Irregular seismic data reconstruction based on exponential threshold model of POCS method

Gao, Jianjun; Chen, Xiaohong; Li, Jingye; Liu, Guochang; Ma, Jian

doi:10.1007/s11770-010-0246-5

Cited by 62 publications

(35 citation statements)

References 20 publications

(21 reference statements)

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“…Projection onto convex sets reconstruction in the frequency-space domain Gao et al (2010) transformed the POCS reconstruction method from the time-domain to the frequencydomain and then applied thresholds to every frequency component in the iteration process to eliminate the noncoherent noise, successfully recovering the missing traces. In the time-domain method, a forward and inverse Fourier transform are performed at each iteration.…”

Section: Theory and Methodologymentioning

confidence: 99%

“…They pointed out that the threshold is the key parameter in POCS reconstruction, and used a linear threshold in the iterations. Galloway and Sacchi (2007) and Gao et al (2010) used an exponential threshold to improve the convergence of the POCS reconstruction method. Wang et al (2010) used graphics processing units (GPU) to accelerate the POCS interpolation.…”

Section: Introductionmentioning

confidence: 99%

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A fast-convergence POCS seismic denoising and reconstruction method

Pan

et al. 2015

Appl. Geophys.

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The effi ciency, precision, and denoising capabilities of reconstruction algorithms are critical to seismic data processing. Based on the Fourier-domain projection onto convex sets (POCS) algorithm, we propose an inversely proportional threshold model that defi nes the optimum threshold, in which the descent rate is larger than in the exponential threshold in the large-coeffi cient section and slower than in the exponential threshold in the small-coeffi cient section. Thus, the computation efficiency of the POCS seismic reconstruction greatly improves without affecting the reconstructed precision of weak refl ections. To improve the fl exibility of the inversely proportional threshold, we obtain the optimal threshold by using an adjustable dependent variable in the denominator of the inversely proportional threshold model. For random noise attenuation by completing the missing traces in seismic data reconstruction, we present a weighted reinsertion strategy based on the data-driven model that can be obtained by using the percentage of the data-driven threshold in each iteration in the threshold section. We apply the proposed POCS reconstruction method to 3D synthetic and fi eld data. The results suggest that the inversely proportional threshold model improves the computational effi ciency and precision compared with the traditional threshold models; furthermore, the proposed reinserting weight strategy increases the SNR of the reconstructed data.

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Section: Theory and Methodologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A fast-convergence POCS seismic denoising and reconstruction method

Pan

et al. 2015

Appl. Geophys.

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“…This incompleteness can lead to logical contradictions during the generation of digital spatial plans (Worboys and Duckham 2004). There are several approaches proposed in the literature for handling incomplete data, including logistic regression (Williams et al 2005), Bayesian networks (Beal and Ghahramani 2003), and Hilbert space (Gao et al 2010). Williams et al (2005) main contribution was the derivation of a missingdata logistic regression classification algorithm.…”

Section: The Definition Of Uncertainty In Spatial Planningmentioning

confidence: 99%

“…Beal and Ghahramani (2003) presented an efficient procedure for estimating the marginal likelihood of probabilistic models with latent variables or incomplete data. Gao et al (2010) proposed a method widely used in image restoration to apply to the reconstruction of irregular spaced seismic data by interpolating missing traces. They conclude that their method is method is fit for interpolating reconstruction of linear and quasi-linear events.…”

Section: The Definition Of Uncertainty In Spatial Planningmentioning

confidence: 99%

Dealing with the Uncertainty of Having Incomplete Sources of Geo-Information in Spatial Planning

Vullings

Blok

Wessels³

et al. 2012

Appl. Spatial Analysis

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The Dutch spatial planning legal act of 2008 was aimed at improving efficiency and effectiveness in the development, evaluation and monitoring of spatial planning policy (Ministry of VROM, 2006a). One of the main effects of this legal act was the widespread availability and use of digital spatial plans (Ministry of VROM 2006a, b). This reform led to the expectation that all digital spatial plans would be exchangeable and comparable. In practice, this exchange and comparison required carrying out complex procedures due to uncertainty caused by differences in the scope of spatial plans as well as their intended use. Furthermore the uncertainty resulted in a lack of confidence in spatial plans by policymakers and supporting GIS staff. Our overarching research question was: how can uncertainty caused by incomplete geo-information sources be dealt with? We proposed two techniques-fuzzy logic and visualisation-for policy makers to deal with uncertainty resulting from incomplete geo-information sources in spatial planning at the regional and national planning levels. We used two case studies in the Netherlands to illustrate the results of applying these techniques. The fuzzy set theory provides extra information by converting the discrete borders of continuous objects into fuzzy borders that improve the resemblance to the real object and thus make it more realistic. As shown in the second case study, visualisation also improves the degree of realism and thus provides additional information. Both case studies showed that providing additional information reduces the uncertainty felt by policymakers.

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“…Due to the slow convergence rate of these existing algorithms, researchers have studied the techniques to improve the convergence performance: Beck and Teboulle (2009) proposed a fast iterative shrinkage-thresholding algorithm (FISTA) from a more general mathematical background; Gao et al (2010) and Yang et al (2011) utilized the exponential decreasing thresholding strategy as the substitute of the linear one employed by Abma and Kabir;Gao et al (2011) even proposed a data-driven schedule.…”

Section: Introductionmentioning

confidence: 99%