Wavelet-based reconstruction for limited-angle X-ray tomography

Rantala, Marjaana; Vänskä, Simopekka; Järvenpää, Seppo; Kalke, Martti; Lassas, Matti; Moberg, John; Siltanen, Samuli

doi:10.1109/tmi.2005.862206

Cited by 150 publications

(80 citation statements)

References 35 publications

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“…This regularity information can be used for example in denoising, classification, or re-construction of signals [16,19,21]. However, due to its isotropic nature, wavelets are not optimal for analyzing anisotropic features like edges.…”

Section: Introductionmentioning

confidence: 99%

Estimations of Hölder Regularities and Direction of Singularity by Hart Smith and Curvelet Transforms

Sampo

Sumetkijakan

2008

J Fourier Anal Appl

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Using Hart Smith's and curvelet transforms, new necessary and new sufficient conditions for an L 2 (R 2 ) function to possess Hölder regularity, uniform and pointwise, with exponent α > 0 are given. Similar to the characterization of Hölder regularity by the continuous wavelet transform, the conditions here are in terms of bounds of the transforms across fine scales. However, due to the parabolic scaling, the sufficient and necessary conditions differ in both the uniform and pointwise cases. We also investigate square-integrable functions with sufficiently smooth background. Specifically, sufficient and necessary conditions, which include the special case with 1-dimensional singularity line, are derived for pointwise Hölder exponent. Inside their "cones" of influence, these conditions are practically the same, giving near-characterization of direction of singularity.

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Section: Introductionmentioning

confidence: 99%

Estimations of Hölder Regularities and Direction of Singularity by Hart Smith and Curvelet Transforms

Sampo

Sumetkijakan

2008

J Fourier Anal Appl

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“…This performance resembles the characteristics of limited projection x-ray tomosynthesis over x-ray CT, but in the diffusive photon regime. 56,57 The use of prior information can reduce the ill-posed nature of the limited-projection-angle FMT inverse problem. The use of priors has shown to improve the imaging performance of 360 deg projection FMT, but it is even more essential for limited-projection-angle FMT, since reducing the information contained in the data collected increases the ill-posed nature of the reconstruction problem.…”

Section: Discussionmentioning

confidence: 99%

Improving limited-projection-angle fluorescence molecular tomography using a co-registered x-ray computed tomography scan

et al. 2012

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Abstract. We examine the improvement in imaging performance, such as axial resolution and signal localization, when employing limited-projection-angle fluorescence molecular tomography (FMT) together with x-ray computed tomography (XCT) measurements versus stand-alone FMT. For this purpose, we employed living mice, bearing a spontaneous lung tumor model, and imaged them with FMT and XCT under identical geometrical conditions using fluorescent probes for cancer targeting. The XCT data was employed, herein, as structural prior information to guide the FMT reconstruction. Gold standard images were provided by fluorescence images of mouse cryoslices, providing the ground truth in fluorescence bio-distribution. Upon comparison of FMT images versus images reconstructed using hybrid FMT and XCT data, we demonstrate marked improvements in image accuracy. This work relates to currently disseminated FMT systems, using limited projection scans, and can be employed to enhance their performance.

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“…dim E h f ). These spectra are useful in denoising, classification, or reconstruction of signals (see [22,23,35]). Definition 1.1.…”

Section: Introductionmentioning

confidence: 99%

Baire Typical Results for Mixed Hölder Spectra on Product of Continuous Besov or Oscillation Spaces

Slimane

2015

Mediterr. J. Math.

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In this paper, we show that the mixed Hölder spectra of finitely many functions can be recovered from a Legendre transform of a concave scaling function based on simultaneous wavelet leaders. We first prove that this Legendre transform yields an upper bound valid for uniform Hölder functions. We then study the typical optimality (in the sense of Baire's category) of this upper bound in a product of continuous Besov or oscillation spaces.Mathematics Subject Classification. 26A30, 42C40, 54E52, 28A80, 28A78.

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Wavelet-based reconstruction for limited-angle X-ray tomography

Cited by 150 publications

References 35 publications

Estimations of Hölder Regularities and Direction of Singularity by Hart Smith and Curvelet Transforms

Estimations of Hölder Regularities and Direction of Singularity by Hart Smith and Curvelet Transforms

Improving limited-projection-angle fluorescence molecular tomography using a co-registered x-ray computed tomography scan

Baire Typical Results for Mixed Hölder Spectra on Product of Continuous Besov or Oscillation Spaces

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