Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

A single antenna ambient noise cancellation method for in-situ radiated EMI measurements in the time-domain

This paper presents a single antenna ambient noise cancellation method for in-situ radiated emissions measurements performed using an entirely time-domain approach and the sliding window Empirical Mode Decomposition. The method requires a pair of successive measurements, an initial one for characterizing the ambient noise and a final one for the EMI measurement in the presence of ambient noise. The method assumes the spectral content of the ambient noise is stable between both measurements. The measured time-domain EMI is decomposed into a finite set of intrinsic mode functions. Some modes contain the ambient noise signals while other modes contain the actual components of the EMI. A brute-force search algorithm determines which mode, or combination of modes, maximize the absolute difference between the magnitude of their spectrum and the ambient noise levels for every frequency bin in the measurement bandwidth. Experimental results show the effectiveness of this method for attenuating several ambient noise signals in the 30 MHz – 1 GHz band.Postprint (published version

A Tutorial on Speckle Reduction in Synthetic Aperture Radar Images

Speckle is a granular disturbance, usually modeled as a multiplicative noise, that affects synthetic aperture radar (SAR) images, as well as all coherent images. Over the last three decades, several methods have been proposed for the reduction of speckle, or despeckling, in SAR images. Goal of this paper is making a comprehensive review of despeckling methods since their birth, over thirty years ago, highlighting trends and changing approaches over years. The concept of fully developed speckle is explained. Drawbacks of homomorphic filtering are pointed out. Assets of multiresolution despeckling, as opposite to spatial-domain despeckling, are highlighted. Also advantages of undecimated, or stationary, wavelet transforms over decimated ones are discussed. Bayesian estimators and probability density function (pdf) models in both spatial and multiresolution domains are reviewed. Scale-space varying pdf models, as opposite to scale varying models, are promoted. Promising methods following non-Bayesian approaches, like nonlocal (NL) filtering and total variation (TV) regularization, are reviewed and compared to spatial- and wavelet-domain Bayesian filters. Both established and new trends for assessment of despeckling are presented. A few experiments on simulated data and real COSMO-SkyMed SAR images highlight, on one side the costperformance tradeoff of the different methods, on the other side the effectiveness of solutions purposely designed for SAR heterogeneity and not fully developed speckle. Eventually, upcoming methods based on new concepts of signal processing, like compressive sensing, are foreseen as a new generation of despeckling, after spatial-domain and multiresolution-domain method

The Multistep Beveridge-Nelson Decomposition

The Beveridge-Nelson decomposition defines the trend component in terms of the eventual forecast function, as the value the series would take if it were on its long-run path. The paper introduces the multistep Beveridge-Nelson decomposition, which arises when the forecast function is obtained by the direct autoregressive approach, which optimizes the predictive ability of the AR model at forecast horizons greater than one. We compare our proposal with the standard Beveridge-Nelson decomposition, for which the forecast function is obtained by iterating the one-step-ahead predictions via the chain rule. We illustrate that the multistep Beveridge-Nelson trend is more efficient than the standard one in the presence of model misspecification and we subsequently assess the predictive validity of the extracted transitory component with respect to future growth.Trend and Cycle; Forecasting; Filtering.

Designing an Interval Type-2 Fuzzy Logic System for Handling Uncertainty Effects in Brain–Computer Interface Classification of Motor Imagery Induced EEG Patterns

One of the urgent challenges in the automated analysis and interpretation of electrical brain activity is the effective handling of uncertainties associated with the complexity and variability of brain dynamics, reflected in the nonstationary nature of brain signals such as electroencephalogram (EEG). This poses a severe problem for existing approaches to the classification task within brain–computer interface (BCI) systems. Recently emerged type-2 fuzzy logic (T2FL) methodology has shown a remarkable potential in dealing with uncertain information given limited insight into the nature of the data generating mechanism. The objective of this work is thus to examine the applicability of T2FL approach to the problem of EEG pattern recognition. In particular, the focus is two-fold: i) the design methodology for the interval T2FL system (IT2FLS) that can robustly deal with inter-session as well as within-session manifestations of nonstationary spectral EEG correlates of motor imagery (MI), and ii) the comprehensive examination of the proposed fuzzy classifier in both off-line and on-line EEG classification case studies. The on-line evaluation of the IT2FLS-controlled real-time neurofeedback over multiple recording sessions holds special importance for EEG-based BCI technology. In addition, a retrospective comparative analysis accounting for other popular BCI classifiers such as linear discriminant analysis (LDA), kernel Fisher discriminant (KFD) and support vector machines (SVMs) as well as a conventional type-1 FLS (T1FLS), simulated off-line on the recorded EEGs, has demonstrated the enhanced potential of the proposed IT2FLS approach to robustly handle uncertainty effects in BCI classification

Robust time series models with trend and seasonal components

We describe observation driven time series models for Student-t and EGB2 conditional distributions in which the signal is a linear function of past values of the score of the conditional distribution. These specifications produce models that are easy to implement and deal with outliers by what amounts to a soft form of trimming in the case of t and a soft form of Winsorizing in the case of EGB2. We show how a model with trend and seasonal components can be used as the basis for a seasonal adjustment procedure. The methods are illustrated with US and Spanish data.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s13209-015-0134-