Bayesian Nonstationary Spatial Modeling for Very Large Datasets

With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial datasets observed on large spatial domains. Statistical analyses of such datasets provide two main challenges: First, traditional spatial-statistical techniques are often unable to handle large numbers of observations in a computationally feasible way. Second, for large and heterogeneous spatial domains, it is often not appropriate to assume that a process of interest is stationary over the entire domain. We address the first challenge by using a model combining a low-rank component, which allows for flexible modeling of medium-to-long-range dependence via a set of spatial basis functions, with a tapered remainder component, which allows for modeling of local dependence using a compactly supported covariance function. Addressing the second challenge, we propose two extensions to this model that result in increased flexibility: First, the model is parameterized based on a nonstationary Matern covariance, where the parameters vary smoothly across space. Second, in our fully Bayesian model, all components and parameters are considered random, including the number, locations, and shapes of the basis functions used in the low-rank component. Using simulated data and a real-world dataset of high-resolution soil measurements, we show that both extensions can result in substantial improvements over the current state-of-the-art.Comment: 16 pages, 2 color figure

Adaptive image noise filtering using transform domain local statistics

Accepted ManuscriptPublishe

A comparison of SAR image speckle filters

High quality images of Earth produced by synthetic aperture radar (SAR) systems have become increasingly available, however, SAR images are difficult to interpret. Speckle reduction remains one of the major issues in SAR imaging process, although speckle has been extensively studied for decades. Many reconstruction filters have been proposed and they can be classified into two categories: multilook and/or minimum mean-square error (MMSE) despeckling using the speckle model; and maximum a posteriori (MAP) or maximum likihood (ML) despeckling using the product model. The most well known Lee, Kuan, and Frost filters belong to first category. These filters are based on conventional techniques that were originally derived for stationary signals, such as MMSE. In the second category, filters are based on the product model, such as the MAP Gaussian filter and the Gamma filter, and require knowledge of the a priori probability density function. These filters force speckle to have nonstationary Gaussian or gamma distributed intensity mean. The speckle filtering is mainly Bayesian model fitting that optimizes the MAP criteria. Scene reconstruction is performed using an inversion of the ascending chain. An objective measure is required to compare the technical merits of these filters, and Shi et al. presented a comparison 15 years ago. In this paper, a brief introduction of speckle, product, and filter models is summarized. A review of some most widely used SAR image speckle filters is given. And stationary speckle filters, like Lee, Kuan, and Frost filters, and nonstationary speckle filters like Gamma MAP filter are studied. Despeckling results on stationary and nonstationary SAR image of these speckle filters are presented. © 2009 Copyright SPIE - The International Society for Optical Engineering.published_or_final_versio

Fully Point-wise Convolutional Neural Network for Modeling Statistical Regularities in Natural Images

Modeling statistical regularity plays an essential role in ill-posed image processing problems. Recently, deep learning based methods have been presented to implicitly learn statistical representation of pixel distributions in natural images and leverage it as a constraint to facilitate subsequent tasks, such as color constancy and image dehazing. However, the existing CNN architecture is prone to variability and diversity of pixel intensity within and between local regions, which may result in inaccurate statistical representation. To address this problem, this paper presents a novel fully point-wise CNN architecture for modeling statistical regularities in natural images. Specifically, we propose to randomly shuffle the pixels in the origin images and leverage the shuffled image as input to make CNN more concerned with the statistical properties. Moreover, since the pixels in the shuffled image are independent identically distributed, we can replace all the large convolution kernels in CNN with point-wise ($1*1$) convolution kernels while maintaining the representation ability. Experimental results on two applications: color constancy and image dehazing, demonstrate the superiority of our proposed network over the existing architectures, i.e., using 1/10$\sim$1/100 network parameters and computational cost while achieving comparable performance.Comment: 9 pages, 7 figures. To appear in ACM MM 201

Two-dimensional adaptive block Kalman filtering of SAR imagery

Includes bibliographical references.Speckle effects are commonly observed in synthetic aperture radar (SAR) imagery. In airborne SAR systems the effect of this degradation reduces the accuracy of detection substantially. Thus, the elimination of this noise is an important task in SAR imaging systems. In this paper a new method for speckle noise removal is introduced using 2-D adaptive block Kalman filtering (ABKF). The image process is represented by an autoregressive (AR) model with nonsymmetric half-plane (NSHP) region of support. New 2-D Kalman filtering equations are derived which take into account not only the effect of speckles as a multiplicative noise but also those of the additive receiver thermal noise and the blur. This method assumes local stationarity within a processing window, whereas the image can be assumed to be globally nonstationary. A recursive identification process using the stochastic Newton approach is also proposed which can be used on-line to estimate the filter parameters based upon the information within each new block of the image. Simulation results on several images are provided to indicate the effectiveness of the proposed method when used to remove the effects of speckle noise as well as that of the additive noise