# Seminars Academic Year 2017-2018

- IP2018: Workshop on Inverse Problems, September 17-19
- Andreea-Paula Voinea-Marinescu (University of Bucharest)

Inverse Geometric Problems -
B. Tomas Johansson (Aston University, Birmingham, UK)

Iterative methods for elliptic Cauchy problems -
Dinh Nho Hào (Hanoi Institute of Mathematics)

STABLE DETERMINATION OF THE VERY WEAK SOLUTION TO A CAUCHY PROBLEM FOR AN ELLIPTIC EQUATION - Tran Nhan Tam Quyen (Georg-August-Universität Göttingen)

Total variation regularization with finite element methods and applications

- Gujji Murali Mohan Reddy (University of São Paulo)

A simple adaptive algorithm for the 1D one phase Inverse Stefan problem using the Method of Fundamental Solutions

- Liviu Marin (University of Bucharest)

Comparison of Gradient Method Based Algorithms for the Cauchy Problem in Steady-State Anisotropic Heat Conduction

- Karel Van Bockstal (Ghent University)

Identification of a memory kernel in a nonlinear parabolic integro-differential problem

- Marián Slodička (Ghent University)

Some inverse problems in time-fractional evolutionary partial differential equations

- Mihai Bucătaru (University of Bucharest)

FDM for Inverse Problems Associated with the Diffusion–Transport Equation in various 2D Domains

- Daniel Lesnic (University of Leeds)

Inverse problems for degenerate parabolic PDE’s

- Andreea-Paula Voinea-Marinescu (University of Bucharest)
- 07/05/2018

Dinh Nho Hao (Hanoi Institute of Mathematics, Vietnam Academy of Science and Technology)

Stable reconstruction of the initial condition in parabolic equations - 07/03/2018

Mikhail Klibanov ( University of North Carolina at Charlotte)

Phaseless inverse scattering and global convergence for inverse problems - 07/02/2018

Matus Tibensky (Bratislava)

PDEs in image processing

## Stable reconstruction of the initial condition in parabolic equations

The problem of reconstructing the initial condition in parabolic equations from final time, or boundary or interior observations is discussed. This problem is frequently arising in practice, but unfortunately, is severely ill-posed in the sense that a small perturbation in the observations may course arbitrarily large errors in the solution. We present some stability estimates for this problem and propose variational methods for solving it in a stable way. Several numerical examples are presented for showing the efficiency of the approach.

This work has been completed in collaboration with Nguyen Thi Ngoc Oanh (Thai Nguyen University), Phan Xuan Thanh (Hanoi University of Technology and Science), Nguyen Van Duc (University of Vinh).

## Phaseless inverse scattering and global convergence for inverse problems

Inverse coefficient problems without the phase information are very important in optical imaging of nanostructures and biological cells. We will present some uniqueness results and reconstruction techniques along with numerical results. The second topic is the topic of globally convergent numerical methods for coefficient inverse problems. We will present the so-called "convexification" method. Numerical results for experimental data will also be presented along with the theory.

## PDEs in image processing

In our talk we would like to introduce some topics from computer vision and image processing. We will describe basic ideas and models based on PDEs used here. We will take a look on the numerical methods as well and put these into the context of image processing problems. The main focus will be on the method used in the dissertation thesis of the author - Finite volume method and the usage of the method in the image segmentation will be demonstrated. We will briefly go through the numerical analysis of the problem and highlight the challenges. Numerical experiments will be shown in the last part of the presentation.