A Geometric Construction of Multivariate Sinc Functions

Ye, Wenxing; Entezari, Alireza

doi:10.1109/tip.2011.2162421

Cited by 25 publications

(28 citation statements)

References 37 publications

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“…In the dual space, a signal can be recovered from with , where is the indicator function , . The signal recovery corresponds to , and as such, is also known as the ideal interpolant of the sampling lattice Ш [2].…”

Section: Sampling On the Diamond Gridmentioning

confidence: 99%

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Sampling and Reconstruction on a Diamond Grid and the Tetrahedral Digital Waveguide Mesh

Hamilton

2013

IEEE Signal Process. Lett.

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It is shown that half of the points on the diamond grid are redundant for sampling and reconstructing a bandlimited 3-D signal. This redundancy is then exploited to show that the tetrahedral digital waveguide mesh requires four times more computational density and twice the memory storage for the same approximation as a finite difference scheme on the face-centered cubic lattice.Index Terms-Artificial reverberation, digital waveguide mesh, finite difference method, multidimensional sampling.

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Section: Sampling On the Diamond Gridmentioning

confidence: 99%

“…The face-centered cubic (FCC) lattice is nearly-optimal [1], [2] and is another viable alternative to the standard cubic lattice. The suitability of the diamond grid [3] for 3-D sampling has also been studied [4], [5].…”

Section: Introductionmentioning

confidence: 99%

Sampling and Reconstruction on a Diamond Grid and the Tetrahedral Digital Waveguide Mesh

Hamilton

2013

IEEE Signal Process. Lett.

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“…Bicubic and B-spline interpolation techniques provide a less degree of blurring in comparison to bilinear interpolation. Lanczos is another spatial domain interpolation technique which is implemented by multiplying a sinc function with a sinc window which is scaled to be wider and truncated to zero outside of a range [6]. Even if Lanczos interpolation gives good results, it is slower than other approaches and provides a blurring effect in the reconstructed image.…”

Section: Introductionmentioning

confidence: 99%

Local Adaptive Laplacian for Better 2-D Up-sampling

Acharya¹,

Meher²

2013

Proceedings of the 2nd International Symposium on Computer, Communication, Control and Automation

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Abstract-Most of the existing up-sampling techniques through interpolation produce undesirable blurring artefacts while converting a low resolution image to its high resolution counterpart. The blurring is caused by the loss of high frequency information during the down sampling and upsampling process. To overcome this problem, a no reference, local adaptive, 2-D Laplacian based post processing technique is proposed here. The proposed method sharpens the DCT (Discrete cosine transform) based up-sampled video intraframe based on its local statistics so as to compensate the high frequency loss. Generally, the degree of blurring is more in the high variance regions in an image. Therefore, to restore the high frequency information, the sharpening should be more in the high variance regions than the low variance regions. Therefore, in this proposed method, a 2-D Laplacian kernel is made adaptive as per the statistical local variance of a 3×3 neighbourhood. If the local variance is more, the central kernel weight becomes proportionately high and vice versa based on the direct mapping basis. The remaining pixel weights of the Laplacian kernel are adjusted as per the central pixel weight such that the sum of all weights in the adaptive Laplacian kernel is zero. Experimental results reveal that the proposed method outperforms most of the widely used existing interpolation techniques in terms of objective and subjective measures.

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“…We follow the approach of Cary and Lawton (2003) who smear the trace using a sinc-function filter. The examples to follow use a related Lanczos filter, which in some cases may provide a more stable output (Ye and Entezari, 2012). Again following Cary and Lawton (2003), we set the radius of the smoothing filter to the bin size.…”

Section: D-ps Survey-design Case Study 341 Overview Of Design Methmentioning

confidence: 99%

“…This method is similar to that used by Cary and Lawton (2003). The design algorithm used here employs a Lanczos smoothing function for improved stability (Ye and Entezari, 2012) and is applied prestack to allow for an investigation of offset-azimuth distribution.…”

Section: Survey Designmentioning

confidence: 99%

Resolution enhancement in shallow 3D-PS seismic reflection

Strong¹

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This thesis aims to advance methodology for acquiring and processing 3D multicomponent seismic data for shallow (< 300 m) exploration targets. The primary focus is to improve seismic resolution, and hence geological interpretation, for coal-scale targets.The coal industry is a significant contributor to the energy security and economy of Australia and the world. Conventional P-wave seismic methods are widely used in this industry, providing economic, safety and environmental benefits. There is potential for expanding these benefits by including multicomponent procedures. In this thesis, the primary focus is on converted-wave (PS) reflection, which is a logical extension to the standard approach. This has theoretical potential to provide extra geological information. It has also been proposed that there may be resolution advantages for shallower targets such as coal.A valuable starting point for understanding resolution in shallow P and PS reflection is via visco-elastic finite-difference simulation. This provides a useful indication of the reflection response of different targets, and can include the influence of different processing flows. For typical coal-scale environments, modelling with reasonable anelasticity assumptions suggests that PS resolution is unlikely to be superior to P resolution, even with idealised acquisition and processing. In real-world situations, achieving good PS resolution may be even more challenging. There are a number of factors across the acquisition and processing flow which incrementally influence resolution.Survey design is intrinsically more complex for PS surveys than for P, primarily because of ray-path asymmetry. In addition, phase and amplitude effects require careful analysis, and finite-difference modelling provides a useful tool. Such modelling suggests that for shallow surveys in particular, it may be possible to incorporate longer relative offsets, compared to the petroleum scale. An examination of bin fold, and offset/azimuth distribution, suggests that the natural bin size of a PS survey is mostly dependent on the receiver spacing, and is generally larger than for P waves. This favours the use of higher receiver densities for multicomponent surveys. These observations can be more important at the shallow scale, again because of greater ray-path asymmetry and potentially higher V P /V S value.One of the most critical steps in the shallow PS processing sequence is correcting for the S-wave receiver statics. Three relatively conventional approaches have been evaluated. A surface-consistent inversion approach has been shown to fail for shallow targets, or in the presence of strong noise. For our 3D data set, PPS refraction analysis provided the preferred solution. In other cases where PPS refractions are poorly defined, our robust statistical approach may be useful for determining short-wavelength statics, although additional long-wavelength control would then be needed.ii In exploration seismology, surface waves are commonly considered to be noise. However, the d...

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A Geometric Construction of Multivariate Sinc Functions

Cited by 25 publications

References 37 publications

Sampling and Reconstruction on a Diamond Grid and the Tetrahedral Digital Waveguide Mesh

Sampling and Reconstruction on a Diamond Grid and the Tetrahedral Digital Waveguide Mesh

Local Adaptive Laplacian for Better 2-D Up-sampling

Resolution enhancement in shallow 3D-PS seismic reflection

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