Uncertainty Quantification for Scale-Space Blob Detection.

We consider the problem of blob detection for uncertain images, such as images that have to be inferred from noisy measurements. Extending recent work motivated by astronomical applications, we propose an approach that represents the uncertainty in the position and size of a blob by a region in a three-dimensional scale space. Motivated by classic tube methods such as the taut-string algorithm, these regions are obtained from level sets of the minimizer of a total variation functional within a high-dimensional tube.

Synthetic dataset for visco-acoustic imaging.

We provide computationally generated dataset simulating propagation of ultrasonic waves in viscous tissues in two and three dimensional domains. The dataset contains physical parameters of a human breast with a high-contrast inclusion, the acquisition setup with positions of sources and receivers, and the associated pressure-wave data at ultrasonic frequencies. We simulated the wave propagation based on seven different viscous models using the physical parameters of the breast.

On convergence rates of adaptive ensemble Kalman inversion for linear ill-posed problems.

In this paper we discuss a deterministic form of ensemble Kalman inversion as a regularization method for linear inverse problems. By interpreting ensemble Kalman inversion as a low-rank approximation of Tikhonov regularization, we are able to introduce a new sampling scheme based on the Nyström method that improves practical performance. Furthermore, we formulate an adaptive version of ensemble Kalman inversion where the sample size is coupled with the regularization parameter.

A workflow for sizing oligomeric biomolecules based on cryo single molecule localization microscopy.

Single molecule localization microscopy (SMLM) has enormous potential for resolving subcellular structures below the diffraction limit of light microscopy: Localization precision in the low digit nanometer regime has been shown to be achievable. In order to record localization microscopy data, however, sample fixation is inevitable to prevent molecular motion during the rather long recording times of minutes up to hours. Eventually, it turns out that preservation of the sample's ultrastructure during fixation becomes the limiting factor.

Regularization with Metric Double Integrals of Functions with Values in a Set of Vectors.

We present an approach for variational regularization of inverse and imaging problems for recovering functions with values in a set of vectors. We introduce regularization functionals, which are derivative-free double integrals of such functions. These regularization functionals are motivated from double integrals, which approximate Sobolev semi-norms of intensity functions.

A Range Condition for Polyconvex Variational Regularization.

In the context of variational regularization, it is a known result that, under suitable differentiability assumptions, source conditions in the form of variational inequalities imply range conditions, while the converse implication only holds under an additional restriction on the operator. In this article, we prove the analogous result for regularization. More precisely, we show that the variational inequality derived by the authors in 2017 implies that the derivative of the regularization functional must lie in the range of the dual-adjoint of the derivative of the operator.

The inverse scattering problem for orthotropic media in polarization-sensitive optical coherence tomography.

In this paper we provide for a first time, to our knowledge, a mathematical model for imaging an anisotropic, orthotropic medium with polarization-sensitive optical coherence tomography. The imaging problem is formulated as an inverse scattering problem in three dimensions for reconstructing the electrical susceptibility of the medium using Maxwell's equations. Our reconstruction method is based on the second-order Born-approximation of the electric field.

Shape-Aware Matching of Implicit Surfaces Based on Thin Shell Energies.

A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane energy measuring the rate of tangential distortion when deforming the reference shell into the template shell, and a bending energy measuring the bending under the deformation in terms of the change of the shape operators from the undeformed into the deformed configuration. The variational method applies to surfaces described as level sets.

Inverse problems of combined photoacoustic and optical coherence tomography.

Optical coherence tomography (OCT) and photoacoustic tomography are emerging non-invasive biological and medical imaging techniques. It is a recent trend in experimental science to design experiments that perform photoacoustic tomography and OCT imaging at once. In this paper, we present a mathematical model describing the dual experiment.

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Although the residual method, or constrained regularization, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov regularization, where a series of new results for regularization in Banach spaces has been published in the recent years. The present paper intends to bridge the gap between the existing theories as far as possible.

On the use of frequency-domain reconstruction algorithms for photoacoustic imaging.

We investigate the use of a frequency-domain reconstruction algorithm based on the nonuniform fast Fourier transform (NUFFT) for photoacoustic imaging (PAI). Standard algorithms based on the fast Fourier transform (FFT) are computationally efficient, but compromise the image quality by artifacts. In our previous work we have developed an algorithm for PAI based on the NUFFT which is computationally efficient and can reconstruct images with the quality known from temporal backprojection algorithms.

A reconstruction algorithm for photoacoustic imaging based on the nonuniform FFT.

Fourier reconstruction algorithms significantly outperform conventional backprojection algorithms in terms of computation time. In photoacoustic imaging, these methods require interpolation in the Fourier space domain, which creates artifacts in reconstructed images. We propose a novel reconstruction algorithm that applies the one-dimensional nonuniform fast Fourier transform to photoacoustic imaging.

Thermoacoustic tomography with integrating area and line detectors.

Thermoacoustic (optoacoustic, photoacoustic) tomography is based on the generation of acoustic waves by illumination of a sample with a short electromagnetic pulse. The absorption density inside the sample is reconstructed from the acoustic pressure measured outside the illuminated sample. So far measurement data have been collected with small detectors as approximations of point detectors.