M. Quyen Pham (IFPEN\, Paris): Proximal methods for multiple removal in seismic data

Date(s) : 28/03/2014   iCal
14 h 00 min - 15 h 00 min

Proximal methods for multiple removal in seismic data by Mai Quyen Pham (IFPEN\, Paris.\n\nJoint work Caroline Chaux\, Laurent Duval and Jean-Christophe Pesquet\n\nAbstract:\nDuring the acquisition of seismic data\, undesirable coherent seismic events such as multiples\, are also recorded\, often resulting in a degradation of the signal of interest [1]. The complexity of these data has historically contributed to the development of several efficient signal processing tools\; for instance complex wavelet transforms [2\,3] or robust l1-based sparse restoration [4]. The objective of this work is to propose an original approach to the multiple removal problem. A variational framework is adopted here\, but instead of assuming some knowledge on the kernel\, we assume that templates are available. Consequently\, it turns out that the problem reduces to estimate Finite Impulse Response filters\, the latter ones being assumed to vary slowly along time.\nWe assume that the characteristics of the signal of interest are appropriately described through a prior statistical model in a frame of signals\, e.g. a wavelet basis. The data fidelity term thus takes into account the statistical properties of the frame coefficients (one can choose an l1-norm to induce sparsity)\, the regularization term models prior informations that are available on the filters and a last constraint modelling the smooth variations of the filters along time is added.\nIn particular\, the problem is completely reformulated as a constrained minimization problem\, in order to simplify the determination of data-based parameters\, as compared with our previous regularized approach involving hyper-parameters.\nThe resulting minimization is achieved by using recent primal-dual proximal approaches [5].\n\nReferences\n[1] S. Ventosa\, S. Le Roy\, I. Huard\, A. Pica\, H. Rabeson\, P. Ricarte\, and L. Duval. Adaptive multiple subtraction with wavelet-based complex unary Wiener filters. Geophysics\, 77(6):V183–V192\, Nov.-Dec. 2012.\n[2] J. Morlet\, G. Arens\, E. Fourgeau\, and D. Giard. Wave propagation and sampling theory\, part I: Complex signal and scattering in multilayered media. Geophysics\, 47(2):203–221\, 1982.\n[3] J. Morlet\, G. Arens\, E. Fourgeau\, and D. Giard. Wave propagation and sampling theory\, part II: Sampling theory and complex waves. Geophysics\, 47(2):222–236\, 1982.\n[4] J. F. Claerbout and F. Muir. Robust modeling with erratic data. Geophysics\, 38(5):826–844\, Oct. 1973.\n[5] P. L. Combettes and J.-C. Pesquet. Primal-dual splitting algorithm for solving inclusions with mixtures of composite\, Lipschitzian\, and parallel-sum type monotone operators. Set-Valued Var. Anal.\, 20(2):307–330\, Jun. 2012.

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