Performance Variability Analysis of Photonic Circuits with Many Correlated Parameters

We propose a method to analyze the performance variability caused by fabrication uncertainty in photonic circuits with a large number of correlated parameters. By combining a sparse polynomial chaos expansion model with dimensionality reduction in the form of Karhunen-Loève transform and principal component analysis, we demonstrate the stochastic analysis of the transfer function of cascaded Mach-Zehnder interferometers with up to 38 correlated uncertain parameters

Recognition and reconstruction of coherent energy with application to deep seismic reflection data

Reflections in deep seismic reflection data tend to be visible on only a limited number of traces in a common midpoint gather. To prevent stack degeneration, any noncoherent reflection energy has to be removed. In this paper, a standard classification technique in remote sensing is presented to enhance data quality. It consists of a recognition technique to detect and extract coherent energy in both common shot gathers and fi- nal stacks. This technique uses the statistics of a picked seismic phase to obtain the likelihood distribution of its presence. Multiplication of this likelihood distribution with the original data results in a “cleaned up” section. Application of the technique to data from a deep seismic reflection experiment enhanced the visibility of all reflectors considerably. Because the recognition technique cannot produce an estimate of “missing” data, it is extended with a reconstruction method. Two methods are proposed: application of semblance weighted local slant stacks after recognition, and direct recognition in the linear tau-p domain. In both cases, the power of the stacking process to increase the signal-to-noise ratio is combined with the direct selection of only specific seismic phases. The joint application of recognition and reconstruction resulted in data images which showed reflectors more clearly than application of a single technique

Performance analysis of the Karhunen–Loève Transform for artificial and astrophysical transmissions: denoizing and detection

In this work, we propose a new method of computing the Karhunen–Loève Transform (KLT) applied to complex voltage data for the detection and noise level reduction in astronomical signals. We compared this method with the standard KLT techniques based on the Toeplitz correlation matrix and we conducted a performance analysis for the detection and extraction of astrophysical and artificial signals via Monte Carlo (MC) simulations. We applied our novel method to a real data study-case: the Voyager 1 telemetry signal. We evaluated the KLT performance in an astrophysical context: our technique provides a remarkable improvement in computation time and MC simulations show significant reconstruction results for signal-to-noise ratio (SNR) down to −10 dB and comparable results with standard signal detection techniques. The application to artificial signals, such as the Voyager 1 data, shows a notable gain in SNR after the KLT

Adaptive distributed transforms for irregularly sampled Wireless Sensor Networks

We develop energy-efficient, adaptive distributed transforms for data gathering in wireless sensor networks. In particular, we con-sider a class of unidirectional transforms that are computed as data is forwarded to the sink along a given routing tree and develop a tree-based Karhunen-Loève Transform (KLT) that is optimal in that it achieves maximum data de-correlation among this class of trans-forms. As an alternative to this KLT (which incurs communication overhead in order to learn second order data statistics), we propose a backward adaptive filter optimization algorithm for distributed wavelet transforms that i) achieves near optimal performance and ii) has no communication overhead in learning statistics

Recent advances in theory and methods for nonstationary signal analysis

[No abstract available

Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size and architecture

Towards effective information content assessment: analytical derivation of information loss in the reconstruction of random fields with model uncertainty

Structures are abundant in both natural and human-made environments and usually studied in the form of images or scattering patterns. To characterize structures a huge variety of descriptors is available spanning from porosity to radial and correlation functions. In addition to morphological structural analysis, such descriptors are necessary for stochastic reconstructions, stationarity and representativity analysis. The most important characteristic of any such descriptor is its information content - or its ability to describe the structure at hand. For example, from crystallography it is well known that experimentally measurable $S_2$ correlation function lacks necessary information content to describe majority of structures. The information content of this function can be assessed using Monte-Carlo methods only for very small 2D images due to computational expenses. Some indirect quantitative approaches for this and other correlation function were also proposed. Yet, to date no methodology to obtain information content for arbitrary 2D or 3D image is available. In this work, we make a step toward developing a general framework to perform such computations analytically. We show, that one can assess the entropy of a perturbed random field and that stochastic perturbation of fields correlation function decreases its information content. In addition to analytical expression, we demonstrate that different regions of correlation function are in different extent informative and sensitive for perturbation. Proposed model bridges the gap between descriptor-based heterogeneous media reconstruction and information theory and opens way for computationally effective way to compute information content of any descriptor as applied to arbitrary structure.Comment: Keywords: correlation functions, structure characterization, structural descriptors, image analysis, information conten