Generalised finite radon transform for N×N images

Kingston, Andrew; Svalbe, Imants

doi:10.1016/j.imavis.2006.03.002

Cited by 23 publications

(17 citation statements)

References 17 publications

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“…Similarly the intensity component of the panchromatic image is also separated using the forward IHS transform. Then the intensity components of both multispectral and panchromatic images are transformed separately using Radon Transform using equation (6).The yintersect and the inclination are calculated using equations (8) and (9).The inclination and the y-intersect are used to find the xmin, ymin, xmax, ymax using the trigonometric functions. After taking Radon transfom, the Radon transformed intensity components of both panchromatic and multispectral images are fused using maximum fusion rule.…”

Section: Image Fusion Methodsmentioning

confidence: 99%

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Hybrid fusion approach of panchromatic and multispectral images using IHS and radon transform

Sujitha

Selvathi²,

Azees

2013

2013 Ieee Conference on Information and Communication Technologies

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In remote sensing applications there is a need of an image with high spatial resolution and high spectral resolution. To obtain this kind of image the panchromatic image is fused with the multispectral image using hybrid transform. The basic ideas behind this method is that the extraction of the spectral information from the multispectral image and fuse this information with the new intensity component obtained from the radon transform of panchromatic and multispectral image. The fusion used in this method is maximum coefficient scheme, which takes the largest magnitude while comparing. In this fusion method, higher value Radon transformed coefficients of intensity component are injected. To this, hue and saturation components are added. So High Resolution Multispectral Image (HRMI) is obtained with high spectral and spatial quality which is better than the image obtained from IHS method.

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Section: Image Fusion Methodsmentioning

confidence: 99%

“…There are two distinct Radon transforms. The source can either be a single point or it can be an array of sources [9]. Radon transform is used to extract the suitable and important information from the images [10].…”

Section: Introductionmentioning

confidence: 99%

Hybrid fusion approach of panchromatic and multispectral images using IHS and radon transform

Sujitha

Selvathi²,

Azees

2013

2013 Ieee Conference on Information and Communication Technologies

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“…14) respectively, for the set of translates t as (1) compute the 2D NTT of the image. The NRT may also be extended to arbitrary composite sizes using the work of Kingston and Svalbe [21].…”

Section: Performancementioning

confidence: 99%

Exact image representation via a number‐theoretic Radon transform

Chandra

Svalbe²

2014

IET Computer Vision

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This study presents an integer‐only algorithm to exactly recover an image from its discrete projected views that can be computed with the same computational complexity as the fast Fourier transform (FFT). Most discrete transforms for image reconstruction rely on the FFT, via the Fourier slice theorem (FST), in order to compute reconstructions with low‐computational complexity. Consequently, complex arithmetic and floating point representations are needed, the latter of which is susceptible to round‐off errors. This study shows that the slice theorem is valid within integer fields, via modulo arithmetic, using a circulant theory of the Radon transform (RT). The resulting number‐theoretic RT (NRT) provides a representation of images as discrete projections that is always exact and real‐valued. The NRT is ideally suited as part of a discrete tomographic algorithm, an encryption scheme or for when numerical overflow is likely, such as when computing a large number of convolutions on the projections. The low‐computational complexity of the NRT algorithm also provides an efficient method to generate discrete projected views of image data.

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“…To completely tile all elements of the entire space at least once, i.e. cover all possible coefficients in the DFT space, a total of slices (and hence projections) are required [13]. For the simplest prime case , projections are required and space is then tiled exactly [11].…”

Section: A Discrete Fourier Slice Theoremmentioning

confidence: 99%

“…For the simplest prime case , projections are required and space is then tiled exactly [11]. For the case , projections are required resulting in a certain amount of oversampling, which is easily and exactly corrected by dividing each coefficient for all slices by [13]. Orthogonal forms of the discrete FST also exist which do not require this sampling correction [14], [15].…”

Section: A Discrete Fourier Slice Theoremmentioning

confidence: 99%

Robust Digital Image Reconstruction via the Discrete Fourier Slice Theorem

Chandra

Normand²,

Kingston

et al. 2014

IEEE Signal Process. Lett.

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International audienceThe discrete Fourier slice theorem is an important tool for signal processing, especially in the context of the exact reconstruction of an image from its projected views. This paper presents a digital reconstruction algorithm to recover a two dimensional (2-D) image from sets of discrete one dimensional (1-D) projected views. The proposed algorithm has the same computational complexity as the 2-D fast Fourier transform and remains robust to the addition of significant levels of noise. A mapping of discrete projections is constructed to allow aperiodic projections to be converted to projections that assume periodic image boundary conditions. Each remapped projection forms a 1-D slice of the 2-D Discrete Fourier Transform (DFT) that requires no interpolation. The discrete projection angles are selected so that the set of remapped 1-D slices exactly tile the 2-D DFT space. This permits direct and mathematically exact reconstruction of the image via the inverse DFT. The reconstructions are artefact free, except for projection inconsistencies that arise from any additive and remapped noise. We also present methods to generate compact sets of rational projection angles that exactly tile the 2-D DFT space. The improvement in noise suppression that comes with the reconstruction of larger sized images needs to be balanced against the corresponding increase in computation time

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Generalised finite radon transform for N×N images

Cited by 23 publications

References 17 publications

Hybrid fusion approach of panchromatic and multispectral images using IHS and radon transform

Hybrid fusion approach of panchromatic and multispectral images using IHS and radon transform

Exact image representation via a number‐theoretic Radon transform

Robust Digital Image Reconstruction via the Discrete Fourier Slice Theorem

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