Improving 2‐DE gel image denoising using contourlets

One of the most commonly used methods for protein separation is 2‐DE. After 2‐DE gel scanning, images with a plethora of spot features emerge that are usually contaminated by inherent noise. The objective of the denoising process is to remove noise to the extent that the true spots are recovered correctly and accurately i.e. without introducing distortions leading to the detection of false‐spot features. In this paper we propose and justify the use of the contourlet transform as a tool for 2‐DE gel images denoising. We compare its effectiveness with state‐of‐the‐art methods such as wavelets‐based multiresolution image analysis and spatial filtering. We show that contourlets not only achieve better average S/N performance than wavelets and spatial filters, but also preserve better spot boundaries and faint spots and alter less the intensities of informative spot features, leading to more accurate spot volume estimation and more reliable spot detection, operations that are essential to differential expression proteomics for biomarkers discovery.     

一个新的脑电信号分析系统：小波分析理论的运用

小波变换是一种把时间、频率（或尺度）两域结合起来的分析方法。它被誉为“分析信号的数学显微镜”。本系统将小波变换用于脑电信号分析,是一个在Ｗｉｎｄｏｗｓ３．１下开发的脑电分析系统。     

Inference on fractal processes using multiresolution approximation

We consider Bayesian inference via Markov chain Monte Carlofor a variety of fractal Gaussian processes on the real line.These models have unknown parameters in the covariance matrix,requiring inversion of a new covariance matrix at each Markovchain Monte Carlo iteration. The processes have no suitableindependence properties so this becomes computationally prohibitive.We surmount these difficulties by developing a computationalalgorithm for likelihood evaluation based on a ‘multiresolutionapproximation’ to the original process. The method iscomputationally very efficient and widely applicable, makinglikelihood-based inference feasible for large datasets. A simulationstudy indicates that this approach leads to accurate estimatesfor underlying parameters in fractal models, including fractionalBrownian motion and fractional Gaussian noise, and functionalparameters in the recently introduced multifractional Brownianmotion. We apply the method to a variety of real datasets andillustrate its application to prediction and to model selection.     

Coregionalized single- and multiresolution spatially varying growth curve modeling with application to weed growth

Modeling of longitudinal data from agricultural experiments using growth curves helps understand conditions conducive or unconducive to crop growth. Recent advances in Geographical Information Systems (GIS) now allow geocoding of agricultural data that help understand spatial patterns. A particularly common problem is capturing spatial variation in growth patterns over the entire experimental domain. Statistical modeling in these settings can be challenging because agricultural designs are often spatially replicated, with arrays of subplots, and interest lies in capturing spatial variation at possibly different resolutions. In this article, we develop a framework for modeling spatially varying growth curves as Gaussian processes that capture associations at single and multiple resolutions. We provide Bayesian hierarchical models for this setting, where flexible parameterization enables spatial estimation and prediction of growth curves. We illustrate using data from weed growth experiments conducted in Waseca, Minnesota, that recorded growth of the weed Setaria spp. in a spatially replicated design.