&lt;title&gt;Controlled redundancy for image coding and high-speed transmission&lt;/title&gt;

Normand, Nicolas; Guédon, Jean-Pierre; Philippe, Olivier; Barba, Dominique

doi:10.1117/12.233180

Cited by 18 publications

(28 citation statements)

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“…This result has been extended in an independent manner by Normand and Guédon [14] to apply to data with compact support of any shape.…”

Section: Conditions For Reconstructabilitymentioning

confidence: 79%

“…The inverse Mojette transform is a fast and simple algorithm [14]. Searching for and updating 1-1 pixel-bin correspondence enables a simple iterative procedure to recover the image.…”

Section: Reconstruction From Mojette Projectionsmentioning

confidence: 99%

“…The number of pixels belonging to the corresponding bins is also decremented. The algorithmic complexity of the inverse Mojette transform for a P ⇥ Q image with I projections is O(P QI) [14]. This "accounting" inverse was improved by Normand et al in [15] where the need to search for 1-1 pixel-bin correspondence was removed.…”

Section: Reconstruction From Mojette Projectionsmentioning

confidence: 99%

See 2 more Smart Citations

Lossless image compression via predictive coding of discrete Radon projections

Kingston¹,

Autrusseau²

2008

Signal Processing: Image Communication

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“…This result has been extended in an independent manner by Normand and Guédon [14] to apply to data with compact support of any shape.…”

Section: Conditions For Reconstructabilitymentioning

confidence: 79%

“…The inverse Mojette transform is a fast and simple algorithm [14]. Searching for and updating 1-1 pixel-bin correspondence enables a simple iterative procedure to recover the image.…”

Section: Reconstruction From Mojette Projectionsmentioning

confidence: 99%

Section: Reconstruction From Mojette Projectionsmentioning

confidence: 99%

See 1 more Smart Citation

Lossless image compression via predictive coding of discrete Radon projections

Kingston¹,

Autrusseau²

2008

Signal Processing: Image Communication

View full text Add to dashboard Cite

“…Some degree of information redundancy arises in this more general Mojette projection representation. However this redundancy may be exploited usefully in the design of very efficient data transmission, storage and encryption schemes [16,17]. The algorithms to reconstruct images from Mojette projections [6] are more complex than for the FRT, largely because of the increased level of redundancy.…”

Section: Existing Digital Angle Schemesmentioning

confidence: 99%

Quantised Angular Momentum Vectors and Projection Angle Distributions for Discrete Radon Transformations

Svalbe

Chandra

Kingston

et al. 2006

Discrete Geometry for Computer Imagery

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Abstract. A quantum mechanics based method is presented to generate sets of digital angles that may be well suited to describe projections on discrete grids. The resulting angle sets are an alternative to those derived using the Farey fractions from number theory. The Farey angles arise naturally through the definitions of the Mojette and Finite Radon Transforms. Often a subset of the Farey angles needs to be selected when reconstructing images from a limited number of views. The digital angles that result from the quantisation of angular momentum (QAM) vectors may provide an alternative way to select angle subsets. This paper seeks first to identify the important properties of digital angles sets and second to demonstrate that the QAM vectors are indeed a candidate set that fulfils these requirements. Of particular note is the rare occurrence of degeneracy in the QAM angles, particularly for the half-integral angular momenta angle sets.

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“…Note that one can easily over-specify the projection set (i.e., μ > μ min ) [10]. When the Katz criterion is not satisfied, ghosts or phantoms arise in the reconstructed image [11,5].…”

Section: The Mojette Transform (Mt)mentioning

confidence: 99%

An Exact, Non-iterative Mojette Inversion Technique Utilising Ghosts

Chandra

Svalbe

Guédon

Discrete Geometry for Computer Imagery

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Abstract. Mojette projections of discrete pixel arrays form good approximations to experimental parallel-beam x-ray intensity absorption profiles. They are discrete sums taken at angles defined by rational fractions. Mojette-like projections form a "half-way house" between a conventional sinogram and fully digital projection data. A new direct and exact image reconstruction technique is proposed here to invert arbitrary but sufficient sets of Mojette data. This new method does not require iterative, statistical solution methods, nor does it use the efficient but noise-sensitive "corner-based" inversion method. It instead exploits the exact invertibility of the prime-sized array Finite Radon Transform (FRT), and the fact that all Mojette projections can be mapped directly into FRT projections. The algorithm uses redundant or "calibrated" areas of an image to expand any asymmetric Mojette set into the smallest symmetric FRT set that contains all of the Mojette data without any re-binning. FRT data will be missing at all angles where Mojette data is not provided, but can be recovered exactly from the "ghost projections" that are generated by back-projecting all the known data across the calibrated regions of the reconstructed image space. Algorithms are presented to enable efficient image reconstruction from any exact Mojette projection set, with a view to extending this approach to invert real x-ray data.

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<title>Controlled redundancy for image coding and high-speed transmission</title>

Cited by 18 publications

References 0 publications

Lossless image compression via predictive coding of discrete Radon projections

Lossless image compression via predictive coding of discrete Radon projections

Quantised Angular Momentum Vectors and Projection Angle Distributions for Discrete Radon Transformations

An Exact, Non-iterative Mojette Inversion Technique Utilising Ghosts

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