Linear Inverse Problems.- Large-Scale Inverse Problems in Imaging.- Regularization Methods for Ill-Posed Problems.- Distance Measures and Applications to Multi-Modal Variational Imaging.- Energy Minimization Methods.- Compressive Sensing.- Duality and Convex Programming.- EM Algorithms.- Iterative Solution Methods.- Level Set Methods for Structural Inversion and Image Reconstructions.- Expansion Methods.- Sampling Methods.- Inverse Scattering.- Electrical Impedance Tomography.- Synthetic Aperture Radar Imaging.- Tomography.- Optical Imaging.- Photoacoustic and Thermoacoustic Tomography: Image Formation Principles.- Mathematics of Photoacoustic and Thermoacoustic Tomography.- Wave Phenomena.- Statistical Methods in Imaging.- Supervised Learning by Support Vector Machines.- Total Variation in Imaging.- Numerical Methods and Applications in Total Variation Image Restoration.- Mumford and Shah Model and its Applications in Total Variation Image Restoration.- Local Smoothing Neighbourhood Filters.- Neighbourhood Filters and the Recovery of 3D Information.- Splines and Multiresolution Analysis.- Gabor Analysis for Imaging.- Shaper Spaces.- Variational Methods in Shape Analysis.- Manifold Intrinsic Similarity.- Image Segmentation with Shape Priors: Explicit Versus Implicit Representations.- Starlet Transform in Astronomical Data Processing.- Differential Methods for Multi-Dimensional Visual Data Analysis.- Wave fronts in Imaging, Quinto.- Ultrasound Tomography, Natterer.- Optical Flow, Schnoerr.- Morphology, Petros.- Maragos.- PDEs, Weickert. - Registration, Modersitzki. - Discrete Geometry in Imaging, Bobenko, Pottmann.-Visualization, Hege.- Fast Marching and Level Sets, Osher.- Couple Physics Imaging, Arridge.- Imaging in Random Media, Borcea.- Conformal Methods, Gu.- Texture, Peyre.- Graph Cuts, Darbon.- Imaging in Physics with Fourier Transform (i.e. Phase Retrieval e.g Dark field imaging), J. R. Fienup.- Electron Microscopy, Oktem Ozan.- Mathematical Imaging OCT (this is also FFT based), Mark E. Brezinski.- Spect, PET, Faukas, Louis.

/pdf/handbook-of-mathematical-methods-in-imaging-mpoi7xkf0v.pdf

Handbook of mathematical methods in imaging

the radon transform and some of its applications is available in our book collection an online access to it is set as public so you can get it instantly. Our digital library spans in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the the radon transform and some of its applications is universally compatible with any devices to read.

The Radon Transform And Some Of Its Applications

Hard X-ray fluorescence tomography — an emerging tool for structural visualization

X-rays have been used for non-invasive high-resolution imaging of thick biological specimens since their discovery in 1895. They are widely used for structural imaging of bone, metal implants, and cavities in soft tissue. Recently, a number of new contrast methodologies have emerged which are expanding X-ray's biomedical applications to functional as well as structural imaging. These techniques are promising to dramatically improve our ability to study in situ biochemistry and disease pathology. In this review, we discuss how X-ray absorption, X-ray fluorescence, and X-ray excited optical luminescence can be used for physiological, elemental, and molecular imaging of vasculature, tumors, pharmaceutical distribution, and the surface of implants. Imaging of endogenous elements, exogenous labels, and analytes detected with optical indicators will be discussed.

Advances in functional X-ray imaging techniques and contrast agents

The processing of tomographic synchrotron data requires advanced and efficient software to be able to produce accurate results in reasonable time. In this paper, the integration of two software toolboxes, TomoPy and the ASTRA toolbox, which, together, provide a powerful framework for processing tomographic data, is presented. The integration combines the advantages of both toolboxes, such as the user-friendliness and CPU-efficient methods of TomoPy and the flexibility and optimized GPU-based reconstruction methods of the ASTRA toolbox. It is shown that both toolboxes can be easily installed and used together, requiring only minor changes to existing TomoPy scripts. Furthermore, it is shown that the efficient GPU-based reconstruction methods of the ASTRA toolbox can significantly decrease the time needed to reconstruct large datasets, and that advanced reconstruction methods can improve reconstruction quality compared with TomoPy's standard reconstruction method.

