An algorithm for computing the discrete Radon transform with some applications

Ramesh, G.; Srinivasa, Narayan; Rajgopal, K.

doi:10.1109/tencon.1989.176899

Cited by 3 publications

(4 citation statements)

References 11 publications

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“…We report the average peak signal-to-noise ratio (PSNR) with respect to ground truth, for each of the three used datasets. For each dataset, we compare the results of our "FIT: TRec + FBP" and "FIT: TRec" setups to results obtained with the filtered backprojection (FBP) (15,16) baseline, and the two ablation studies described in Section 4.5.…”

Section: Data and Metrics For Computed Tomography Datamentioning

confidence: 99%

“…the columns of a sinogram) are back-transformed into a 2D image. A common method for this transformation is the filtered backprojection (FBP)(15,16). Since each projection maps to a line of coefficients in 2D Fourier space, a limited number of projections in a sinogram leads to visible streaking artefacts due to missing/unobserved Fourier coefficients.…”

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confidence: 99%

“…We show three qualitative results for each used datasets. From left to right, we show the input sinogram, reconstruction results obtained with filtered backprojection (FBP)(15,16), our results obtained with the "FIT: TRec" setup, our results obtained with the "FIT: TRec + FBP" setup, and the corresponding ground truth images. In the top left corner of each reconstruction we show the peak signal-to-noise ratio (PSNR) with respect to the ground truth image.…”

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confidence: 99%

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Fourier Image Transformer

Buchholz¹,

Jug²

2021

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Transformer architectures show spectacular performance on NLP tasks and have recently also been used for tasks such as image completion or image classification. Here we propose to use a sequential image representation, where each prefix of the complete sequence describes the whole image at reduced resolution. Using such Fourier Domain Encodings (FDEs), an autoregressive image completion task is equivalent to predicting a higher resolution output given a low-resolution input. Additionally, we show that an encoder-decoder setup can be used to query arbitrary Fourier coefficients given a set of Fourier domain observations. We demonstrate the practicality of this approach in the context of computed tomography (CT) image reconstruction. In summary, we show that Fourier Image Transformer (FIT) can be used to solve relevant image analysis tasks in Fourier space, a domain inherently inaccessible to convolutional architectures.

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Section: Data and Metrics For Computed Tomography Datamentioning

confidence: 99%

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confidence: 99%

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Fourier Image Transformer

Buchholz¹,

Jug²

2021

Preprint

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“…The application of the operator can be performed by means of a sequence of Fourier transforms in virtue of the Projection Slice Theorem [28]. This relates the Fourier transform of a projection of any function , e.g., its Radon transform , to a slice of its two-dimensional Fourier transform [29], [30] (30) where indicates the Fourier transform from the -domain to the -domain. For the specific application, the th estimation of the array current source in (21) can be operatively performed as (31) Due to the linearity of all the considered operators, the previous expression may be rewritten by changing the orders of the Fourier transforms as (32) where is the frequency domain array factor.…”

Section: Appendix Calculation Ofmentioning

confidence: 99%