There was a special session on "Seismic Signal Processing" at International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2014, Florence. Our talk was on simplified optimization techniques to solve multiple reflections via adaptive filtering techniques in wavelet frame domains.
Special session on "SS5 - Seismic Signal Processing", International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2014, Florence, Italy [journal paper+blog+arxiv+paper+slides]
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 modelling 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.
This paper has focused on the constrained convex formulation of adaptive multiple removal. The proposed approach, based on proximal methods, is quite flexible and allows us to integrate a large panel of hard constraints corresponding to a priori knowledge on the data to be estimated (i.e. primary signal and time-varying filters). A key observation is that some of the related constraint sets can be expressed through hyperplanes, which are not only more convenient to design, but also easier to implement through straightforward projections. Since sparsifying transforms and constraints strongly interact [Pham-2014-TSP], we now study the class of hyperplane constraints of interest as well as their inner parameters, together with the extension to higher dimensions