robust compressive sensing of multichannel eeg signals in the presence of impulsive noise abstract latest studies have shown that combining cosparsity and low rank property usually results in efficient compressive sensing cs recovery approaches for multichannel electroencephalogram eeg signals however existing methods rarely consider noise or consider only the influence of gaussian noise generated during transmission when the measurement is corrupted by impulsive noise the performance of these cs approaches will degrade in this study a new robust cs approach is proposed to accurately recover multichannel eeg signals from noisy measurements in the presence of impulsive noise we first employ welsch estimator to depress the influence of impulsive noise in cs reconstruction we further develop an efficient iterative scheme based on half quadratic theory and alternating direction method of multipliers to solve the resulting nonconvex optimization problem experimental results show that our approach can obtain better reconstruction results than those of existing state of the art cs methods when measurements are corrupted by impulsive noise

compressive sensing via nonlocal low rank regularization sparsity has been widely exploited for exact reconstruction of a signal from a small number of random measurements recent advances have suggested that structured or group sparsity often leads to more powerful signal reconstruction techniques in various compressed sensing cs studies in this paper we propose a nonlocal low rank regularization nlr approach toward exploiting structured sparsity and explore its application into cs of both photographic and mri images we also propose the use of a nonconvex log det x as a smooth surrogate function for the rank instead of the convex nuclear norm and justify the benefit of such a strategy using extensive experiments to further improve the computational efficiency of the proposed algorithm we have developed a fast implementation using the alternative direction multiplier method technique experimental results have shown that the proposed nlr cs algorithm can significantly outperform existing state of the art cs techniques for image recovery

model assisted adaptive recovery of compressed sensing with imaging applications in compressive sensing cs a challenge is to find a space in which the signal is sparse and hence faithfully recoverable since many natural signals such as images have locally varying statistics the sparse space varies in time spatial domain as such cs recovery should be conducted in locally adaptive signal dependent spaces to counter the fact that the cs measurements are global and irrespective of signal structures on the contrary existing cs reconstruction methods use a fixed set of bases e g wavelets dct and gradient spaces for the entirety of a signal to rectify this problem we propose a new framework for model guided adaptive recovery of compressive sensing marx and show how a 2 d piecewise autoregressive model can be integrated into the marx framework to make cs recovery adaptive to spatially varying second order statistics of an image in addition marx offers a mechanism of characterizing and exploiting structured sparsities of natural images greatly restricting the cs solution space simulation results over a wide range of natural images show that the proposed marx technique can improve the reconstruction quality of existing cs methods by 2 7 db

a douglas rachford splitting approach to compressed sensing image recovery using low rank regularization in this paper we study the compressed sensing cs image recovery problem the traditional method divides the image into blocks and treats each block as an independent sub cs recovery task this often results in losing global structure of an image in order to improve the cs recovery result we propose a nonlocal nl estimation step after the initial cs recovery for denoising purpose the nl estimation is based on the well known nl means filtering that takes an advantage of self similarity in images we formulate the nl estimation as the low rank matrix approximation problem where the low rank matrix is formed by the nl similarity patches an efficient algorithm nonlocal douglas rachford nldr based on douglas rachford splitting is developed to solve this low rank optimization problem constrained by the cs measurements experimental results demonstrate that the proposed nldr algorithm achieves significant performance improvements over the state of the art in cs image recovery

a homotopy classification of certain 7 manifolds this paper gives a homotopy classification of wallach spaces and a partial homotopy classification of closely related spaces obtained by free sl actions on su 3 and on s3 x s5

