F‐xy Cadzow noise suppression

Trickett, Stewart

doi:10.1190/1.3063880

Cited by 154 publications

(36 citation statements)

References 6 publications

(8 reference statements)

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“…For convenience, we choose L ¼ b N 2 c þ 1 to make the Hankel matrix approximately square (Trickett, 2008;Oropeza and Sacchi, 2011), MðωÞ ∈ C L×ðN−Lþ1Þ . We will omit the symbol ω and understand that the analysis is carried out for all frequencies.…”

Section: Singular Spectrum Analysismentioning

confidence: 99%

“…For instance, eigenimage filtering (Ulrych et al, 1988), similar to filtering via the Karhunen-Loève transform (Jones and Levy, 1987), can operate directly on the seismic data in the t-x or f-x-y domain (Trickett, 2003). Recently, the singular spectrum analysis (SSA) method (Sacchi, 2009;Oropeza and Sacchi, 2011), also known as Cadzow filtering (Trickett, 2008;Trickett and Burroughs, 2009), was introduced to attenuate incoherent noise and for seismic data reconstruction (Oropeza and Sacchi, 2011;Gao et al, 2013). It is also important to note that reduced-rank filtering based on SSA has been also used to suppress coherent noise (Nagarajappa, 2012;Chiu, 2013).…”

Section: Introductionmentioning

confidence: 99%

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Robust reduced-rank filtering for erratic seismic noise attenuation

2015

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Singular spectrum analysis (SSA) or Cadzow reduced-rank filtering is an efficient method for random noise attenuation. SSA starts by embedding the seismic data into a Hankel matrix. Rank reduction of this Hankel matrix followed by antidiagonal averaging is utilized to estimate an enhanced seismic signal. Rank reduction is often implemented via the singular value decomposition (SVD). The SVD is a nonrobust matrix factorization technique that leads to suboptimal results when the seismic data are contaminated by erratic noise. The term erratic noise designates non-Gaussian noise that consists of large isolated events with known or unknown distribution. We adopted a robust low-rank factorization that permitted use of the SSA filter in situations in which the data were contaminated by erratic noise. In our robust SSA method, we replaced the quadratic error criterion function that yielded the truncated SVD solution by a bisquare function. The Hankel matrix was then approximated by the product of two lower dimensional factor matrices. The iteratively reweighed least-squares method was used to approximately solve for the optimal robust factorization. Our algorithm was tested with synthetic and real data. In our synthetic examples, the data were contaminated with band-limited Gaussian noise and erratic noise. Then, denoising was carried out by means of f-x deconvolution, the classical SSA method, and the proposed robust SSA method. The f-x deconvolution and the classical SSA method failed to properly eliminate the noise and to preserve the desired signal. On the other hand, the robust SSA method was found to be immune to erratic noise and was able to preserve the desired signal. We also tested the robust SSA method with a data set from the Western Canadian Sedimentary Basin. The results with this data set revealed improved denoising performance in portions of data contaminated with erratic noise.

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Section: Singular Spectrum Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust reduced-rank filtering for erratic seismic noise attenuation

2015

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“…The DL methods have proven to perform well for denoising seismic data (Beckouche and Ma, 2014;Liang et al, 2014;Yu et al, 2015Yu et al, , 2016Zhu et al, 2015;Turquais et al, 2017). Another data-driven method, the Cadzow filtering method (Trickett, 2002(Trickett, , 2008, also called singular spectrum analysis (SSA) (Sacchi, 2009;Chen and Sacchi, 2015), uses rank reduction for denoising. This method embeds each frequency slice of the data into a Hankel matrix, mutes the low singular values, and averages the antidiagonal elements.…”

Section: Introductionmentioning

confidence: 99%

Coherent noise suppression by learning and analyzing the morphology of the data

2017

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We have developed a method for suppressing coherent noise from seismic data by using the morphological differences between the noise and the signal. This method consists of three steps: First, we applied a dictionary learning method on the data to extract a redundant dictionary in which the morphological diversity of the data is stored. Such a dictionary is a set of unit vectors called atoms that represent elementary patterns that are redundant in the data. Because the dictionary is learned on data contaminated by coherent noise, it is a mix of atoms representing signal patterns and atoms representing noise patterns. In the second step, we separate the noise atoms from the signal atoms using a statistical classification. Hence, the learned dictionary is divided into two subdictionaries: one describing the morphology of the noise and the other one describing the morphology of the signal. Finally, we separate the seismic signal and the coherent noise via morphological component analysis (MCA); it uses sparsity with respect to the two subdictionaries to identify the signal and the noise contributions in the mixture. Hence, the proposed method does not use prior information about the signal and the noise morphologies, but it entirely adapts to the signal and the noise of the data. It does not require a manual search for adequate transforms that may sparsify the signal and the noise, in contrast to existing MCA-based methods. We develop an application of the proposed method for removing the mechanical noise from a marine seismic data set. For mechanical noise that is coherent in space and time, the results show that our method provides better denoising in comparison with the standard FX-Decon, FX-Cadzow, and the curvelet-based denoising methods.

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“…Conventionally, random noise in seismic data are assumed to have a Gaussian distribution, with SNR related to √ N where N is the number of sensors. Assuming noise with Gaussian distribution, rank reduction based methods work pretty well for denoising data [8,9,10,11]. Rank reduction methods work on the assumption that within a small spatio-temporal seismic window, seismic reflections are linear events with different dips (gradients).…”

Section: Introductionmentioning

confidence: 99%

“…Rank reduction methods work on the assumption that within a small spatio-temporal seismic window, seismic reflections are linear events with different dips (gradients). In these methods [8,9,10,11], data are first transformed to the Fourier domain in the temporal direction (also known as Fx transform [7]) and then for every frequency slice, rank reduction is applied on the Hankel matrix to remove incoherent signals. Cadzow's algorithm [12], popular in array processing, can also be applied for further noise reduction [9].…”

Section: Introductionmentioning

confidence: 99%

M-Estimate robust PCA for Seismic Noise Attenuation

Akhondi-Asl

Nelson

2016

2016 IEEE International Conference on Image Processing (ICIP)

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The robust principal component analysis (PCA) method has shown very promising results in seismic ambient noise attenuation when dealing with outliers in the data. However, the model assumes a general Gaussian distribution plus sparse outliers for the noise. In seismic data however, the noise standard variation could vary from one place to another leading to a more heavy-tailed noise distribution. In this paper, we present a new method which solves a convex minimisation problem of the robust PCA method with an M-estimate penalty function. Our empirical results show that the proposed method can outperform the robust PCA method.

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F‐xy Cadzow noise suppression

Cited by 154 publications

References 6 publications

Robust reduced-rank filtering for erratic seismic noise attenuation

Robust reduced-rank filtering for erratic seismic noise attenuation

Coherent noise suppression by learning and analyzing the morphology of the data

M-Estimate robust PCA for Seismic Noise Attenuation

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