|Significance index related to Student's t-test|
A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal [doi+hal+arxiv]
Abstract: Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured ``noises''. As their amplitude may be greater than signals of interest
(primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyper-parameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data.
Lost in multiples: a creeping primary (flat, bootom-right)
All the metrics here are convex. Wait a bit for something completely different with non-convex penalties, namely smoothed versions of the ratio of the L1 norm over the L2 norm: Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed $\ell_1/ell_2$ Regularization, covered in Nuit Blanche, and with arxiv page and pdf.