mixed noise removal via laplacian scale mixture modeling and nonlocal low rank approximation recovering the image corrupted by additive white gaussian noise awgn and impulse noise is a challenging problem due to its difficulties in an accurate modeling of the distributions of the mixture noise many efforts have been made to first detect the locations of the impulse noise and then recover the clean image with image in painting techniques from an incomplete image corrupted by awgn however it is quite challenging to accurately detect the locations of the impulse noise when the mixture noise is strong in this paper we propose an effective mixture noise removal method based on laplacian scale mixture lsm modeling and nonlocal low rank regularization the impulse noise is modeled with lsm distributions and both the hidden scale parameters and the impulse noise are jointly estimated to adaptively characterize the real noise to exploit the nonlocal self similarity and low rank nature of natural image a nonlocal low rank regularization is adopted to regularize the denoising process experimental results on synthetic noisy images show that the proposed method outperforms existing mixture noise removal methods

analysis of sets of two way contingency tables using association models abstract a class of models is introduced for the analysis of group differences in the association between two discrete variables the rc m association model for two way tables is reviewed and alternative weighting systems for identifying interaction parameters are presented this model is generalized for the setting where a two way contingency table is available for two or more groups various restricted models can be used to examine possible sources of intergroup heterogeneity in the association these sources pertain to heterogeneity in the intrinsic association and or in the scores for the row and column variables the importance of weights used to identify the row and column scores is emphasized a classical set of data previously analyzed by many authors is used to illustrate the advantages of the models and methods developed here

image inpainting using reproducing kernel hilbert space and heaviside functions image inpainting a technique of repairing damaged images is an important topic in image processing in this paper we solve the problem from an intensity function estimation perspective we assume the underlying image is defined on a continuous domain and belongs to a space spanned by a basis of a reproducing kernel hilbert space and some variations of the heaviside function the reproducing kernel hilbert space is used to model the smooth component of the image while heaviside function variations are used to model the edges the coefficients of the redundant basis are computed by the discrete intensity at undamaged domain we test the proposed model through various images numerical experiments show the effectiveness of the proposed method especially in recovering edges

robustness of the two independent samples t test when applied to ordinal scaled data one may encounter the application of the two independent samples t test to ordinal scaled data for example data that assume only the values 0 1 2 3 from small samples this situation clearly violates the underlying normality assumption for the t test and one cannot appeal to large sample theory for validity in this paper we report the results of an investigation of the t test s robustness when applied to data of this form for samples of sizes 5 to 20 our approach consists of complete enumeration of the sampling distributions and comparison of actual levels of significance with the significance level expected if the data followed a normal distribution we demonstrate under general conditions the robustness of the t test in that the maximum actual level of significance is close to the declared level

low rank matrix completion in the presence of high coherence prevalent matrix completion methods capture only the low rank property which gives merely a constraint that the data points lie on some low dimensional subspace but generally ignore the extra structures beyond low rank that specify in more detail how the data points lie on the subspace whenever the data points are not uniformly distributed on the low dimensional subspace the row coherence of the target matrix to recover could be considerably high and accordingly prevalent methods might fail even if the target matrix is fairly low rank to relieve this challenge we suggest to consider a model termed low rank factor decomposition lrfd which imposes an additional restriction that the data points must be represented as linear compressive combinations of the bases in a given dictionary we show that lrfd can effectively mitigate the challenges of high row coherence provided that its dictionary is configured properly namely it is mathematically proven that if the dictionary is well conditioned and low rank then lrfd can weaken the dependence on the row coherence in particular if the dictionary itself is low rank then the dependence on the row coherence can be entirely removed subsequently we devise two practical algorithms to obtain proper dictionaries in unsupervised environments one uses the existing matrix completion methods to construct the dictionary in lrfd and the other tries to learn a proper dictionary from the data given experiments on randomly generated matrices and motion datasets show superior performance of our proposed algorithms

assessing interrater agreement from dependent data estimation of interrater agreement for ordered categorical data is examined when the same sample is being assessed by various raters with different methods we investigate the use of a latent model proposed by qu piedmonte and medendorp 1995 biomerics 51 268 275 to estimate the correlation between raters for each method and test for their equality for each of the assessment methods these correlations can be interpreted as the variance components of random effects representing subject and rater this method is applied to an hiv study in which the amount of ectopy on a woman s cervix is measured by both direct visual assessment and a computer planimetry method

