Distributed Adaptive Learning with Multiple Kernels in Diffusion Networks

We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion stage to achieve consensus on the estimates over the whole network. Multiple kernels are incorporated to enhance the approximation of functions with several high and low frequency components common in practical scenarios. We provide a thorough convergence analysis of the proposed scheme based on the metric of the Cartesian product of multiple reproducing kernel Hilbert spaces. To this end, we introduce a modified consensus matrix considering this specific metric and prove its equivalence to the ordinary consensus matrix. Besides, the use of hyperslabs enables a significant reduction of the computational demand with only a minor loss in the performance. Numerical evaluations with synthetic and real data are conducted showing the efficacy of the proposed algorithm compared to the state of the art schemes.Comment: Double-column 15 pages, 10 figures, submitted to IEEE Trans. Signal Processin

Near-Surface Seismic Measurements in Gravel Pit, Over Highway Tunnel and Underground Tubes with Ground Truth Information as an Open Data Set

In this article, we describe in detail three seismic measurement campaigns based on refraction methods that we conducted at different sites in Bavaria, Germany. The measured data is published as an open data set. The particularity of this data set lies in its available ground truth information about each measurement site. Acquiring seismic data from sites with ground truth information is important for validation of seismic inversion algorithms. Since near-surface seismic field data with ground truth information is rather limited, we anticipate this data set to be a valuable contribution to the research community. For the measurements, three sites have been selected: (1) a gravel pit with a ground water layer, (2) a site above a highway tunnel and (3) a surface over underground tubes. The measurements have been conducted using line arrays of geophones, the Geode Seismograph from Geometrics Inc. and hammer strikes as seismic source. To obtain inversion results a travel time tomography based on first-arrivals within the software SeisImager is used. The inversion results show that we are able to image the ground water layer in the gravel pit, the highway tunnel and partly features of underground tubes. Furthermore, the results coincide with available ground truth information about the measurement sites. This paper summarizes the measurement campaigns and the respective data sets obtained through these campaigns. The data have been published by the authors as an open data set under the license CC BY 4.0 on figshare to make it available to the research community for validation of seismic data processing and inversion techniques

Distributed Blind Deconvolution of Seismic Signals Under Sparsity Constraints in Sensor Networks

This work proposes an iterative algorithm for distributed deconvolution of seismic signals for a reflectivity survey by a network of sensors. Distributed deconvolution is particularly relevant for a subsurface exploration by sensor networks or swarms of mobile robots. We envision such an exploration methodology by multiple mobile agents for future explorations of a planet's subsurface. The proposed scheme consists of two steps: distributed estimation of the seismic wavelet, followed by a local estimation of the reflectivity. Both steps are realized using alternating directions method of multipliers algorithms where we exploit sparsity in the reflectivity. The performance of the scheme is compared to state-of-the-art sparse multichannel blind deconvolution of seismic data and is found to be comparable or even superior

Signal Processing for Distributed Kernel-based Estimation

With an increased utilization of large sensor networks in applications such as environmental monitoring, hazard detection and health care, the methodology of a data processing within the network has been identified as a promising concept. While common approaches rely on centralized processing, in-network processing exploits the interconnections among the nodes to obtain a cooperative result. By that, the network is equipped with estimation capabilities and an increased robustness against node failures within the network. Corresponding algorithms have been widely developed in the literature. However, the majority of these consider linear functions only whereas usually physical phenomena such as the spatial distribution of temperature, humidity, altitude or radioactivity are described by nonlinear functions. Hence, existing in-network processing algorithms will perform poorly when applied to the spatial reconstruction of such physical quantities. To suggest solutions to this issue this thesis aims at deriving algorithms that enable a distributed estimation and regression of nonlinear functions. Within this thesis two core algorithms are proposed that achieve the aforementioned objective by a combination of concepts from kernel methods, set theoretic adaptive filtering and in-network processing. Simulative analyses of the proposed schemes for synthetic data as well as real altitude data show their capability for a distributed reconstruction of nonlinear functions. To enable a comprehensive study of the presented material this thesis provides insights to recent advances in kernel-based estimation, kernel adaptive filtering algorithms and distributed consensus-based schemes