Related papers: Tikhonov regularization-based reconstruction of pa…

This paper addresses the optimization problem of minimizing non-convex continuous functions, which is relevant in the context of high-dimensional machine learning applications characterized by over-parametrization. We analyze a randomized…

We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its…

Inverse scattering and spectral one-dimensional problems are discussed systematically in a self-contained way. Many novel results, due to the author are presented. The classical results are often presented in a new way. Several highlights…

The J-PET scanner, which allows for single bed imaging of the whole human body, is currently under development at the Jagiellonian University. The dis- cussed detector offers improvement of the Time of Flight (TOF) resolution due to the use…

In the quest to image the three-dimensional magnetization structure we show that the technique of magnetic small-angle neutron scattering (SANS) is highly sensitive to the details of the internal spin structure of nanoparticles. By…

A new method for directly sampling the neutron resonance upscattering effect is presented. Alternatives have relied on inefficient rejection sampling techniques or large tabular storage of relative velocities. None of these approaches,…

Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…

We study the inverse medium scattering problem to reconstruct the unknown inhomogeneous medium from the far-field patterns of scattered waves. The inverse scattering problem is generally ill-posed and nonlinear, and the iterative…

Improving the quality of positron emission tomography (PET) images, affected by low resolution and high level of noise, is a challenging task in nuclear medicine and radiotherapy. This work proposes a restoration method, achieved after…

Motivated by the fact that the pseudo-Helmholtz function is a valid Lyapunov function for characterizing asymptotic stability of complex balanced mass action systems (MASs), this paper develops the generalized pseudo-Helmholtz function for…

Adaptive spectral (AS) decompositions associated with a piecewise constant function $u$ yield small subspaces where the characteristic functions comprising $u$ are well approximated. When combined with Newton-like optimization methods for…

The robust low-rank tensor completion problem addresses the challenge of recovering corrupted high-dimensional tensor data with missing entries, outliers, and sparse noise commonly found in real-world applications. Existing methodologies…

Tikhonov regularization is a widely used technique in solving inverse problems that can enforce prior properties on the desired solution. In this paper, we propose a Krylov subspace based iterative method for solving linear inverse problems…

In this paper we study the structure of solutions of the one dimensional weighted total variation regularisation problem, motivated by its application in signal recovery tasks. We study in depth the relationship between the weight function…

We present a finite element analysis of electrical impedance tomography for reconstructing the conductivity distribution from electrode voltage measurements by means of Tikhonov regularization. Two popular choices of the penalty term, i.e.,…

We consider the identification of scattering and absorption rates in the stationary radiative transfer equation. For a stable solution of this parameter identification problem, we consider Tikhonov regularization within Banach spaces. A…

Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, which are a necessity due to the ill-posedness of inverse problems. Tikhonov-type regularization methods are very popular in…

The forward doubly-virtual Compton scattering (VVCS) off the nucleon contains a wealth of information on nucleon structure, relevant to the calculation of the two-photon-exchange effects in atomic spectroscopy and electron scattering. We…

We study the inverse problem of recovering the spatial support of parameter variations in a system of partial differential equations (PDEs) from boundary measurements. A reconstruction method is developed based on the monotonicity…

In this paper, we investigate tensor recovery problems within the tensor singular value decomposition (t-SVD) framework. We propose the partial sum of the tubal nuclear norm (PSTNN) of a tensor. The PSTNN is a surrogate of the tensor tubal…