segmentation of multivariate mixed data via lossy data coding and compression in this paper based on ideas from lossy data coding and compression we present a simple but effective technique for segmenting multivariate mixed data that are drawn from a mixture of gaussian distributions which are allowed to be almost degenerate the goal is to find the optimal segmentation that minimizes the overall coding length of the segmented data subject to a given distortion by analyzing the coding length rate of mixed data we formally establish some strong connections of data segmentation to many fundamental concepts in lossy data compression and rate distortion theory we show that a deterministic segmentation is approximately the asymptotically optimal solution for compressing mixed data we propose a very simple and effective algorithm that depends on a single parameter the allowable distortion at any given distortion the algorithm automatically determines the corresponding number and dimension of the groups and does not involve any parameter estimation simulation results reveal intriguing phase transition like behaviors of the number of segments when changing the level of distortion or the amount of outliers finally we demonstrate how this technique can be readily applied to segment real imagery and bioinformatic data

group based image decomposition using 3 d cartoon and texture priors we propose a novel image decomposition method to decompose an image into its cartoon and texture components to exploit the nonlocal self similarity of cartoon plus texture images we construct groups by stacking together similar image patches into 3 d arrays and consider group as the basic unit of decomposition we decompose each group via a convex optimization model consisting of 3 d cartoon and texture priors these priors characterize the local properties of the cartoon and texture components and the nonlocal similarity within each component in a unified and natural manner we develop the alternating direction method of multipliers admm to efficiently solve the proposed model for further improvement we investigate an adaptive rule for the estimation of the regularization parameter the proposed method is also extended to tackle noisy images numerical experiments confirm that the performance of the proposed method is competitive with some of the state of the art schemes

improved tests for comparing treatments against a control and other one sided problems abstract three multivariate one sided testing problems are studied all problems concern a independent normal populations with unknown means and common unknown variance for the first problem the null hypothesis is that all means are zero while the alternative is that each mean is nonnegative and at least one is positive for the second problem the null hypothesis is that all means are equal and the alternative is that all of the first k 1 means are greater than or equal to the mean of the last population with strict inequality for at least one the alternative for the second problem is called the tree top alternative for the third problem the null hypothesis is that all means are equal while the alternative is that the means are ordered say nonincreasing this latter alternative is called the simple order alternative all three of these problems are discussed extensively in the book by robertson wright and dykstra we will assume that random samples of size n are drawn from each population

nonlocal image restoration with bilateral variance estimation a low rank approach simultaneous sparse coding ssc or nonlocal image representation has shown great potential in various low level vision tasks leading to several state of the art image restoration techniques including bm3d and lssc however it still lacks a physically plausible explanation about why ssc is a better model than conventional sparse coding for the class of natural images meanwhile the problem of sparsity optimization especially when tangled with dictionary learning is computationally difficult to solve in this paper we take a low rank approach toward ssc and provide a conceptually simple interpretation from a bilateral variance estimation perspective namely that singular value decomposition of similar packed patches can be viewed as pooling both local and nonlocal information for estimating signal variances such perspective inspires us to develop a new class of image restoration algorithms called spatially adaptive iterative singular value thresholding saist for noise data saist generalizes the celebrated bayesshrink from local to nonlocal models for incomplete data saist extends previous deterministic annealing based solution to sparsity optimization through incorporating the idea of dictionary learning in addition to conceptual simplicity and computational efficiency saist has achieved highly competent often better objective performance compared to several state of the art methods in image denoising and completion experiments our subjective quality results compare favorably with those obtained by existing techniques especially at high noise levels and with a large amount of missing data

