods. For instance, the singular value decomposition (SVD) is a useful tool from linear algebra for the investigation and regularization of small to medium-sized inverse ill-posed problems. However, the SVD cannot be applied to large-scale problems due to its high computational cost. Instead Krylov subspace iterative methods can be used to reduce the given large problem to smaller size. The latter can then be solved with the aid of the SVD.

Purpose of the Summer School

The last 20 years has seen significant development in methods for analyzing and solving inverse ill-posed problems. Many of these methods can be expressed with the tools of Numerical Linear Algebra. The course will provide an overview of many of established and new techniques for the analysis and solution of inverse ill-posed problems. The theory presented is illustrated with computed examples. Participants in the summer school will be assigned homework that expands the theory that is presented in lectures, and programming exercises that will show how the methods discussed perform.

Poster session

Participants who like to present their research activities can present a poster during the poster session. Each poster will be introduced with a short presentation of 5 minutes.

Application

Participation is open to Ph.D students and young researchers. Prerequisites for participants of the summer school include basic knowledge of Linear Algebra and MATLAB programming.
The number of participants in the summer school is limited. Applications can be submitted to the e-mail address clip22@bugs.unica.it before May 20, 2022, and should include an application letter by the applicant, a CV of the applicant, and a letter of recommendation describing the background of the applicant. The letter should include a title and an abstract if the applicant intends to present a poster. Applicants will be notified of acceptance by June 5, 2022.
Participation in the summer school is free.

Event Lecturers

Here are our lecturers

Speaker 1

Lothar Reichel

Kent State University, Kent (OH), USA

Speaker 1

Marco Donatelli

Università dell' Insubria, Como, Italy

Speaker 2

Shiwei Lan

Arizona State University, Tempe (AZ), USA

Speaker 3

Mirjeta Pasha

Arizona State University, Tempe (AZ), USA

Speaker 4

Felipe Uribe

Technical University of Denmark, Denmark

Event Schedule

Here is our event schedule

Lothar Reichel

Lothar Reichel

Solution methods for ill-posed problem

Abstract

Break

Marco Donatelli

Image deblurring and structured matrices Marco Donatelli

Abstract

Lunch break

Marco Donatelli

Image deblurring and structured matrices Marco Donatelli

Abstract

Lothar Reichel

Lothar Reichel

Solution methods for ill-posed problem

Abstract

Break

Felipe Uribe

A practical introduction to Bayesian inverse problems Felipe Uribe

Abstract

Lunch break

Felipe Uribe

A practical introduction to Bayesian inverse problems Felipe Uribe

Abstract

Shiwei Lan

Bayesian SpatioTemporal Modeling for Inverse Problems Shiwei Lan

Abstract

Break

Shiwei Lan

Bayesian SpatioTemporal Modeling for Inverse Problems Shiwei Lan

Abstract

Lunch break

Poster Session

Abstracts

Lothar Reichel

Lothar Reichel

Solution methods for ill-posed problem

Abstract

Break

Computationally Efficient Methods for Large-Scale Inverse Problems: From Learning to Sparsity and Edge-Preserving Mirjeta Pasha

Abstract

Lunch break

Computationally Efficient Methods for Large-Scale Inverse Problems: From Learning to Sparsity and Edge-Preserving Mirjeta Pasha

Abstract

Lothar Reichel

Lothar Reichel

Solution methods for ill-posed problem

Abstract

Participants

Event Venue

Event venue location info

Mathematics and Computer Science Department
Cagliari, Italy

Hotels

Sardinia is a tourist destination, especially during summer. Therefore, participants should make flight and hotel reservations as soon as possible, after acceptance.

Hostel Marina

Hostel Marina

0.5 Mile from the Venue

Cheap accommodation for the school participants will be available at Hostel Marina.
Detailed information about rooms and prices:

  • SINGLE ROOM: euro 45,00 per night;
  • DOUBLE ROOM: euro 70,00 per night;
  • PRIVATE ROOM UP TO 4 BEDS: euro 27,00 per person per night;
  • DORMITORY (up to 6 beds, female or male): euro 25,00 per person per night.
All rooms are with private bathroom. Breakfast is not included. People interested in staying at the Hostel Marina should contact the hostel directly to make their reservations, by sending an email mentioning the Scientific School.

If you prefer another accomodation, you can use Google Maps to obtain a list of hotels and a list of Bed and Breakfast.

Starting from July 1, a City tax of euro 1.5 per day will be due.

Cagliari is a small town, you can move across the centre walking. In case your accomodation is far from the school venue, CTM provides bus connections.

Sponsors