Generalized Bayesian model selection for speckle on remote sensing images

Synthetic aperture radar (SAR) and ultrasound (US) are two important active imaging techniques for remote sensing, both of which are subject to speckle noise caused by coherent summation of back-scattered waves and subsequent nonlinear envelope transformations. Estimating the characteristics of this multiplicative noise is crucial to develop denoising methods and to improve statistical inference from remote sensing images. In this paper, reversible jump Markov chain Monte Carlo (RJMCMC) algorithm has been used with a wider interpretation and a recently proposed RJMCMC-based Bayesian approach, trans-space RJMCMC, has been utilized. The proposed method provides an automatic model class selection mechanism for remote sensing images of SAR and US where the model class space consists of popular envelope distribution families. The proposed method estimates the correct distribution family, as well as the shape and the scale parameters, avoiding performing an exhaustive search. For the experimental analysis, different SAR images of urban, forest and agricultural scenes, and two different US images of a human heart have been used. Simulation results show the efficiency of the proposed method in finding statistical models for speckle

Cauchy-Rician model for backscattering in urban SAR images

This paper presents a new statistical model for urban scene SAR images by combining the Cauchy distribution, which is heavy-tailed, with the Rician back-scattering. The literature spans various well-known models most of which are derived under the assumption that the scene consists of multitudes of random reflectors. This idea specifically fails for urban scenes since they accommodate a heterogeneous collection of strong scatterers such as buildings, cars, wall corners. Moreover, when it comes to analysing their statistical behaviour, due to these strong reflectors, urban scenes include a high number of high amplitude samples, which implies that urban scenes are mostly heavy-tailed. The proposed Cauchy-Rician model contributes to the literature by leveraging non-zero location (Rician) heavy-tailed (Cauchy) signal components. In the experimental analysis, the Cauchy-Rician model is investigated in comparison to state-of-the-art statistical models that include G0, generalized gamma, and the lognormal distribution. The numerical analysis demonstrates the superior performance and flexibility of the proposed distribution for modelling urban scenes

The effect of convolutional encoder memory on the sphere decoding search radius in MIMO systems

In the new generation communication systems Multiple-Input-Multiple-Output systems are frequently used. The processing load of the Maximum Likelihood (ML) Detector which is the optimum detector for these systems, increases exponentially as a function of system dimension and memory due to testing all possible points. Sphere Decoding (SD) method which tests only the probable points, decreases the processing load dramatically. System memory changes by system dimensions and length of the convolutional encoder. This, in turn, affects the radius of the hyper sphere centered at the observation in the observation space at which SD attains the performance of the ML detector. This effect is investigated via simulation studies. In these simulations, it is observed that the radius of the SD is relatively smaller than the one in ML, and the ratio between the radius values varies from 6,61 in the case of memoryless 2×2 MIMO system to 1,02 in the case of 8x8 MIMO system with memory K=10 according to increased antenna numbers and system memory. In addition to these, it is observed that the radius of the hyper sphere is directly proportional to the memory of the encoder

One-day ahead wind speed/power prediction based on polynomial autoregressive model

Wind has been one of the popular renewable energy generation methods in the last decades. Foreknowledge of power to be generated from wind is crucial especially for planning and storing the power. It is evident in various experimental data that wind speed time series has non-linear characteristics. It has been reported in the literature that nonlinear prediction methods such as artificial neural network (ANN) and adaptive neuro fuzzy inference system (ANFIS) perform better than linear autoregressive (AR) and AR moving average models. Polynomial AR (PAR) models, despite being non-linear, are simpler to implement when compared with other non-linear AR models due to their linear-in-the-parameters property. In this study, a PAR model is used for one-day ahead wind speed prediction by using the past hourly average wind speed measurements of Ceşme and Bandon and performance comparison studies between PAR and ANN-ANFIS models are performed. In addition, wind power data which was published for Global Energy Forecasting Competition 2012 has been used to make power predictions. Despite having lower number of model parameters, PAR models outperform all other models for both of the locations in speed predictions as well as in power predictions when the prediction horizon is longer than 12 h

