A constrained-based optimization approach for seismic data recovery problems

Abstract

Random and structured noise both affect seismic data, hiding the reflections of interest (primaries) that carry meaningful geophysical interpretation. When the structured noise is composed of multiple reflections, its adaptive cancellation is obtained through time-varying filtering, compensating inaccuracies in given approximate templates. The under-determined problem can then be formulated as a convex optimization one, providing estimates of both filters and primaries. Within this framework, the criterion to be minimized mainly consists of two parts: a data fidelity term and hard constraints modeling a priori information. This formulation may avoid, or at least facilitate, some parameter determination tasks, usually difficult to perform in inverse problems. Not only classical constraints, such as sparsity, are considered here, but also constraints expressed through hyperplanes, onto which the projection is easy to compute. The latter constraints lead to improved performance by further constraining the space of geophysically sound solutions.

Sparse adaptive template matching and filtering for 2D seismic images with dual-tree wavelets and proximal methods

“…In other words, a careful partnership between sparse representations and adaptive filtering was deemed beneficial in 1D, with respect to traditional 2D methods. To account for additional properties, including statistical distributions for primaries [7] and slow filter variations, [8,9] pursued seismic data adaptive filtering with 1D wavelet frames. Meanwhile, seismic images possess geometric regularity that advises a 2D approach for improved per-…”

Generalized Minkowski sets for the regularization of inverse problems

“…m ∈ p i=1 C i . See, e.g., [Gragnaniello et al, 2012, Pham et al, 2014a,b, Smithyman et al, 2015, Peters and Herrmann, 2017, Esser et al, 2018, Yong et al, 2018, Peters et al, 2018. Alternatively, we can also formulate certain types of inverse problems directly as a feasibility (also known as set-theoretic estimation) or projection problem [Youla and Webb, 1982, Trussell and Civanlar, 1984, Combettes, 1993, 1996.…”