Convergence improvement and noise attenuation considerations for beyond alias projection onto convex sets reconstruction

Gao, Jianjun; Stanton, Aaron; Naghizadeh, Mostafa; Sacchi, Mauricio D.; Chen, Xiaohong

doi:10.1111/j.1365-2478.2012.01103.x

Cited by 79 publications

(28 citation statements)

References 31 publications

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“…The value T λ represents a thresholding operator with an input threshold parameter λ defined by an exponential decreasing function. Gao et al (2013) demonstrate that the exponential thresholding scheme can significantly improve the convergence rate. The thresholding operator can be divided into two types: soft and hard thresholdings.…”

Section: Iterative Blending Noise Estimation and Subtraction With A Cmentioning

confidence: 97%

A periodically varying code for improving deblending of simultaneous sources in marine acquisition

Chen

et al. 2016

GEOPHYSICS

103

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We have designed a periodically varying code that can avoid the problem of the local coherency and make the interference distribute uniformly in a given range; hence, it was better at suppressing incoherent interference (blending noise) and preserving coherent useful signals compared with a random dithering code. We have also devised a new form of the iterative method to remove interference generated from the simultaneous source acquisition. In each iteration, we have estimated the interference using the blending operator following the proposed formula and then subtracted the interference from the pseudodeblended data.To further eliminate the incoherent interference and constrain the inversion, the data were then transformed to an auxiliary sparse domain for applying a thresholding operator. During the iterations, the threshold was decreased from the largest value to zero following an exponential function. The exponentially decreasing threshold aimed to gradually pass the deblended data to a more acceptable model subspace. Two numerically blended synthetic data sets and one numerically blended practical field data set from an ocean bottom cable were used to demonstrate the usefulness of our proposed method and the better performance of the periodically varying code over the traditional random dithering code.

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Section: Iterative Blending Noise Estimation and Subtraction With A Cmentioning

confidence: 97%

A periodically varying code for improving deblending of simultaneous sources in marine acquisition

Chen

et al. 2016

GEOPHYSICS

103

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“…It is shown to be an effective method for seismic data reconstruction (Abma and Kabir, 2006;Stein et al, 2010;Wang et al, 2010;Gao et al, 2012), but it typically requires many iterations to achieve good results. A data-driven thresholding schedule has been shown to give a significant improvement in the number of iterations required while still achieving good results (Gao et al, 2012). A modification to the reinsertion operator allows for the algorithm to also be used for denoising of seismic data (Gao et al, 2012).…”

Section: Projection Onto Convex Setsmentioning

confidence: 99%

Vector reconstruction of multicomponent seismic data

Stanton

Sacchi

2013

GEOPHYSICS

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A multicomponent seismic record was transformed to the frequency-wavenumber domain using the quaternion Fourier transform. This transform was integrated into the projection onto convex sets algorithm to allow for the reconstruction of vector signals. The method took advantage of the spectral overlap of components in the frequency-wavenumber domain. The results of the method were compared with standard component-by-component reconstruction. Results were found for synthetic and real data including an example of 5D reconstruction of a converted-wave data set acquired over a heavy oil reservoir. We found an improvement in reconstruction quality producing fully sampled radial and transverse offset-azimuth gathers with a preserved vector relationship.

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“…where Q k denotes the new threshold at iteration k, p dri k denotes the data-driven threshold (Gao et al, 2013), p max and p min correspond to the maximum and minimum threshold, and Q max and Q min are respectively the maximum (Q max = 1) and minimum weight (Q min = 0).…”

Section: Descending Weight Coefficient and The Datadriven Modelmentioning

confidence: 99%

“…Oropeza and Sacchi (2011) presented a rank reduction algorithm for the simultaneous reconstruction and random noise attenuation of seismic data, and used a linear descending weight coeffi cient with increasing number of iterations to increase the SNR of the reconstructed data. Gao et al (2013) presented a data-driven threshold to improve the convergence of the POCS algorithm. In addition, a constant reinserting weight was used to minimize the effect of noise in the fi nal reconstruction of the seismic volume.…”

Section: Introductionmentioning

confidence: 99%

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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Convergence improvement and noise attenuation considerations for beyond alias projection onto convex sets reconstruction

Cited by 79 publications

References 31 publications

A periodically varying code for improving deblending of simultaneous sources in marine acquisition

A periodically varying code for improving deblending of simultaneous sources in marine acquisition

Vector reconstruction of multicomponent seismic data

A fast-convergence POCS seismic denoising and reconstruction method

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