Multidimensional simultaneous random plus erratic noise attenuation and interpolation for seismic data by joint low-rank and sparse inversion

Abstract

We have developed an efficient convex optimization strategy enabling the simultaneous attenuation of random and erratic noise with interpolation in prestack seismic data. For a particular analysis window, frequency slice spatial data were reorganized into a block Toeplitz matrix with Toeplitz blocks as in Cadzow/singular spectrum analysis methods. The signal and erratic noise were, respectively, modeled as low-rank and sparse components of this matrix, and then a joint low-rank and sparse inversion (JLRSI) enabled us to recover the low-rank signal component from noisy and incomplete data thanks to joint minimization of a nuclear norm term and an L 1-norm term. The convex optimization framework, related to recent developments in the field of compressed sensing, enabled the formulation of a well-posed problem as well as the use of state-of-the-art algorithms. We proposed an alternating directions method of multipliers scheme associated with an efficient singular value thresholding kernel. Numerical results on field data illustrated the effectiveness of the JLRSI approach at recovering missing data and increasing the signal-to-noise ratio.

Low‐rank seismic data reconstruction and denoising by CUR matrix decompositions

“…Low-rank seismic reconstruction methods were first introduced in the form of Cadzow filtering (Trickett et al, 2010) and multichannel singular spectrum analysis (MSSA) (Oropeza and Sacchi, 2011). These approaches are often conducted in the frequency-space domain, where the multidimensional signal is embedded in Hankel/Toeplitz matrices for each fixed temporal frequency (Gao et al, 2013;Sternfels et al, 2015;Chen et al, 2016;Zhang et al, 2016Zhang et al, , 2017Carozzi and Sacchi, 2021;Oboué et al, 2021). Reduced-rank tensor completion has also been used for multidimensional seismic data recovery (Kreimer and Sacchi, 2012;Kreimer et al, 2013;Gao et al, 2015;Carozzi and Sacchi, 2019;Cavalcante and Porsani, 2021).…”

Seismic erratic noise attenuation using unsupervised anomaly detection

“…To examine the performance of the proposed workflow, the LoOP‐denoising result was compared with results obtained by well‐established denoising methodologies. Figure 10(c–h) shows the results and their corresponding residuals obtained by an f – x deconvolution, a multi‐stage median filtering (Tsingas et al ., 2016) and a rank reduction filtering that applies a joint sparse and low rank approximation (Sternfels et al ., 2015; Jeong et al ., 2020a), respectively. Figure 11 depicts an SNR plot for each result.…”

“…An iterative application of the sparsity‐promoting filters can effectively suppress the seismic erratic noise by employing special constraints or thresholds (Chen et al ., 2014; Gan et al ., 2016; Zhao et al ., 2018). A joint sparse and low rank approximation, which is a robust implementation of rank reduction method, has been proven to be an effective denoising methodology, which can be based either on alternating direction method of multipliers or accelerated proximal gradient methods (Candès et al ., 2011; Sternfels et al ., 2015; Jeong et al ., 2020a). In addition, there have been machine learning‐based methods that are erratic noise removal applications of hybrid‐sparsity constrained dictionary learning and convolutional neural networks (Zu et al ., 2019; Baardman and Hegge, 2020).…”

Non-Parametric Simultaneous Reconstruction and Denoising via Sparse and Low-Rank Regularization

“…The method needs to tune only one regularization parameter. Sternfels et al (2015) show that the method of joint low-rank and sparse inversion is suitable for random and erratic noise. To deal with the extremely noisy cube, Chen et al (2016b) introduced a damped rank-reduction method to formulate the Cadzow rank-reduction and proposed a 5-D reconstruction and denoising method.…”