Recovering Missing Slices of the Discrete Fourier Transform Using Ghosts

Chandra, Shekhar S.; Svalbe, Imants; Guédon, Jean-Pierre; Kingston, Andrew; Normand, Nicolas

doi:10.1109/tip.2012.2206033

Cited by 15 publications

(17 citation statements)

References 63 publications

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“…Image reconstruction methods can even be created that learn their characteristics to remove them given enough training data [23]. Other methods for reducing Ghosts include fusion of multi-modal data [24], minimising the 1norm in reconstructions [25,26], solving certain system of equations [27] or by fast direct deconvolution of Ghost artefacts if no noise is present [28]. See Chandra et al [28] for a summary of the work in Ghosts during the last century.…”

Section: A Previous Workmentioning

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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Section: A Previous Workmentioning

confidence: 99%

Chaotic Sensing

Chandra

Ruben

Jin

et al. 2018

IEEE Trans. on Image Process.

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“…This figure presents a comparison between the coefficients of the analytical solution expansion (32) by the formula (12) and coefficients obtained from solving the inverse problem by the system of Equations (19). Coefficients (12) in the solution to the inverse problem start to oscillate from a certain value and they differ significantly from the coefficients of the analytical solution. From Figure 5, it appears that with the increase of the disturbance vector b (data disturbances on the outer boundary of the ring), the number of nf components of the Fourier transform, which should be considered when solving the inverse problem, decreases.…”

Section: Introductionmentioning

confidence: 96%

“…The Fourier transform is universally used for solving image reconstruction inverse problems in astronomy [11] and medicine (computed tomography), [12,13] among others. In inverse heat conduction problems, an integral Fourier transform is applied to identify boundary conditions [14,15] and to identify the source function.…”

Section: Introductionmentioning

confidence: 99%

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Regularization of the inverse heat conduction problem by the discrete Fourier transform

Wróblewska

Frąckowiak

Ciałkowski

2015

Inverse Problems in Science and Engineering

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Two methods of solving the inverse heat conduction problem with employment of the discrete Fournier transform are presented in this article. The first one operates similarly to the SVD algorithm and consists in reducing the number of components of the discrete Fournier transform which are taken into account to determine the solution to the inverse problem. The second method is related to the regularization of the solution to the inverse problem in the discrete Fournier transform domain. Those methods were illustrated by numerical examples. In the first example, an influence of the boundary conditions disturbance by a random error on the solution to the inverse problem (its stability) was examined. In the second example, the temperature distribution on the inner boundary of the multiply connected domain was determined. Results of calculations made in both ways brought very good outcomes and confirm the usefulness of applying the discrete Fournier transform to solving inverse problems.

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“…Jung overcame the Gibbs phenomenon and improved the reconstructed image quality [15]. Chandra introduced the finite-angle iterative image reconstruction of model fusion, which effectively preserves the original target features and improves the quality of small-angle projection data reconstruction [16]. Muldoon et al of the University of Edinburgh improved the FBP ultrasonic tomography method to identify the hole defects in the grouting pipe of the post-tensioned prestressed reinforced concrete beam and verified the test [17].…”

Section: Introductionmentioning

confidence: 99%

Improved image reconstruction based on ultrasonic transmitted wave computerized tomography on concrete

Fan

Zhu

2018

J Image Video Proc.

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Considering the non-uniqueness and instability of concrete defect detection in construction engineering, ultrasonic time of flight data and maximum likelihood expectation maximization algorithm were proposed to improve the readability of the ultrasonic reconstruction image. Ultrasonic transmitted waves reflect internal information when through concrete structures. Measurement signals were regularized and processed as transit time parameters. Maximum likelihood expectation maximization algorithm was optimized for image reconstruction of the concrete structure. The interpolation data as the density of measurement data was used to improve the readability of reconstruction images. The experimental measurement system, improved image reconstruction algorithm, and interpolation method were verified in detail by using simulation and concrete phantoms. The proposed image reconstruction technique based on maximum likelihood expectation maximization overcame the disadvantages of the traditional image reconstruction method, and it was effective to improve the accuracy and the quality of image reconstruction on concrete. Time of flight data and normalized interpolation were discussed in detail during image reconstruction. The results showed that it could make the position of an abnormal object more obvious, and it was more accurate for reflecting the internal structure of concrete.

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Recovering Missing Slices of the Discrete Fourier Transform Using Ghosts

Cited by 15 publications

References 63 publications

Chaotic Sensing

Chaotic Sensing

Regularization of the inverse heat conduction problem by the discrete Fourier transform

Improved image reconstruction based on ultrasonic transmitted wave computerized tomography on concrete

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