Robust tensor-completion algorithm for 5D seismic-data reconstruction

Abstract

Multidimensional seismic data reconstruction has emerged as a primary topic of research in the field of seismic data processing. Although there exists a large number of algorithms for multidimensional seismic data reconstruction, they often adopt the [Formula: see text] norm to measure the discrepancy between observed and reconstructed data. Strictly speaking, these algorithms assume well-behaved noise that ideally follows a Gaussian distribution. When erratic noise contaminates the seismic traces, a 5D reconstruction must adopt a robust criterion to measure the difference between observed and reconstructed data. We develop a new formulation to the parallel matrix factorization tensor completion method and adapt it for coping with erratic noise. We use synthetic and field-data examples to examine our robust reconstruction technique.

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

“…Although there is no guarantee that r iterations will approximate the SVD-derived reduced-rank matrix, numerical tests show that they lead to similar results (Gao et al, 2013). Carozzi and Sacchi (2019) adopt the randomized QR decomposition for rank reduction, which shows higher computational efficiency in comparison to applying SVD, due to the reduction of the size of the original matrix. The randomized QR factorization also provides flexibility regarding the actual rank, similar to the proposed CUR decompositions.…”

“…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). All the aforementioned applications are deeply rooted in the following assumption: Clean and complete seismic data can be represented as low-rank matrices or tensors.…”

“…To alleviate the cost, Oropeza and Sacchi (2011) suggest the use of a randomized SVD (R-SVD), whereas Gao et al (2013) propose the Lanczos bidiagonalization as an alternative to the SVD. Carozzi and Sacchi (2019), Wu et al (2020) and provide other SVD-free approaches for data reconstruction and noise suppression.…”

“…A single-imputation algorithm with the form of equations ( 5) and ( 8) is used by Tomasi and Bro (2005) to handle missing data in PARAFAC, another generalization for multilinear arrays (Kolda and Bader, 2009). The parallel matrix factorization algorithms for seismic tensor reconstruction described by Gao et al (2015) and Carozzi and Sacchi (2019) lead to similar equations. These equations also represent the projection on to convex sets reconstruction methods, which use some thresholding strategy, for instance, in the frequencywavenumber domain (Abma and Kabir, 2006), instead of rank reduction.…”

Divide and Conquer Partition for Fourier Reconstruction Sparse Inversion with its Applications

“…To solve this problem, numerous non-uniformly reconstruction algorithms have been raised. These algorithms can be classified into three categories: operators-based [4], prediction error filter (PEF)-based [5], transformation-based [6][7][8], and machine learning-based [9][10][11] reconstruction.…”