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

the score test for independence in r x c contingency tables with missing data in this paper the score test statistic for testing independence in r x c contingency tables with missing data is proposed under the null hypothesis of independence the statistic has an approximate chi squared distribution with r 1 c 1 degrees of freedom the proposed test statistic is quite similar to the pearson chi squared statistic with complete data and unlike the likelihood ratio statistic for testing independence its computation is simple and noniterative in addition a score test statistic is proposed for testing independence when the rows and columns of the r x c table are ordinal finally extensions of the score statistics to test for conditional independence in a set of r x c contingency tables with missing data are described this yields score test statistics that are natural extensions of the mantel haenszel statistic an example using a subset of data from the six cities study is presented to illustrate the methods

analyzing bivariate ordinal data using a global odds ratio abstract a moment method is proposed for regression analysis of bivariate ordered categorical data using the global odds ratio as the measure of association for modeling the margins this method utilizes the stochastic ordering implicit in the data this method allows for covariate effects in modeling the association between responses an application of the proposed model is illustrated using the ophthalmological data from the wisconsin epidemiologic study of diabetic retinopathy for identifying risk factors among younger onset diabetics this model is also extended to a longitudinal data setting with more than two repeated measures

robust pca via ell _ 0 ell _ 1 regularization we study the problem of low rank and sparse decomposition from possibly noisy observations known as robust pca where the sparse component can be seen as outliers we first propose a modified objective function where the nuclear norm captures the low rank term ell 0 norm addresses the sparse outlier term and an ell 1 norm to deal with the additive noise term the associated algorithm termed sparsity regularized principal component pursuit srpcp is shown to converge under certain model and algorithm parameter settings it is shown that srpcp can recover the low rank component and sparse component exactly in the noiseless case in the noisy case we first prove that the widely used principal component pursuit pcp method which was designed for the noiseless case is actually stable to dense noise then we show that srpcp has smaller estimation error bound and can identify outlier entries without any false alarm another important byproduct of our analysis is the result that pcp with missing entries is also stable to dense noise we further propose another objective function which replaces the above nuclear norm by the log determinant the proposed algorithm termed iterative reweighted sparsity regularized principal component pursuit is also shown to converge in each iteration it solves a weighted nuclear norm regularized robust matrix completion problem we propose an alternating direction method of multipliers algorithm to solve this nonconvex subproblem which also converges empirical studies demonstrate the efficacy of the proposed ell 0 ell 1 regularization framework to deal with the outliers as well as its advantage over the existing state of the art methods

compressive sensing image restoration using adaptive curvelet thresholding and nonlocal sparse regularization compressive sensing cs is a recently emerging technique and an extensively studied problem in signal and image processing which suggests a new framework for the simultaneous sampling and compression of sparse or compressible signals at a rate significantly below the nyquist rate maybe designing an effective regularization term reflecting the image sparse prior information plays a critical role in cs image restoration recently both local smoothness and nonlocal self similarity have led to superior sparsity prior for cs image restoration in this paper first an adaptive curvelet thresholding criterion is developed trying to adaptively remove the perturbations appeared in recovered images during cs recovery process imposing sparsity furthermore a new sparsity measure called joint adaptive sparsity regularization jasr is established which enforces both local sparsity and nonlocal 3 d sparsity in transform domain simultaneously then a novel technique for high fidelity cs image recovery via jasr is proposed cs jasr to efficiently solve the proposed corresponding optimization problem we employ the split bregman iterations extensive experimental results are reported to attest the adequacy and effectiveness of the proposed method comparing with the current state of the art methods in cs image restoration

rank minimization with applications to image noise removal abstract rank minimization problem has a wide range of applications in different areas however since this problem is np hard and non convex the frequently used method is to replace the matrix rank minimization with nuclear norm minimization nuclear norm is the convex envelope of the matrix rank and it is more computationally tractable matrix completion is a special case of rank minimization problem in this paper we consider directly using matrix rank as the regularization term instead of nuclear norm in the cost function for matrix completion problem the solution is analyzed and obtained by a hard thresholding operation on the singular values of the observed matrix then by exploiting patch based nonlocal self similarity scheme we apply the proposed rank minimization algorithm to remove white gaussian additive noise in images gamma multiplicative noise is also removed in logarithm domain the experimental results illustrate that the proposed algorithm can remove noises in images more efficiently than nuclear norm can do and the results are also competitive with those obtained by using the existing state of the art noise removal methods in the literature

