1,485 research outputs found
Phase retrieval beyond the homogeneous object assumption for X-ray in-line holographic imaging
X-ray near field holography has proven to be a powerful 2D and 3D imaging
technique with applications ranging from biomedical research to material
sciences. To reconstruct meaningful and quantitative images from the
measurement intensities, however, it relies on computational phase retrieval
which in many cases assumes the phase-shift and attenuation coefficient of the
sample to be proportional. Here, we demonstrate an efficient phase retrieval
algorithm that does not rely on this homogeneous-object assumption and is a
generalization of the well-established contrast-transfer-function (CTF)
approach. We then investigate its stability and present an experimental study
comparing the proposed algorithm with established methods. The algorithm shows
superior reconstruction quality compared to the established CTF-based method at
similar computational cost. Our analysis provides a deeper fundamental
understanding of the homogeneous object assumption and the proposed algorithm
will help improve the image quality for near-field holography in biomedical
application
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Computational Inverse Problems for Partial Differential Equations
The problem of determining unknown quantities in a PDE from measurements of (part of) the solution to this PDE arises in a wide range of applications in science, technology, medicine, and finance. The unknown quantity may e.g. be a coefficient, an initial or a boundary condition, a source term, or the shape of a boundary. The identification of such quantities is often computationally challenging and requires profound knowledge of the analytical properties of the underlying PDE as well as numerical techniques. The focus of this workshop was on applications in phase retrieval, imaging with waves in random media, and seismology of the Earth and the Sun, a further emphasis was put on stochastic aspects in the context of uncertainty quantification and parameter identification in stochastic differential equations. Many open problems and mathematical challenges in application fields were addressed, and intensive discussions provided an insight into the high potential of joining deep knowledge in numerical analysis, partial differential equations, and regularization, but also in mathematical statistics, homogenization, optimization, differential geometry, numerical linear algebra, and variational analysis to tackle these challenges
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