Mathematical methods in image reconstruction

By Frank Natterer, F. Wübbeling. SIAM monographs on mathematical modeling and computation, 2001

1,077 citations recorded by the source corpus.

Subfields: Computational Mechanics, Modeling and Simulation, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/de2e3012bab66fc35b7524f09f33e75413e3b2d4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Modeling and Simulation

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Removing Multiplicative Noise by Douglas-Rachford Splitting Methods (2010, methodology): “For the expectation-maximization (EM) approach related to the I-divergence model in deblurring problems see [49, 52] and the references therein and for the EM–total variation (TV) model we refer to [51, 56].”
Optical tomography: forward and inverse problems (2009, neutral): “Nonlinear Kaczmarz Method The non-linear Kaczmarz method is widely used in non-linear tomography [129].”
Characterization and reduction of artifacts in limited angle tomography (2013, background): “This tomographic problem has been extensively studied in the last decades and many reconstruction algorithms are available for complete data, see for example [27, 28].”
Inverse transport theory and applications (2009, background): “When σ = σ(x) depends only on position however, then the X-ray transform of σ uniquely determines σ with an explicit inversion formula [59, 101].”
Determination of the fibre orientation in composites using the structure tensor and local X-ray transform (2010, background): “The mathematics of CT is explained in detail in [1, 10–12].”
An algorithm for the rapid evaluation of special function transforms (2010, background): “1 Introduction Special function transforms are a widely used and well-understood tool of applied mathematics; they are encountered, inter alia, in weather and climate modeling [19], [20], [21], tomography [14], [9], electromagnetics [13], and acoustics [6], [16].”
Regularization Tools version 4.0 for Matlab 7.3 (2007, methodology): “The function art implements the method by Kaczmarz, also known as the algebraic reconstruction technique (ART) [11].”
Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT (2006, neutral): “11 in [1] and Section 5.3.1 in [2]) and the expectation-maximization (EM) algorithm (see e.g. Section 5.3.2 in [2] and Section 15.4.6 in [3]).”
Fast Fourier Transform (2011, methodology): “As general reference we recommend the books of Natterer [101] and Natterer, Wübbeling [102].”
Applied Iterative Methods (2007, background): “For in-depth discussion of these issues, the reader should consult the books by Herman [93, 98], Kak and Slaney [110], Natterer [130], Natterer and Wübbeling [131], and Wernick and Aarsvold [148] .”
A Perspective on Deep Imaging (2016, background): “t, but these should be addressable. Taking computed tomography as an example, image reconstruction is theoretically not unique from a finite number of projections in an unconstrained functional space [29]. However, the non-uniqueness is avoided in practice where we have a priori knowledge that an un”
Thermoacoustic computed tomography with large planar receivers (2004, neutral): “[14]).”
AIR Tools - A MATLAB package of algebraic iterative reconstruction methods (2012, background): “Both parallel- and fan beam tomography arise from transmission tomography [32], [31], [28] where we study an object with nondiffractive radiation, i.”