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 ProblemsMany 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.
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 SchoolThe 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 sessionParticipants 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.
The number of participants in the summer school is limited. Applications can be submitted to the e-mail address email@example.com 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.
Here are our lecturers
Here is our event schedule
Event venue location info
Mathematics and Computer Science Department
Sardinia is a tourist destination, especially during summer. Therefore, participants should make flight and hotel reservations as soon as possible, after acceptance.
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.
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.