Applying Mojette discrete radon transforms to classical tomographic data

Fayad, Hadi; Guédon, Jean-Pierre; Svalbe, Imants; Bizais, Y.; Normand, Nicolas

doi:10.1117/12.770478

Cited by 11 publications

(13 citation statements)

References 8 publications

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“…The Err of the three different methods as a function of the order of Farey series is plot in Fig.4. We can see that MCS has already got the good reconstruction result with 4 projections, where the Err of Mift and FBP is still larger than 50%. Fig.4 also shows that FBP can gain better results than Mift with the increasing number of projections.…”

Section: A Noise-free Reconstructionmentioning

confidence: 91%

“…A lot of research [4] has been done, committed to applying Mojette transform to classical tomographic data, which implies the advantage of Mojette transform on one hand and improves the potential of Mojette transform in practical application on the other hand. Paper [4] claims that any set of real, acquired tomographic data can be rebinned into a compatible Mojette projection space, without any loss of reconstruction power.…”

Section: Introductionmentioning

confidence: 99%

“…The other is that the angle and bin set is different from practical CT machine, i.e., classical tomograph acquires are equally distributed over 2π with a fixed number of bins onto each projection, while Mojette transform is defined over Farey angles with varying orientation and number of bins onto each projection. A lot of research [4] has been done, committed to applying Mojette transform to classical tomographic data, which implies the advantage of Mojette transform on one hand and improves the potential of Mojette transform in practical application on the other hand. Paper [4] claims that any set of real, acquired tomographic data can be rebinned into a compatible Mojette projection space, without any loss of reconstruction power.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Parallel-Beam CT Reconstruction Based on Mojette Transform and Compressed Sensing

Hou¹,

Zhang²

2013

IJCEE

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Abstract-A novel frame of parallel-beam Computerized Tomography (CT) reconstruction is proposed. The CT projections are firstly converted to Mojette projections. Then 1D Fourier transform is applied to the modified Mojette projections, followed by an exact mapping of the gained Fourier coefficients to the 2D Fourier domain of the scanning object. Finally the scanning object can be reconstructed from the partial Fourier coefficients by compressed sensing (CS). Experimental results show that using this frame, the purpose of reducing the radiation dosage during CT examinations without compromising the image quality can be achieved.

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Section: A Noise-free Reconstructionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Parallel-Beam CT Reconstruction Based on Mojette Transform and Compressed Sensing

Hou¹,

Zhang²

2013

IJCEE

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“…The MT has been applied to data transmission, encryption and file storage, to reconstruct images from arbitrary sets of projected views of discrete data, and for tomography using real x-ray data [3].…”

Section: Introductionmentioning

confidence: 99%

Erasure Coding with the Finite Radon Transform

Normand¹,

Svalbe²,

Parrein³

et al. 2010

2010 IEEE Wireless Communication and Networking Conference

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Abstract-The Mojette transform and the finite Radon transform (FRT) are discrete data projection methods that are exactly invertible and are computed using simple addition operations. The FRT is also Maximum Distance Separable (MDS). Incorporation of a known level of redundancy into data and projection spaces enables the use of forward error correction to recover the exact, original data when network packets are lost or corrupted during data transmission. By writing the above transforms in Vandermonde form, explicit expressions for discrete projection and inversion as matrix operations have been obtained. A cyclic, prime-sized Vandermonde form for the FRT approach is shown here to yield explicit polynomial expressions for the recovery of image rows from projected data and vice-versa. These polynomial solutions are consistent with the heuristic algorithms for "rowsolving" that have been published previously. This formalism also opens the way to link "ghost" projections in FRT space and "anti-images" in data space that may provide a key to an efficient method of encoding and decoding general data sets in a systematic form.

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“…We will discuss how this work can be extended to infer the nature and degree of the noise from the observed data. For the case where there is little noise, non-probabilistic approaches (such as [13] and [6]) are preferable.…”

Section: Introductionmentioning

confidence: 99%

Information-Theoretic Image Reconstruction and Segmentation from Noisy Projections

Visser

Dowe

Svalbe

2009

AI 2009: Advances in Artificial Intelligence

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Abstract. The minimum message length (MML) principle for inductive inference has been successfully applied to image segmentation where the images are modelled by Markov random fields (MRF). We have extended this work to be capable of simultaneously reconstructing and segmenting images that have been observed only through noisy projections. The noise added to each projection depends on the classes of the pixels (material) that it passes through. The intended application is in low-dose (low-flux) X-ray computed tomography (CT) where irregular projections are used.

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Applying Mojette discrete radon transforms to classical tomographic data

Cited by 11 publications

References 8 publications

Parallel-Beam CT Reconstruction Based on Mojette Transform and Compressed Sensing

Parallel-Beam CT Reconstruction Based on Mojette Transform and Compressed Sensing

Erasure Coding with the Finite Radon Transform

Information-Theoretic Image Reconstruction and Segmentation from Noisy Projections

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