Variational Bayesian Learning for Decentralized Blind Deconvolution of Seismic Signals Over Sensor Networks

Abstract

This work discusses a variational Bayesian learning approach towards decentralized blind deconvolution of seismic signals within a sensor network. Blind seismic deconvolution is cast into a probabilistic framework based on Sparse Bayesian learning developed for blind image deconvolution. The posterior distribution of the signals of interest is then approximated using a variational Bayesian method. Depending on a particular form of selected variational factors, the scheme is shown to generalize the state-of-the-art distributed seismic blind deconvolution algorithm. The algorithm operates by repeatedly alternating between two stages: (i) estimation of seismic source wavelet and (ii) reflectivity estimation. The wavelet is estimated in a distributed fashion using Alternating Direction Method of Multipliers. Based on this estimate, each sensor then locally obtains a sparse reflectivity estimate. Numerical evaluation with synthetic seismic data shows that the proposed method outperforms existing deconvolution algorithms in a high signal-to-noise ratio (SNR) region. In low SNR regime a higher sensitivity of sparse Bayesian learning regarding model mismatches in the estimated source wavelet is observed. Also, processing of seismic data generated with an acoustic wave equation showed that the proposed method is able recover the original reflectivities more accurately, with more distinct support of the reflectivities, as compared to existing methods despite present model mismatches. The algorithm is also applied to the estimation of real seismic data, and shows improved performance as compared to state-of-the-art estimation method.

Swarm Exploration and Communications: A First Step towards Mutually-Aware Integration by Probabilistic Learning

“…The key to these computations is a decomposition of a network-global objective function into a sum of "local" sub-objectives, typically with additional constraints that ensure a network-wide convergence to a specific solution. A special class of such algorithms is called consensus-based algorithms, see, e.g., [13][14][15][16][17][18]. This class of algorithms enforces consensus over the whole network, i.e., each node converges to the same solution.…”