Wavefield recovery with limited-subspace weighted matrix factorizations

Near-Optimal Weighted Matrix Completion

“…In many applications, prior knowledge of the data's structure is available. Incorporating this information appropriately into a reconstruction program has been shown to significantly improve the success of matrix recovery (Aravkin et al 2014;Zhang et al 2019Zhang et al , 2020Abernethy et al 2009;Bayat and Daei 2020;Chiang et al 2015;Eftekhari et al 2018b;Chen 2015;Xu et al 2013;Yi et al 2013;Jain and Dhillon 2013;Chen et al , 2014.…”

“…However, note that program (9) from the previous section agrees with (10) when ω 2 = 1. Spurring from the original program, similar methodologies have been proposed in the literature (Eftekhari et al 2018b;Zhang et al 2019Zhang et al , 2020Bayat and Daei 2020) but other approaches more related to program (8) have also been considered (Xu et al 2013;Chiang et al 2015;Yi et al 2013;Jain and Dhillon 2013;Abernethy et al 2009;Chen 2015). To attempt producing a result that provides some level of insight for many of these variations, a more general notion of incoherence is required.…”

“…Many authors have considered how to efficiently include prior information into matrix reconstruction problems. The papers by Aravkin et al 2014;Zhang et al 2019Zhang et al , 2020 focus on applications to seismology and numerical aspects of the problem, adopting an approach that spurred from program (10) first proposed by Aravkin et al 2014. A distinct approach is considered by Chen et al , 2014Eftekhari et al 2018a, where the prior information is used to bias the sampling scheme according to the array's leverage scores.…”

A practical workflow for land seismic wavefield recovery with weighted matrix factorization

“…In this expression, the Li ∈ C (Nsx×Nrx)×r and Ri ∈ C (Nsy×Nry)×r represent the low-rank factorization of Xi with rank r min(N sx × N rx , N sy × N ry ) [Zhang et al, 2020]. While wavefield recovery based on weighted matrix factorization has been applied successfully (see e.g., Zhang et al [2019] and Zhang et al [2020]), its performance is challenged by data that contains strongamplitude aliased ground roll. Because of its large-amplitude, ground roll dominates the reconstruction at the expense of body waves that are of prime interest.…”

“…To solve this problem, Aravkin et al [2014], Eftekhari et al [2018], and Zhang et al [2019] used the wavefield recovery via weighted matrix factorization to reconstruct seismic data by introducing matrix weights defined in terms of factorizations at neighboring frequencies that live in close-by subspaces. By moving the matrix weights from the constraint to the data-misfit term, Zhang et al [2020] proposed a computationally more efficient scheme capable of handling high frequencies.…”