A Unified Analysis of Structured Sonar-Terrain Data Using Bayesian Functional Mixed Models

Sonar emits pulses of sound and uses the reflected echoes to gain information about target objects. It offers a low cost, complementary sensing modality for small robotic platforms. Although existing analytical approaches often assume independence across echoes, real sonar data can have more complicated structures due to device setup or experimental design. In this article, we consider sonar echo data collected from multiple terrain substrates with a dual-channel sonar head. Our goals are to identify the differential sonar responses to terrains and study the effectiveness of this dual-channel design in discriminating targets. We describe a unified analytical framework that achieves these goals rigorously, simultaneously, and automatically. The analysis was done by treating the echo envelope signals as functional responses and the terrain/channel information as covariates in a functional regression setting. We adopt functional mixed models that facilitate the estimation of terrain and channel effects while capturing the complex hierarchical structure in data. This unified analytical framework incorporates both Gaussian models and robust models. We fit the models using a full Bayesian approach, which enables us to perform multiple inferential tasks under the same modeling framework, including selecting models, estimating the effects of interest, identifying significant local regions, discriminating terrain types, and describing the discriminatory power of local regions. Our analysis of the sonar-terrain data identifies time regions that reflect differential sonar responses to terrains. The discriminant analysis suggests that a multi- or dual-channel design achieves target identification performance comparable with or better than a single-channel design. Supplementary materials for this article are available online.     

An efficient numerical algorithm for multi-dimensional time dependent partial differential equations

An efficient and robust numerical scheme based on Haar wavelets and finite differences is suggested for the solution of two-dimensional time dependent linear and nonlinear partial differential equations (PDEs). Excellent feature of the scheme is the conversion of linear and non-linear PDEs to algebraic equations which are comparatively easy to handle. Convergence of the scheme, which guarantees small error norm as the resolution level increases, is also an important part of this work. Different error norms are computed to check efficiency of the technique. Computations verify accuracy, flexibility and low computational cost of the method.     

Frequency domain image analysis for the characterization of porous products

Many pharmaceutical products are obtained via freeze-drying of liquid solutions to obtain stable long lasting preparations. The freeze-dry process produces porous cakes whose structure strongly depends on the freezing phase, so that monitoring and optimizing this phase can help both reducing the product cost and insuring its constant quality. Nowadays the optimization is usually performed by determining the cake mass transfer coefficient via a costly process in pilot plants, while the quality is assured only by controlling the process conditions. This paper describes an alternative way of approximately estimating the mass transfer coefficient, which is based on the observation of the product structure by a simple electron microscope followed by a frequency domain imaging process. While the process has been designed and characterized specifically for pharmaceutical products, the proposed approach can be used in several other fields where the characteristics of porous material have to be monitored.     

Short term solar irradiance forecasting using a mixed wavelet neural network

In modern smart grids and deregulated electricity markets, accurate forecasting of solar irradiance is critical for determining the total energy generated by PV systems. We propose a mixed wavelet neural network (WNN) in this paper for short-term solar irradiance forecasting, with initial application in tropical Singapore. The key advantage of using wavelet transform (WT) based methods is the high signal compression ability of wavelets, making them suitable for modeling of nonstationary environmental parameters with high information content, such as short timescale solar irradiance. In this WNN, a combination of the commonly known Morlet and Mexican hat wavelets is used as the activation function for hidden-layer neurons of a feed forward artificial neural network (ANN). To demonstrate the effectiveness of the proposed approach, hourly predictions of solar irradiance, which is an aggregate sum of irradiance value observed using 25 sensors across Singapore, are considered. The forecasted results show that WNN delivers better prediction skill when compared with other forecasting techniques.     

A multiresolution homogenization of modal analysis with application to layered media

We apply multiresolution techniques to study the effective properties of boundary value problems. Conditions under which boundary values are preserved in the effective (‘homogenized') formulation are developed and discussed. Relations between the eigenfunctions and eigenvalues of the generic formulation and those of the effective formulation are explored. Applications to the construction of effective Green function in a complex lamination are discussed. The analytic results are demonstrated via numerical computations.     

Fast Ray Tracing of Implicit Surfaces

A ray-tracing algorithm is described for rendering implicit surfaces formed with C¹-continuous bounded functions f ( x , y , z ). This class of functions includes such popular implicit models as blobby molecules, metaballs, soft objects and convolution surfaces. The algorithm employs analytical methods only, which makes it fast, robust, and numerically stable.
An earlier version of this work was presented at the 3rd International Workshop on Implicit Surfaces held in Seattle in 1998.     

Multiresolution Curve and Surface Representation: Reversing Subdivision Rules by Least-Squares Data Fitting

This work explores how three techniques for defining and representing curves and surfaces can be related efficiently. The techniques are subdivision, least-squares data fitting , and wavelets . We show how least-squares data fitting can be used to "reverse" a subdivision rule, how this reversal is related to wavelets, how this relationship can provide a multilevel representation, and how the decomposition/reconstruction process can be carried out in linear time and space through the use of a matrix factorization.
Some insights that this work brings forth are that the inner product used in a multiresolution analysis in uences the support of a wavelet, that wavelets can be constructed by straightforward matrix observations, and that matrix partitioning and factorization can provide alternatives to inverses or duals for building efficient decomposition and reconstruction processes. We illustrate our findings using an example curve, grey-scale image, and tensor-product surface.     

A wavelet collocation method for the static analysis of sandwich plates using a layerwise theory

A study of bending deformations of sandwich plates using a layerwise theory of laminated or sandwich plates is presented. The analysis is based on a wavelet collocation technique to produce highly accurate results. Numerical results for symmetric laminated composite and sandwich plates are presented and discussed.     

Wavelet-Based Synthesis of the Multifractional Brownian Motion

The multifractional Brownian motion （mBm） is introduced as a natural extension of traditional fractional Brownian motion （fBm）. The selling point of mBm is that its Hǒlder regularity is allowed to vary from point to point, such that makes it a promising model for those stochastic processes whose regularity evolves in time. A wavelet-based algorithm to synthesize a realization of mBm is proposed in this work. The desired local regularity of the multifractional process is obtained by controlling the weights of the wavelet expansion of the Gaussian white noise. This approach is not only time saving, also appro-priate for generating the multifractional process that is non-Gaussian and autocovariance function unknown in ad- vance. The validity is verified by numerical experiments and real-world data.     

镜像滤波器收敛到小波的条件及小波的构造

本文从论述了镜像滤波器的性质,并在理论上给出了并证明了镜像滤波器成为收敛的小波条件.