image deblurring with an inaccurate blur kernel using a group based low rank image prior abstract we address the problem of restoring an original image from its blurry and noisy observation together with inaccurate information of the blurring process for this purpose we propose an enhanced regularized structured total least squares rstls model that can estimate the latent image and blur kernel simultaneously in the proposed model both the image and the blur kernel are characterized by a group based low rank prior which assumes that a group of vectorized similar data patches can be well approximated by a low rank matrix we develop an alternating minimization algorithm to solve the proposed model efficiently numerical experiments demonstrate the effectiveness of our method in terms of both quantitative measures and visual quality

weighted nuclear norm minimization and its applications to low level vision as a convex relaxation of the rank minimization model the nuclear norm minimization nnm problem has been attracting significant research interest in recent years the standard nnm regularizes each singular value equally composing an easily calculated convex norm however this restricts its capability and flexibility in dealing with many practical problems where the singular values have clear physical meanings and should be treated differently in this paper we study the weighted nuclear norm minimization wnnm problem which adaptively assigns weights on different singular values as the key step of solving general wnnm models the theoretical properties of the weighted nuclear norm proximal wnnp operator are investigated albeit nonconvex we prove that wnnp is equivalent to a standard quadratic programming problem with linear constrains which facilitates solving the original problem with off the shelf convex optimization solvers in particular when the weights are sorted in a non descending order its optimal solution can be easily obtained in closed form with wnnp the solving strategies for multiple extensions of wnnm including robust pca and matrix completion can be readily constructed under the alternating direction method of multipliers paradigm furthermore inspired by the reweighted sparse coding scheme we present an automatic weight setting method which greatly facilitates the practical implementation of wnnm the proposed wnnm methods achieve state of the art performance in typical low level vision tasks including image denoising background subtraction and image inpainting

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

total variation regularized tensor rpca for background subtraction from compressive measurements background subtraction has been a fundamental and widely studied task in video analysis with a wide range of applications in video surveillance teleconferencing and 3d modeling recently motivated by compressive imaging background subtraction from compressive measurements bscm is becoming an active research task in video surveillance in this paper we propose a novel tensor based robust principal component analysis tenrpca approach for bscm by decomposing video frames into backgrounds with spatial temporal correlations and foregrounds with spatio temporal continuity in a tensor framework in this approach we use 3d total variation to enhance the spatio temporal continuity of foregrounds and tucker decomposition to model the spatio temporal correlations of video background based on this idea we design a basic tensor rpca model over the video frames dubbed as the holistic tenrpca model to characterize the correlations among the groups of similar 3d patches of video background we further design a patch group based tensor rpca model by joint tensor tucker decompositions of 3d patch groups for modeling the video background efficient algorithms using the alternating direction method of multipliers are developed to solve the proposed models extensive experiments on simulated and real world videos demonstrate the superiority of the proposed approaches over the existing state of the art approaches

exact inference for contingency tables with ordered categories abstract this article proposes an efficient numerical algorithm for small sample exact inferences in contingency tables having ordinal classifications the inferences which apply conditional on the observed marginal totals also provide an exact analysis for the log linear model of linear by linear association for cell probabilities an exact test of independence has a one sided p value equal to the null probability that model based maximum likelihood estimates of odds ratios are at least as large as the observed estimates the conditional nonnull distribution yields confidence intervals for odds ratios having a linear by linear structure the computations utilize an extension of the network algorithm proposed by mehta and patel 1983

