The Krĕın-Langer integral representation of a matrix-valued generalized Nevanlinna function arises in problems of spectral theory and interpolation. A version of this formula which is suitable for such problems, and a corresponding Stieltjes inversion formula, are derived. Some classes of generalized Nevanlinna functions which are defined in terms of behavior at infinity are characterized in te...

We relate the fixed argument pairing inversion problems (FAPI) and the discrete logarithm problem on an elliptic curve. This is done using the reduction from the DLP to the Diffie-Hellman problem developed by Boneh, Lipton, Maurer and Wolf. This approach fails when only one of the FAPI problems can be solved. In this case we use Cheon’s algorithm to get a reduction.

The problem of Radon transform inversion arises in fields as diverse as medical imaging, synthetic aperture radar, and radio astronomy. In this paper, we model the Radon transform as a convolution integral over the Euclidean motion group and provide a novel deconvolution method for its inversion. The deconvolution method presented here is a special case of the Wiener filtering framework in abst...

the direct way to access the petrophysical property of hydrocarbon reservoir is based on well data but due to its high cost, the seismic data has been used to obtain these parameters. for this purpose, many different methods are available and each has its own advantages and limitations. from these methods the seismic inversion is the best tool to study the reservoir characterization. the outcom...

Recently, the Wasserstein loss function has been proven to be effective when applied deterministic full-waveform inversion (FWI) problems. We consider application of this in Ba...

A variety of new imaging modalities, such as optical diffusion tomography, require the inversion of a forward problem that is modeled by the solution to a three-dimensional partial differential equation. For these applications, image reconstruction can be formulated as the solution to a non-quadratic optimization problem. In this paper, we discuss the use of nonlinear multigrid methods as both ...

The difficulties of providing a guarantee of meeting transaction deadlines in hard real-time database systems lie in the problems of priority inversion and of deadlocks. Priority inversion and deadlock problems ensue when concurrency control protocols are adapted in priority-driven scheduling. The blocking delay due to priority inversion can be unbounded, which is unacceptable in the mission-cr...

Deep-learning has achieved good performance and demonstrated great potential for solving forward inverse problems. In this work, two categories of innovative deep-learning-based modeling methods are proposed compared. The first category is deep-learning surrogate-based inversion methods, in which the Theory-guided Neural Network (TgNN) constructed as a surrogate problems with uncertain model pa...

2] suggests that multiscale methods are a useful tool for purposes of computational efficiency. In this paper we explore a multiresolution approach We consider inverse problems described by that class to solving one dimensional inverse problems. The apof operators which are made sparse under the action proach we take is motivated by the work of Chou, of the wavelet transform [2]. Thus, the inve...

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 of the new results include: 1) Analysis of the invertibility of the steps in the Gel’fand-Levitan and Marchenko inversion procedures, 2) Theory of the inverse ...