Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations

DOI10.1088/1361-6420/ac2749zbMath1505.65125arXiv2104.07990OpenAlexW3199185602MaRDI QIDQ5860799

Monika Ritsch-Marte, Michael Quellmalz, Clemens Kirisits, Eric Setterqvist, Gabriele Drauschke, Otmar Scherzer

Publication date: 23 November 2021

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.07990

zbMATH Keywords

backpropagationoptical imagingoptical diffraction tomographyFourier diffraction theoremnonequispaced discrete Fourier transform

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Biomedical imaging and signal processing (92C55) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Numerical methods for discrete and fast Fourier transforms (65T50) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)

Related Items

Total Variation-Based Reconstruction and Phase Retrieval for Diffraction Tomography ⋮ Motion detection in diffraction tomography by common circle methods ⋮ An Inversion Scheme for Elastic Diffraction Tomography Based on Mode Separation

Uses Software

• Regularization tools
• NFFT

Cites Work

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• Reference free structure determination through eigenvectors of center of mass operators
• Methods of integral geometry and recovering a function with compact support from its projections in unknown directions
• A note on fast Fourier transforms for nonequispaced grids
• The analysis of linear partial differential operators. I: Distribution theory and Fourier analysis.
• Non trivial \(L^q\) solutions to the Ginzburg-Landau equation
• Numerical Fourier analysis
• On the fast Fourier transform of functions with singularities
• Regularization tools version \(4.0\) for matlab \(7.3\)
• Mathematical Methods in Image Reconstruction
• Orientation Determination of Cryo-EM Images Using Least Unsquared Deviations
• Three-Dimensional Structure Determination from Common Lines in Cryo-EM by Eigenvectors and Semidefinite Programming
• Stability Results for Scattered Data Interpolation by Trigonometric Polynomials
• Distributions and Operators
• ON RULES FOR STOPPING THE CONJUGATE GRADIENT TYPE METHODS IN ILL‐POSED PROBLEMS
• Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
• Fast Fourier Transforms for Nonequispaced Data
• Motion reconstruction for optical tomography of trapped objects
• Inverse acoustic and electromagnetic scattering theory