/pdf/integration-of-tomopy-and-the-astra-toolbox-for-advanced-2dfua0lwnu.pdf

Integration of TomoPy and the ASTRA toolbox for advanced processing and reconstruction of tomographic synchrotron data

We describe a new approach for the inversion of the generalized attenuated radon transform in X-ray fluorescence computed tomography (XFCT). The approach consists of using the radon inverse as an approximation for the actual one, followed by an iterative refinement. Also, we analyze the problem of retrieving the attenuation map directly from the emission data, giving rise to a novel alternating method for the solution. We applied our approach to real and simulated XFCT data and compared its performance to previous inversion algorithms for the problem, showing its main advantages: better images than those obtained by other analytic methods and much faster than iterative methods in the discrete setting.

Iterative Reconstruction in X-ray Fluorescence Tomography Based on Radon Inversion

A fast algorithm for ring artefact reduction in high-resolution micro-tomography with synchrotron radiation is presented The new method is a generalization of the one proposed by Titarenko and collaborators, with a complete sinogram restoration prior to reconstruction with classical algorithms The generalized algorithm can be performed in linear time and is easy to implement Compared with the original approach, with an explicit solution, this approach is fast through the use of the conjugate gradient method Also, low/high-resolution sinograms can be restored using higher/lower-order derivatives of the projections Using different order for the derivative is an advantage over the classical Titarenko's approach Several numerical results using the proposed method are provided, supporting our claims

Generalized Titarenko's algorithm for ring artefacts reduction.

X-ray fluorescence computed tomography (XFCT) is a relatively new synchrotron-based imaging modality aiming at reconstructing the distribution of nonradiative elements within a sample irradiated with high-intensity monochromatic x-rays. In a recent paper La Riviere (2004 Phys. Med. Biol. 49 2391-405) presented an approximated inversion method based on reducing the problem to the inversion of the exponential radon transform. In this paper we compare La Riviere's results with recently derived 'exact' analytic formulae for the generalized attenuated radon transform. We present numerical experiments with real and simulated data.

Exact analytic reconstruction in x-ray fluorescence CT and approximated versions

Fast image reconstruction techniques are becoming important with the increasing number of scientific cases in high resolution micro and nano tomography. The processing of the large scale 3D data demands new mathematical tools for the tomographic reconstruction. Due to the high computational complexity of most current algorithms, big data sizes demands powerful hardware and more sophisticated numerical techniques. Several reconstruction algorithms are dependent on a mathematical tool called backprojection (a transposition process). A conventional implementation of the backprojection operator has cubic computational complexity. In the present manuscript we propose a new fast backprojection operator for the processing of tomographic data, providing a low-cost algorithm for this task. We compare our formula against other fast transposition techniques, using real and simulated large data sets.

A Backprojection Slice Theorem for Tomographic Reconstruction

A hybrid method of stitching X-ray computed tomography (CT) datasets is proposed and the feasibility to apply the scheme in a synchrotron tomography beamline with micrometre resolution is shown. The proposed method enables the field of view of the system to be extended while spatial resolution and experimental setup remain unchanged. The approach relies on taking full tomographic datasets at different positions in a mosaic array and registering the frames using Fourier phase correlation and a residue-based correlation. To ensure correlation correctness, the limits for the shifts are determined from the experimental motor position readouts. The masked correlation image is then minimized to obtain the correct shift. The partial datasets are blended in the sinogram space to be compatible with common CT reconstructors. The feasibility to use the algorithm to blend the partial datasets in projection space is also shown, creating a new single dataset, and standard reconstruction algorithms are used to restore high-resolution slices even with a small number of projections.

Eduardo X. Miqueles

Papers

Iterative Reconstruction in X-ray Fluorescence Tomography Based on Radon Inversion

Generalized Titarenko's algorithm for ring artefacts reduction.

Exact analytic reconstruction in x-ray fluorescence CT and approximated versions

A Backprojection Slice Theorem for Tomographic Reconstruction

Radiography registration for mosaic tomography.