847 research outputs found
Joint Image Reconstruction and Segmentation Using the Potts Model
We propose a new algorithmic approach to the non-smooth and non-convex Potts
problem (also called piecewise-constant Mumford-Shah problem) for inverse
imaging problems. We derive a suitable splitting into specific subproblems that
can all be solved efficiently. Our method does not require a priori knowledge
on the gray levels nor on the number of segments of the reconstruction.
Further, it avoids anisotropic artifacts such as geometric staircasing. We
demonstrate the suitability of our method for joint image reconstruction and
segmentation. We focus on Radon data, where we in particular consider limited
data situations. For instance, our method is able to recover all segments of
the Shepp-Logan phantom from angular views only. We illustrate the
practical applicability on a real PET dataset. As further applications, we
consider spherical Radon data as well as blurred data
Fourier-Domain Inversion for the Modulo Radon Transform
Inspired by the multiple-exposure fusion approach in computational
photography, recently, several practitioners have explored the idea of high
dynamic range (HDR) X-ray imaging and tomography. While establishing promising
results, these approaches inherit the limitations of multiple-exposure fusion
strategy. To overcome these disadvantages, the modulo Radon transform (MRT) has
been proposed. The MRT is based on a co-design of hardware and algorithms. In
the hardware step, Radon transform projections are folded using modulo
non-linearities. Thereon, recovery is performed by algorithmically inverting
the folding, thus enabling a single-shot, HDR approach to tomography. The first
steps in this topic established rigorous mathematical treatment to the problem
of reconstruction from folded projections. This paper takes a step forward by
proposing a new, Fourier domain recovery algorithm that is backed by
mathematical guarantees. The advantages include recovery at lower sampling
rates while being agnostic to modulo threshold, lower computational complexity
and empirical robustness to system noise. Beyond numerical simulations, we use
prototype modulo ADC based hardware experiments to validate our claims. In
particular, we report image recovery based on hardware measurements up to 10
times larger than the sensor's dynamic range while benefiting with lower
quantization noise (12 dB).Comment: 12 pages, submitted for possible publicatio
Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines
In applied mathematics and related disciplines, the
modeling-simulation-optimization workflow is a prominent scheme, with
mathematical models and numerical algorithms playing a crucial role. For these
types of mathematical research data, the Mathematical Research Data Initiative
has developed, merged and implemented ontologies and knowledge graphs. This
contributes to making mathematical research data FAIR by introducing semantic
technology and documenting the mathematical foundations accordingly. Using the
concrete example of microfracture analysis of porous media, it is shown how the
knowledge of the underlying mathematical model and the corresponding numerical
algorithms for its solution can be represented by the ontologies.Comment: Preprint of a Conference Paper to appear in the Proceeding of the
17th International Conference on Metadata and Semantics Researc
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