Related papers: Regularization approaches for quantitative photoac…
The goal of quantitative photoacoustic tomography is to determine optical and acoustical material properties from initial pressure maps as obtained, for instance, from photoacoustic imaging. The most relevant parameters are absorption,…
Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Therefore, in the absence of…
The development of emerging technologies in quantum optics demands accurate models that faithfully capture genuine quantum effects. Mature semiclassical approaches reach their limits when confronted with quantized electromagnetic fields,…
Regularizing a linear ill-posed operator equation can be achieved by manipulating the spectrum of the operator's pseudo-inverse. Tikhonov regularization and spectral cutoff are well-known techniques within this category. This paper…
Optical absorption is a primary, label-defining contrast across biology, pathology, and materials science, yet three-dimensional quantitative absorption imaging has remained largely inaccessible to the brightfield microscopes used in…
We study the direct and an inverse source problem for the radiative transfer equation arising in optical molecular imaging. We show that for generic absorption and scattering coefficients, the direct problem is well-posed and the inverse…
The aim of this paper is to put the problem of vibroacoustic imaging into the mathematical framework of inverse problems (more precisely, coefficient identification in PDEs) and regularization. We present a model in frequency domain, prove…
Photoacoustic imaging (PAI) is a promising medical imaging modality providing the spatial resolution of ultrasound (US) imaging and the contrast of pure optical imaging. For linear-array PAI, a beamformer has to be used as the…
The problem of object restoration in the case of spatially incoherent illumination is considered. A regularized solution to the inverse problem is obtained through a probabilistic approach, and a numerical algorithm based on the statistical…
We systematically investigated the limited inverse discrete Fourier transform of the quasi distributions from the perspective of inverse problem theory. This transformation satisfies two of Hadamard's well-posedness criteria, existence and…
Quantum process tomography (QPT) methods aim at identifying a given quantum process. The present paper focuses on the estimation of a unitary process. This class is of particular interest because quantum mechanics postulates that the…
This paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of…
The scattering and transmission of harmonic acoustic waves at a penetrable material are commonly modelled by a set of Helmholtz equations. This system of partial differential equations can be rewritten into boundary integral equations…
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 survey causality properties of common attenuation models. We…
The ability to perform high-precision optical measurements is paramount to science and engineering. Laser interferometry enables interaction-free sensing with a precision ultimately limited by shot noise. Quantum optical sensors can surpass…
Quantum process tomography (QPT) plays a central role in characterizing quantum gates and circuits, diagnosing quantum devices, calibrating hardware, and supporting quantum error correction. However, conventional QPT methods face challenges…
Based on phase retrieval, lensless coherent imaging and in particular holography offers quantitative phase and amplitude images. This is of particular importance for spectral ranges where suitable lenses are challenging, such as for hard…
While in standard photoacoustic imaging the propagation of sound waves is modeled by the standard wave equation, our approach is based on a generalized wave equation with variable sound speed and material density, respectively. In this…
We deal with the photoacoustic imaging modality using dielectric nanoparticles as contrast agents. Exciting the heterogeneous tissue, localized in a bounded domain $\Omega$, with an electromagnetic wave, at a given incident frequency,…
Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized…