Estimating Gene Signals From Noisy Microarray Images

In oligonucleotide microarray experiments, noise is a challenging problem, as biologists now are studying their organisms not in isolation but in the context of a natural environment. In low photomultiplier tube (PMT) voltage images, weak gene signals and their interactions with the background fluorescence noise are most problematic. In addition, nonspecific sequences bind to array spots intermittently causing inaccurate measurements. Conventional techniques cannot precisely separate the foreground and the background signals. In this paper, we propose analytically based estimation technique. We assume a priori spot-shape information using a circular outer periphery with an elliptical center hole. We assume Gaussian statistics for modeling both the foreground and background signals. The mean of the foreground signal quantifies the weak gene signal corresponding to the spot, and the variance gives the measure of the undesired binding that causes fluctuation in the measurement. We propose a foreground-signal and shapeestimation algorithm using the Gibbs sampling method. We compare our developed algorithm with the existing Mann–Whitney (MW)- and expectation maximization (EM)/iterated conditional modes (ICM)-based methods. Our method outperforms the existing methods with considerably smaller mean-square error (MSE) for all signal-to-noise ratios (SNRs) in computer-generated images and gives better qualitative results in low-SNR real-data images. Our method is computationally relatively slow because of its inherent sampling operation and hence only applicable to very noisy-spot images. In a realistic example using our method, we show that the gene-signal fluctuations on the estimated foreground are better observed for the input noisy images with relatively higher undesired bindings

Image Restoration Using Joint Statistical Modeling in Space-Transform Domain

This paper presents a novel strategy for high-fidelity image restoration by characterizing both local smoothness and nonlocal self-similarity of natural images in a unified statistical manner. The main contributions are three-folds. First, from the perspective of image statistics, a joint statistical modeling (JSM) in an adaptive hybrid space-transform domain is established, which offers a powerful mechanism of combining local smoothness and nonlocal self-similarity simultaneously to ensure a more reliable and robust estimation. Second, a new form of minimization functional for solving image inverse problem is formulated using JSM under regularization-based framework. Finally, in order to make JSM tractable and robust, a new Split-Bregman based algorithm is developed to efficiently solve the above severely underdetermined inverse problem associated with theoretical proof of convergence. Extensive experiments on image inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise removal applications verify the effectiveness of the proposed algorithm.Comment: 14 pages, 18 figures, 7 Tables, to be published in IEEE Transactions on Circuits System and Video Technology (TCSVT). High resolution pdf version and Code can be found at: http://idm.pku.edu.cn/staff/zhangjian/IRJSM

Statistical M-Estimation and Consistency in Large Deformable Models for Image Warping

The problem of defining appropriate distances between shapes or images and modeling the variability of natural images by group transformations is at the heart of modern image analysis. A current trend is the study of probabilistic and statistical aspects of deformation models, and the development of consistent statistical procedure for the estimation of template images. In this paper, we consider a set of images randomly warped from a mean template which has to be recovered. For this, we define an appropriate statistical parametric model to generate random diffeomorphic deformations in two-dimensions. Then, we focus on the problem of estimating the mean pattern when the images are observed with noise. This problem is challenging both from a theoretical and a practical point of view. M-estimation theory enables us to build an estimator defined as a minimizer of a well-tailored empirical criterion. We prove the convergence of this estimator and propose a gradient descent algorithm to compute this M-estimator in practice. Simulations of template extraction and an application to image clustering and classification are also provided

Learning sparse representations of depth

This paper introduces a new method for learning and inferring sparse representations of depth (disparity) maps. The proposed algorithm relaxes the usual assumption of the stationary noise model in sparse coding. This enables learning from data corrupted with spatially varying noise or uncertainty, typically obtained by laser range scanners or structured light depth cameras. Sparse representations are learned from the Middlebury database disparity maps and then exploited in a two-layer graphical model for inferring depth from stereo, by including a sparsity prior on the learned features. Since they capture higher-order dependencies in the depth structure, these priors can complement smoothness priors commonly used in depth inference based on Markov Random Field (MRF) models. Inference on the proposed graph is achieved using an alternating iterative optimization technique, where the first layer is solved using an existing MRF-based stereo matching algorithm, then held fixed as the second layer is solved using the proposed non-stationary sparse coding algorithm. This leads to a general method for improving solutions of state of the art MRF-based depth estimation algorithms. Our experimental results first show that depth inference using learned representations leads to state of the art denoising of depth maps obtained from laser range scanners and a time of flight camera. Furthermore, we show that adding sparse priors improves the results of two depth estimation methods: the classical graph cut algorithm by Boykov et al. and the more recent algorithm of Woodford et al.Comment: 12 page