Total Variation Based Fourier Reconstruction and Regularization for Computer Tomography

Zhang, Xiao-Qun; Froment, Jacques

doi:10.1109/nssmic.2005.1596801

Cited by 22 publications

(21 citation statements)

References 31 publications

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“…Unfortunately, the Shepp-Logan phantom is still largely used in papers that focus on 2D image reconstruction [19, 20, 21, 22, 23, 24, 25, 26, 27, 28]. We attribute this situation to the fact that software for data simulation with the Shepp-Logan phantom is not readily applicable to the FORBILD head phantom.…”

Section: Introductionmentioning

confidence: 99%

Simulation tools for two-dimensional experiments in x-ray computed tomography using the FORBILD head phantom

Noo

Dennerlein

et al. 2012

Phys. Med. Biol.

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Mathematical phantoms are essential for the development and early-stage evaluation of image reconstruction algorithms in x-ray computed tomography (CT). This note offers tools for computer simulations using a two-dimensional (2D) phantom that models the central axial slice through the FORBILD head phantom. Introduced in 1999, in response to a need for a more robust test, the FORBILD head phantom is now seen by many as the gold standard. However, the simple Shepp-Logan phantom is still heavily used by researchers working on 2D image reconstruction. Universal acceptance of the FORBILD head phantom may have been prevented by its significantly-higher complexity: software that allows computer simulations with the Shepp-Logan phantom is not readily applicable to the FORBILD head phantom. The tools offered here address this problem. They are designed for use with Matlab®, as well as open-source variants, such as FreeMat and Octave, which are all widely used in both academia and industry. To get started, the interested user can simply copy and paste the codes from this PDF document into Matlab® M-files.

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Section: Introductionmentioning

confidence: 99%

Simulation tools for two-dimensional experiments in x-ray computed tomography using the FORBILD head phantom

Noo

Dennerlein

et al. 2012

Phys. Med. Biol.

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“…Such images belong to the class BV ( R 2 ) of functions of bounded variation , which plays an essential role in this theory. Important examples of effective TV denoising of such images, in the field of medical computed tomography, are discussed in [27]. …”

Section: Introductionmentioning

confidence: 99%

Fractional diffusion, low exponent Lévy stable laws, and 'slow motion' denoising of helium ion microscope nanoscale imagery

Carasso

Vladár

2012

J. Res. Natl. Inst. Stand. Technol.

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Helium ion microscopes (HIM) are capable of acquiring images with better than 1 nm resolution, and HIM images are particularly rich in morphological surface details. However, such images are generally quite noisy. A major challenge is to denoise these images while preserving delicate surface information. This paper presents a powerful slow motion denoising technique, based on solving linear fractional diffusion equations forward in time. The method is easily implemented computationally, using fast Fourier transform (FFT) algorithms. When applied to actual HIM images, the method is found to reproduce the essential surface morphology of the sample with high fidelity. In contrast, such highly sophisticated methodologies as Curvelet Transform denoising, and Total Variation denoising using split Bregman iterations, are found to eliminate vital fine scale information, along with the noise. Image Lipschitz exponents are a useful image metrology tool for quantifying the fine structure content in an image. In this paper, this tool is applied to rank order the above three distinct denoising approaches, in terms of their texture preserving properties. In several denoising experiments on actual HIM images, it was found that fractional diffusion smoothing performed noticeably better than split Bregman TV, which in turn, performed slightly better than Curvelet denoising.

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“…The feasible methods may be iterative reconstruction methods with prior constraints [6]. The regularization functional is the key to restricting noise and artifacts efficiently during iteration.…”

Section: Introductionmentioning

confidence: 99%

“…The Constrained TV (CTV) minimization reconstruction algorithm was proposed by Xiao-Qun Zhang and Jacques Froment [6], it only regards TV functional as the objective function to be minimized, which reduces the computation, and the simulated experiment in [6] also shows that CTV algorithm is efficient. As the constraint used by CTV is defined in the frequency domain, it is of potential use for MR data reconstruction.…”

Section: Introductionmentioning

confidence: 99%

Improved reconstruction of non-cartesian magnetic resonance imaging data through total variation minimization and POCS optimization

Feng

Liu²,

Li³

et al. 2009

2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society

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In the article, an iterative reconstruction algorithm based on total variation minimization and POCS optimization for non-Cartesian K-space data is proposed. The proposed algorithm interpolates non-Cartesian data onto a 2D Cartesian grid using gridding method first, and then during the iterative process of total variation minimization, the frequency values on grid points near the measured data are replaced with the interpolated ones according to POCS. The experiments on simulated and real data show that the proposed method can reconstruct image more accurately and rapidly than constrained total variation minimization method.

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Total Variation Based Fourier Reconstruction and Regularization for Computer Tomography

Cited by 22 publications

References 31 publications

Simulation tools for two-dimensional experiments in x-ray computed tomography using the FORBILD head phantom

Simulation tools for two-dimensional experiments in x-ray computed tomography using the FORBILD head phantom

Fractional diffusion, low exponent Lévy stable laws, and 'slow motion' denoising of helium ion microscope nanoscale imagery

Improved reconstruction of non-cartesian magnetic resonance imaging data through total variation minimization and POCS optimization

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