a truncated nuclear norm regularization method based on weighted residual error for matrix completion low rank matrix completion aims to recover a matrix from a small subset of its entries and has received much attention in the field of computer vision most existing methods formulate the task as a low rank matrix approximation problem a truncated nuclear norm has recently been proposed as a better approximation to the rank of matrix than a nuclear norm the corresponding optimization method truncated nuclear norm regularization tnnr converges better than the nuclear norm minimization based methods however it is not robust to the number of subtracted singular values and requires a large number of iterations to converge in this paper a tnnr method based on weighted residual error tnnr wre for matrix completion and its extension model etnnr wre are proposed tnnr wre assigns different weights to the rows of the residual error matrix in an augmented lagrange function to accelerate the convergence of the tnnr method the etnnr wre is much more robust to the number of subtracted singular values than the tnnr wre tnnr alternating direction method of multipliers and tnnr accelerated proximal gradient with line search methods experimental results using both synthetic and real visual data sets show that the proposed tnnr wre and etnnr wre methods perform better than tnnr and iteratively reweighted nuclear norm irnn methods

the analysis of multivariate contingency tables by restricted canonical and restricted association models abstract restricted canonical models and restricted association models are proposed and applied to multiway contingency tables these models have been previously applied to two way contingency tables however multivariate generalization has been impeded in the past since canonical and association models both depend on singular value decompositions that apply only to two way arrays in this article this restriction to two way arrays is overcome by division of the cross classified variables into explanatory and response variables the explanatory variables are treated as a single polytomous variable and the response variables are treated as a second single polytomous variable in this fashion the multiway table is reduced to a two way array to which traditional canonical and association models may be applied use of linear restrictions on parameters in canonical and association models is especially important in multiway tables if useful models are to be constructed the class of models considered in th

inference for likelihood ratio ordering in the two sample problem abstract we obtain the maximum likelihood estimators of two multinomial probability vectors under the constraint that they are likelihood ratio ordered we extend this estimation approach to the case of two univariate distributions and show strong consistency of the estimators we also derive and study the asymptotic distribution of the likelihood ratio statistic for testing the equality of two discrete probability distributions against the alternative that one distribution is greater than the other in the likelihood ratio ordering sense finally we examine a data set pertaining to average daily insulin dose from the boston collaborative drug surveillance program and compare our testing procedure to testing procedures for other stochastic orderings

robust low rank tensor recovery via nonconvex singular value minimization tensor robust principal component analysis via tensor nuclear norm tnn minimization has been recently proposed to recover the low rank tensor corrupted with sparse noise outliers tnn is demonstrated to be a convex surrogate of rank however it tends to over penalize large singular values and thus usually results in biased solutions to handle this issue we propose a new definition of tensor logarithmic norm tln as the nonconvex surrogate of rank which can decrease the penalization on larger singular values and increase that on smaller ones simultaneously to preserve the low rank structure of a tensor then the strategy of tensor factorization is combined into the minimization of tln to improve computational performance to handle impulsive scenarios we propose a nonconvex ell p ball projection scheme with 0 instead of the conventional convex scheme with p 1 which enhances the robustness against outliers by incorporating the tln minimization and the ell p ball projection we finally propose two low rank recovery algorithms whose resulting optimization problems are efficiently solved by the alternating direction method of multipliers admm with convergence guarantees the proposed algorithms are applied to the synthetic data recovery and image and video restorations in real world experimental results demonstrate the superior performance of the proposed methods over several state of the art algorithms in terms of tensor recovery accuracy and computational efficiency

quasisymmetric models for the analysis of square contingency tables summary a parametric model is presented for the analysis of square contingency tables where there is a one to one correspondence between the categories of the row variable and the categories of the column variable the model is applicable to cross classifications where the categories are unordered partially ordered or completely ordered but the interpretation of the model and associated parameters is most straightforward when the categories are at least partially ordered connections with the mover stayer model and the usual model of quasisymmetry are described two data sets are used to illustrate the utility of the model