C6 Mathematical Methods and Programming
- C60 General
- C61 Optimization Techniques; Programming Models; Dynamic Analysis
- C62 Existence and Stability Conditions of Equilibrium
- C63 Computational Techniques; Simulation Modeling (Updated!)
- C65 Miscellaneous Mathematical Tools
- C67 Input–Output Models
- C68 Computable General Equilibrium Models
- C69 Other
Refine
Document Type
- Master's Thesis (1)
- Preprint (1)
Language
- English (2)
Has Fulltext
- yes (2)
Keywords
- 3D (1)
- Bildverarbeitung (1)
- Biomedical Imaging (1)
- Deconvolution (1)
- Equiangular (1)
- Equilateral (1)
- Filtering (1)
- Fixed-Angle (1)
- Knoten (1)
- Konfigurationsraum (1)
This work focuses on enhancing the quality of A- and B-scans of a novel linear optical coherence tomography system (LOCT), addressing the image degradation caused by noise and the blurring characteristics of the system’s three-dimensional point spread function. The enhancement procedure includes an initial spatial and frequency-based pre-filtering that is applied to the measured interference pattern. Subsequently, a more robust envelope detection technique based on the Hilbert transform is employed. Lastly, image structures are reconstructed using a deconvolution algorithm based on maximum likelihood estimation, tailored to meet our unique requirements by adapting it to Rician distributed intensity values and employing a sparseness regularization term. For the deconvolution, both the lateral and axial blur of the system are considered. Emphasis is placed on the optimization of signal detection in high-noise regions, while simultaneously preventing image boundary artifacts. The efficacy of this approach is demonstrated across multiple types of measurement objects, including both artificial and biological samples. All results show a significant reduction in noise as well as enhanced resolution. Structure distinguishability is also increased, which plays a crucial role in tomography applications. In summary, the proposed enhancement method substantially improves image quality. This is achieved by still using the same initial measurement data, but incorporating prior knowledge and maximizing the amount of extracted information. Although initially designed for LOCT systems, the processing steps have potential for broader application in other types of optical coherence tomography and imaging systems.
For most classes of chains, it is known if these contain locks, but especially for fixed-angle equilateral equiangular obtuse open polygonal chains in 3D, which can be used to model protein backbones, this is unknown. Fixed-angle equilateral equiangular obtuse closed and open polygonal chains can be used to model polymers. For these, it is clear, that locks based on knots exist, but not which chains are generally locked. We therefore examine both open and closed fixed-angle equilateral equiangular obtuse chains. For this purpose, those chains are divided into various subgroups and, depending on the subgroup, other aspects are investigated to show locks. Techniques from knot theory, graph theory, and specifically robot arm reachability and motion planning are combined. Algorithms are developed to create chains in desired configurations and to study them. It is shown why all fixed-angle equilateral equiangular obtuse closed chains are expected to be locked or in rare cases rigid and non-locked, but never non-locked and non-rigid. For fixed-angle equilateral equiangular obtuse open chains it is shown why it is expected that there are open chains that are locked and that the smallest locked open chain has 𝑛=7.