Bayesian Volterra system identification using reversible jump MCMC algorithm

Volterra systems have had significant success in modelling nonlinear systems in various real-world applications. However, it is generally assumed that the nonlinearity degree of the system is known beforehand. In this paper, we contribute to the literature on Volterra system identification (VSI) with a numerical Bayesian approach which identifies model coefficients and the nonlinearity degree concurrently. Although this numerical Bayesian method, namely reversible jump Markov chain Monte Carlo (RJMCMC) algorithm has been used with success in various model selection problems, our use is in a novel context in the sense that both memory size and nonlinearity degree are estimated. The aforementioned study ensures an anomalous approach to RJMCMC and provides a new understanding on its flexible use which enables trans-structural transitions between different classes of models in addition to transdimensional transitions for which it is classically used. We study the performance of the method on synthetically generated data including OFDM communications over a nonlinear channel

Estimation of the nonlinearity degree for polynomial autoregressive processes with RJMCMC

Despite the popularity of linear process models in signal and image processing, various real life phenomena exhibit nonlinear characteristics. Compromising between the realistic and computationally heavy nonlinear models and the simplicity of linear estimation methods, linear in the parameters nonlinear models such as polynomial autoregressive (PAR) models have been accessible analytical tools for modelling such phenomena. In this work, we aim to demonstrate the potentials of Reversible Jump Markov Chain Monte Carlo (RJMCMC) which is a successful statistical tool in model dimension estimation in nonlinear process identification. We explore the capability of RJMCMC in jumping not only between spaces with different dimensions, but also between different classes of models. In particular, we demonstrate the success of RJMCMC in sampling in linear and nonlinear spaces of varying dimensions for the estimation of PAR processes

Beyond trans-dimensional RJMCMC with a case study in impulsive data modeling

Reversible jump Markov chain Monte Carlo (RJMCMC) is a Bayesian model estimation method, which has been generally used for trans-dimensional sampling and model order selection studies in the literature. In this study, we draw attention to unexplored potentials of RJMCMC beyond trans-dimensional sampling. the proposed usage, which we call trans-space RJMCMC exploits the original formulation to explore spaces of different classes or structures. This provides flexibility in using different types of candidate classes in the combined model space such as spaces of linear and nonlinear models or of various distribution families. As an application, we looked into a special case of trans-space sampling, namely trans-distributional RJMCMC in impulsive data modeling. In many areas such as seismology, radar, image, using Gaussian models is a common practice due to analytical ease. However, many noise processes do not follow a Gaussian character and generally exhibit events too impulsive to be successfully described by the Gaussian model. We test the proposed usage of RJMCMC to choose between various impulsive distribution families to model both synthetically generated noise processes and real-life measurements on power line communications impulsive noises and 2-D discrete wavelet transform coefficients.TUBITAK; College of Natural Resources, University of California Berkele

Frequency Estimation of Sinusoidal Signals in Alpha-Stable Noise Using Subspace Techniques

In the frequency estimation of sinusoidal signals observed in impulsive noise environments, techniques based on Gaussian noise assumption are unsuccessful. One possible way to find better estimates is to model the noise as an alpha-stable process and to use the fractional lower order statistics of data to estimate the signal parameters. In this work noise and signal subspace methods, namely MUSIC and Principal Component-Bartlett, are applied to fractional lower order statistics of sinusoids embedded in alpha-stable noise. The simulation results show that techniques based on lower order statistics are superior to their second order statistics-based counterparts, especially when the noise exhibits a strong impulsive attitude. 1. Introduction Most of the work on the frequency estimation problem assumes that the additive noise has Gaussian distribution. This is partly because of the nice properties of the Gaussian model which allows for simplification of the theoretical work and decreases..