65 citations · 144 across the 18 of their papers we have counts for
18 papers
Full Field Inversion of the Attenuated Wave Equation: Theory and Numerical Inversion
Ngoc Do, Markus Haltmeier, Richard Kowar +2
Standard photoacoustic tomography (PAT) provides data that consist of time-dependent signals governed by the wave equation, which are measured on an observation surface. In contras…
Data-driven Morozov regularization of inverse problems
Markus Haltmeier, Richard Kowar, Markus Tiefenthaler
The solution of inverse problems is crucial in various fields such as medicine, biology, and engineering, where one seeks to find a solution from noisy observations. These problems…
Analysis for Full Field Photoacoustic Tomography with Variable Sound Speed
Linh V. Nguyen, Markus Haltmeier, Richard Kowar +1
Photoacoustic tomography (PAT) is a non-invasive imaging modality that requires recovering the initial data of the wave equation from certain measurements of the solution outside t…
Extension of the principle of least action with focus on dissipative equations
Richard Kowar
In this paper, we extend the \emph{principle of least action} and show that a \emph{Lagrange density} always exists for the usual linear pde or linear fractional problems $\oA\,u=f…
Regularization of systems of nonlinear ill-posed equations: II. Applications
M. Haltmeier, R. Kowar, A. Leitao +1
In part I we introduced modified Landweber-Kaczmarz methods and have established a convergence analysis. In the present work we investigate three applications: an inverse problem r…
Dynamical systems with finite stopping times. Part 1: Relaxation, oscillation and their application to diffusion and wave dissipation
Richard Kowar
In this paper, we derive general theorems for controlling (vector-valued) first order ordinary differential equations such that its solutions stop at a finite time and apply…
A representation formula for solutions of second order ode's with time dependent coefficients and its application to model dissipative oscillations and waves
Richard Kowar
In this paper, we model, classify and investigate the solutions of (normalized) second order ode's with \emph{nonconstant continuous coefficients}. We introduce a generalized \emph…
Iterative Methods for Photoacoustic Tomography in Attenuating Acoustic Media
Markus Haltmeier, Richard Kowar, Linh V. Nguyen
The development of efficient and accurate reconstruction methods is an important aspect of tomographic imaging. In this article, we address this issue for photoacoustic tomography.…
On the nonlocality of the state and wave equation of Treeby and Cox
Richard Kowar
In this paper it is shown that the state equation of Treeby and Cox [B. E. Treeby and B. T. Cox, J. Acoust. Soc. Am. \textbf{127} 5, (2010)] is \emph{nonlocal}, more precisely, a \…
Time reversal for photoacoustic tomography based on the wave equation of Nachman, Smith and Waag
Richard Kowar
The goal of \emph{photoacoustic tomography} (PAT) is to estimate an \emph{initial pressure function} from pressure data measured at a boundary surrounding the object of interes…
On time reversal in photoacoustic tomography for tissue similar to water
Richard Kowar
This paper is concerned with time reversal in \emph{photoacoustic tomography} (PAT) of dissipative media that are similar to water. Under an appropriate condition, it is shown that…
Small frequency approximation of (causal) dissipative pressure waves
Richard Kowar
In this paper we discuss the problem of small frequency approximation of the causal dissipative pressure wave model proposed in \cite{KoScBo:11}. We show that for appropriate situa…
On the causality of electrodynamics and the Aharonov-Bohm effect
Richard Kowar
This paper presents a \emph{non-instant field model} for electrodynamics that permits a causal explanation of the \emph{Aharonov-Bohm effect} and a \emph{covariant quantization} of…
Causal diffusion and its backwards diffusion problem
Richard Kowar
This article starts over the backwards diffusion problem by replacing the \emph{noncausal} diffusion equation, the direct problem, by the \emph{causal} diffusion model developed in…
On the causality of real-valued semigroups and diffusion
Richard Kowar
In this paper we show that a process modeled by a strongly continuous real-valued semigroup (that has a space convolution operator as infinitesimal generator) cannot satisfy causal…
Photoacoustic Imaging Taking into Account Attenuation
Richard Kowar, Otmar Scherzer
First, we review existing attenuation models and discuss their causality properties, which we believe to be essential for algorithms for inversion with attenuated data. Then, we su…
Integral equation models for thermoacoustic imaging of dissipative tissue
Richard Kowar
In case of non-dissipative tissue the inverse problem of thermoacoustic imaging basically consists of two inverse problems. First, a function depending on the \emph{electromagn…
Causality analysis of waves and wave equations obeying attenuation
Richard Kowar
In this paper we show that the standard causality condition for attenuated waves, i.e. the Kramers-Kronig relation that relates the attenuation law and the phase speed of the wave,…