Exact image representation via a number‐theoretic Radon transform

Chandra, Shekhar S.; Svalbe, Imants

doi:10.1049/iet-cvi.2013.0101

Cited by 13 publications

(12 citation statements)

References 81 publications

(154 reference statements)

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“…The versatility of SMILI makes it ideally suited for a range of biomedical studies and has already been successfully utilised for a number of other applications since its release. It has been employed for advanced 3D in vivo visualisation of structures and models in musculoskeletal radiology [28,29], computing and visualising surface distances between models and bone shape [30,31], as well as in recent work on deformation fields in radiotherapy treatment planning [32,33]. The latter has clinical value in not only understanding the effects of…”

Section: Custom Clinical Applicationmentioning

confidence: 99%

A lightweight rapid application development framework for biomedical image analysis

Chandra

Dowling

Engstrom

et al. 2018

Computer Methods and Programs in Biomedicine

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Biomedical imaging analysis typically comprises a variety of complex tasks requiring sophisticated algorithms and visualising high dimensional data. The successful integration and deployment of the enabling software to clinical (research) partners, for rigorous evaluation and testing, is a crucial step to facilitate adoption of research innovations within medical settings. In this paper, we introduce the Simple Medical Imaging Library Interface (SMILI), an object oriented open-source framework with a compact suite of objects geared for rapid biomedical imaging (cross-platform) application development and deployment. SMILI supports the development of both command-line (shell and Python scripting) and graphical applications utilising the same set of processing algorithms. It provides a substantial subset of features when compared to more complex packages, yet it is small enough to ship with clinical applications with limited overhead and has a license suitable for commercial use. After describing where SMILI fits within the existing biomedical imaging software ecosystem, by comparing it to other state-of-the-art offerings, we demonstrate its capabilities in creating a clinical application for manual measurement of cam-type lesions of the femoral head-neck region for the investigation of femoro-acetabular impingement (FAI) from three dimensional (3D) magnetic resonance (MR) images of the hip. This application for the investigation of FAI proved to be convenient for radiological analyses and resulted in high intra (ICC=0.97) and inter-observer (ICC=0.95) reliabilities for measurement of α-angles of the femoral head-neck region. We believe that SMILI is particularly well suited for prototyping biomedical imaging applications requiring user interaction and/or visualisation of 3D mesh, scalar, vector or tensor data.

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Section: Custom Clinical Applicationmentioning

confidence: 99%

A lightweight rapid application development framework for biomedical image analysis

Chandra

Dowling

Engstrom

et al. 2018

Computer Methods and Programs in Biomedicine

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“…Since the slices of the DFT, and therefore R(m, t) space, does not require any interpolation, the backprojection requires no interpolation either and so it can be computed as a convolution without any interpolation error. This is referred to as circulant back-projection (CBP), since the result is a superposition of circulant matrices [54]. Adding slices to the DFT is O(µN ), where µ is the total number of measured slices and there are at most N + 1 slices.…”

Section: Finite Iterative Reconstructionmentioning

confidence: 99%

Chaotic Sensing

Chandra

Ruben

Jin

et al. 2018

IEEE Trans. on Image Process.

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We propose a sparse imaging methodology called Chaotic Sensing (ChaoS) that enables the use of limited yet deterministic linear measurements through fractal sampling. A novel fractal in the discrete Fourier transform is introduced that always results in the artefacts being turbulent in nature. These chaotic artefacts have characteristics that are image independent, facilitating their removal through dampening (via image denoising) and obtaining the maximum likelihood solution. In contrast with existing methods, such as compressed sensing, the fractal sampling is based on digital periodic lines that form the basis of discrete projected views of the image without requiring additional transform domains. This allows the creation of finite iterative reconstruction schemes in recovering an image from its fractal sampling that is also new to discrete tomography. As a result, ChaoS supports linear measurement and optimisation strategies, while remaining capable of recovering a theoretically exact representation of the image. We apply the method to simulated and experimental limited magnetic resonance (MR) imaging data, where restrictions imposed by MR physics typically favour linear measurements for reducing acquisition time.

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“…3. The solution is to use the Number Theoretic Transform and the Number-Theoretic Radon Transform of Chandra [20].…”

Section: Proposition 4 (Kernel Projections) the Projections Of The 2mentioning

confidence: 99%

“…The resulting NRT was constructed specifically to remedy the loss of precision when forming Finite Ghosts. Chandra [20] also showed that the implementation of the NTT is faster than the DFT because of its integer-only operations.…”

Section: Number Theoretic Convolutionmentioning

confidence: 99%

See 1 more Smart Citation

Recovering Missing Slices of the Discrete Fourier Transform Using Ghosts

Chandra¹,

Svalbe²,

Guédon³

et al. 2012

IEEE Trans. on Image Process.

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The Discrete Fourier Transform (DFT) underpins the solution to many inverse problems commonly possessing missing or un-measured frequency information. This incomplete coverage of Fourier space always produces systematic artefacts called Ghosts. In this paper, a fast and exact method for de-convolving cyclic artefacts caused by missing slices of the DFT is presented. The slices discussed here originate from the exact partitioning of DFT space, under the projective Discrete Radon Transform, called the Discrete Fourier Slice Theorem. The method has a computational complexity of O(n log 2 n) (where n = N 2 ) and is constructed from a new Finite Ghost theory. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. The paper concludes with a significant application to fast, exact, non-iterative image reconstruction from sets of discrete slices obtained for a limited range of projection angles.

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Exact image representation via a number‐theoretic Radon transform

Cited by 13 publications

References 81 publications

A lightweight rapid application development framework for biomedical image analysis

A lightweight rapid application development framework for biomedical image analysis

Chaotic Sensing

Recovering Missing Slices of the Discrete Fourier Transform Using Ghosts

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