Computed tomography (CT) imaging is the task of reconstructing a positive attenuation field (in the form of an image) from a finite number of projections (e.g., sinograms). CT reconstruction is often followed by an image segmentation step to partition the image into piecewise smooth/constant regions. The boundaries between such regions often carry valuable information.
In this talk, we will...
Variable exponent Lebesgue spaces $\ell^{(p_n)}$ have been recently proved to be the appropriate functional framework to enforce pixel-adaptive regularisation in signal and image processing applications, combined with gradient descent (GD) or proximal GD strategies. Compared to standard Hilbert or Euclidean settings, however, the application of these algorithms in the Banach setting of...
in recent years new regularisation methods based on neural networks have shown promising performance for the solution of ill-posed problems, e.g., in imaging science. Due to the non-linearity of the networks, these methods often lack profound theoretical justification. In this talk we rigorously discuss convergence for an untrained convolutional network. Untrained networks are particulary...
The author discusses a method for dynamic tensor field tomography, which involves recovering a tensor field from its longitudinal ray transform in an inhomogeneous medium. The refractive index of the medium generates the Riemannian metric in the domain, and the goal is to solve the inverse source problem for the associated transport equation. While there are many results for recovering tensor...
We study the stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in the case of expected information gain criterion in an infinite-dimensional setting, where we obtain the convergence of the expected utility with respect to perturbations. To make the problem more concrete we demonstrate that non-linear Bayesian...
In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems that go beyond the computation of point estimates, we have to draw samples from the posterior distribution. For log-concave but usually high-dimensional posteriors, Markov chain Monte Carlo methods based on time discretizations of Langevin diffusion are a popular tool. If the...
The nonlinear eikonal equation results as a high frequency approximation of the Helmholtz equation, more generally, of the wave equation. We investigate the eikonal equation with respect to the theory of inverse problems in the context of terahertz tomography. We integrate neural networks in the Landweber iteration for the reconstruction of the refractive index $n(x)$, $x\in\Omega$, of an...
The precise knowledge of the material properties is of utmost importance for motor manufacturers to design and develop highly efficient machines. However, due to different manufacturing processes, these material properties can vary greatly locally and the assumption of homogenized global material parameters is no longer feasible for the development process. The goal of our research project is...
It has been shown a long time ago that the discontinuity set of the solution of a denoising problem by total variation minimization ("Rudin-Osher-Fatemi") is a subset of the discontinuity set of the original data, if smooth enough. In this talk, I will review the techniques used in the scalar setting, a variant developed by T. Valkonen which in theory addresses more cases (including...
Dealing with the inverse source problem for the scalar wave equation, we have shown recently that we can reconstruct the spacetime dependent source function from the measurement of the wave, collected on a single point $x$ and a large enough interval of time, generated by a small scaled bubble, enjoying large contrasts of its bulk modulus, injected inside the domain to image. Here, we extend...
We study the time-domain acoustic wave propagation in the presence of a micro-bubble. This micro-bubble is characterized by a mass density and bulk modulus which are both very small as compared to the ones of the uniform and homogeneous background medium. The goal is to estimate the amount of pressure that is created very near (at a distance proportional to the radius of the bubble) to the...
Cardiac pulsations in the human brain have recentlly garnered interest due to their potential involvement in the pathogenesis of neurodegenerative diseases. The (pulse) wave, which describes the velocity of blood flow along an intracranial artery, consists of a forward (anterograde) and backward (retrograde, reflected) part, but the measurement usually consists of a superposition of these...
In acoustics, higher-order-in-time equations arise when taking into account a class of (fractional) thermal relaxation laws in the modeling of sound wave propagation. In this talk, we will discuss the analysis of initial boundary value problems for a family of such equations and determine the behavior of solutions as the relaxation time vanishes. The studied model can be viewed as a...
We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation occuring in high intensity ultrasound propagation as used in acoustic tomography.
In particular, we investigate the recovery of the nonlinearity coefficient commonly labeled as $B/A$ in the literature, which is part of a space dependent coefficient $\kappa$ in the Westervelt equation...
Detecting defects embedded in a medium is a problem of paramount interest in a variety of fields, including medical imaging, non-destructive testing of materials and geophysical exploration.
In this talk we present numerical methods based on topological derivative computations for the detection of multiple objects. The method provides an indicator function capable of classifying each point...
We consider scattering of time-harmonic acoustic waves by an ensemble of compactly supported penetrable scattering objects in 2D.
These scattering objects are illuminated by an incident plane wave.
The resulting total wave is the superposition of incident and scattered wave and solves a scattering problem for the Helmholtz equation.
For guaranteeing uniqueness, the scattered wave must...
