6,317 research outputs found
A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal
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 hyperparameters. The approach demonstrates significantly good
performance in low signal-to-noise ratio conditions, both for simulated and
real field seismic data
A constrained-based optimization approach for seismic data recovery problems
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.Comment: International Conference on Acoustics, Speech and Signal Processing
(ICASSP 2014); Special session "Seismic Signal Processing
Blind Source Separation with Compressively Sensed Linear Mixtures
This work studies the problem of simultaneously separating and reconstructing
signals from compressively sensed linear mixtures. We assume that all source
signals share a common sparse representation basis. The approach combines
classical Compressive Sensing (CS) theory with a linear mixing model. It allows
the mixtures to be sampled independently of each other. If samples are acquired
in the time domain, this means that the sensors need not be synchronized. Since
Blind Source Separation (BSS) from a linear mixture is only possible up to
permutation and scaling, factoring out these ambiguities leads to a
minimization problem on the so-called oblique manifold. We develop a geometric
conjugate subgradient method that scales to large systems for solving the
problem. Numerical results demonstrate the promising performance of the
proposed algorithm compared to several state of the art methods.Comment: 9 pages, 2 figure
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