mistuning based control design to improve closed loop stability margin of vehicular platoons we consider a decentralized bidirectional control of a platoon of n identical vehicles moving in a straight line the control objective is for each vehicle to maintain a constant velocity and inter vehicular separation using only the local information from itself and its two nearest neighbors each vehicle is modeled as a double integrator to aid the analysis we use continuous approximation to derive a partial differential equation pde approximation of the discrete platoon dynamics the pde model is used to explain the progressive loss of closed loop stability with increasing number of vehicles and to devise ways to combat this loss of stability if every vehicle uses the same controller we show that the least stable closed loop eigenvalue approaches zero as o 1 n2 in the limit of a large number n of vehicles we then show how to ameliorate this loss of stability by small amounts of mistuning i e changing the controller gains from their nominal values we prove that with arbitrary small amounts of mistuning the asymptotic behavior of the least stable closed loop eigenvalue can be improved to o 1 n all the conclusions drawn from analysis of the pde model are corroborated via numerical calculations of the state space platoon model

image denoising via sparse and redundant representations over learned dictionaries we address the image denoising problem where zero mean white and homogeneous gaussian additive noise is to be removed from a given image the approach taken is based on sparse and redundant representations over trained dictionaries using the k svd algorithm we obtain a dictionary that describes the image content effectively two training options are considered using the corrupted image itself or training on a corpus of high quality image database since the k svd is limited in handling small image patches we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image we show how such bayesian treatment leads to a simple and effective denoising algorithm this leads to a state of the art denoising performance equivalent and sometimes surpassing recently published leading alternative denoising methods

distributed averaging via lifted markov chains motivated by applications of distributed linear estimation distributed control and distributed optimization we consider the question of designing linear iterative algorithms for computing the average of numbers in a network specifically our interest is in designing such an algorithm with the fastest rate of convergence given the topological constraints of the network as the main result of this paper we design an algorithm with the fastest possible rate of convergence using a nonreversible markov chain on the given network graph we construct such a markov chain by transforming the standard markov chain which is obtained using the metropolis hastings method we call this novel transformation pseudo lifting we apply our method to graphs with geometry or graphs with doubling dimension specifically the convergence time of our algorithm equivalently the mixing time of our markov chain is proportional to the diameter of the network graph and hence optimal as a byproduct our result provides the fastest mixing markov chain given the network topological constraints and should naturally find their applications in the context of distributed optimization estimation and control

constructing free energy approximations and generalized belief propagation algorithms important inference problems in statistical physics computer vision error correcting coding theory and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs the belief propagation bp algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree but only approximate when the factor graph has cycles we show that bp fixed points correspond to the stationary points of the bethe approximation of the free energy for a factor graph we explain how to obtain region based free energy approximations that improve the bethe approximation and corresponding generalized belief propagation gbp algorithms we emphasize the conditions a free energy approximation must satisfy in order to be a valid or maxent normal approximation we describe the relationship between four different methods that can be used to generate valid approximations the bethe method the junction graph method the cluster variation method and the region graph method finally we explain how to tell whether a region based approximation and its corresponding gbp algorithm is likely to be accurate and describe empirical results showing that gbp can significantly outperform bp

image denoising using scale mixtures of gaussians in the wavelet domain we describe a method for removing noise from digital images based on a statistical model of the coefficients of an overcomplete multiscale oriented basis neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables a gaussian vector and a hidden positive scalar multiplier the latter modulates the local variance of the coefficients in the neighborhood and is thus able to account for the empirically observed correlation between the coefficient amplitudes under this model the bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable we demonstrate through simulations with images contaminated by additive white gaussian noise that the performance of this method substantially surpasses that of previously published methods both visually and in terms of mean squared error

derivation of new and existing discrete time kharitonov theorems based on discrete time reactances digital signal processing the author first uses a discrete time reactance approach to give a second proof of existing discrete time kharitonov type results 1979 he then uses the same reactance language to derive a new discrete time kharitonov type theorem which in some sense is a very close analog to the continuous time case he also points out the relation between discrete time reactances and the technique of line spectral pairs lsp used in speech compression

on the limited memory bfgs method for large scale optimization we study the numerical performance of a limited memory quasi newton method for large scale optimization which we call the l bfgs method we compare its performance with that of the method developed by buckley and lenir 1985 which combines cycles of bfgs steps and conjugate direction steps our numerical tests indicate that the l bfgs method is faster than the method of buckley and lenir and is better able to use additional storage to accelerate convergence we show that the l bfgs method can be greatly accelerated by means of a simple scaling we then compare the l bfgs method with the partitioned quasi newton method of griewank and toint 1982a the results show that for some problems the partitioned quasi newton method is clearly superior to the l bfgs method however we find that for other problems the l bfgs method is very competitive due to its low iteration cost we also study the convergence properties of the l bfgs method and prove global convergence on uniformly convex problems

chebyshev polynomials in distributed consensus applications in this paper we analyze the use of chebyshev polynomials in distributed consensus applications it is well known that the use of polynomials speeds up the convergence to the consensus in a significant way however existing solutions only work for low degree polynomials and require the topology of the network to be fixed and known we propose a distributed algorithm based on the second order difference equation that describes the chebyshev polynomials of first kind the contributions of our algorithm are three i since the evaluation of chebyshev polynomials is stable there is no limitation in the degree of the polynomial ii instead of the knowledge of the whole network topology it only requires a partial knowledge or an approximation to it iii it can be applied to time varying topologies in the paper we characterize the main properties of the algorithm for both fixed and time varying communication topologies theoretical results as well as experiments with synthetic data show the benefits of using our algorithm compared to existing methods

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

color image denoising via discriminatively learned iterative shrinkage in this paper we propose a novel model a discriminatively learned iterative shrinkage dlis model for color image denoising the dlis is a generalization of wavelet shrinkage by iteratively performing shrinkage over patch groups and whole image aggregation we discriminatively learn the shrinkage functions and basis from the training pairs of noisy noise free images which can adaptively handle different noise characteristics in luminance chrominance channels and the unknown structured noise in real captured color images furthermore to remove the splotchy real color noises we design a laplacian pyramid based denoising framework to progressively recover the clean image from the coarsest scale to the finest scale by the dlis model learned from the real color noises experiments show that our proposed approach can achieve the state of the art denoising results on both synthetic denoising benchmark and real captured color images

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

active appearance models we describe a new method of matching statistical models of appearance to images a set of model parameters control modes of shape and gray level variation learned from a training set we construct an efficient iterative matching algorithm by learning the relationship between perturbations in the model parameters and the induced image errors

graph diameter eigenvalues and minimum time consensus we consider the problem of achieving average consensus in the minimum number of linear iterations on a fixed undirected graph we are motivated by the task of deriving lower bounds for consensus protocols and by the so called definitive consensus conjecture which states that for an undirected connected graph g with diameter d there exist d matrices whose nonzero pattern complies with the edges in g and whose product equals the all ones matrix our first result is a counterexample to the definitive consensus conjecture which is the first improvement of the diameter lower bound for linear consensus protocols we then provide some algebraic conditions under which this conjecture holds which we use to establish that all distance regular graphs satisfy the definitive consensus conjecture

deep convolutional neural network for inverse problems in imaging in this paper we propose a novel deep convolutional neural network cnn based algorithm for solving ill posed inverse problems regularized iterative algorithms have emerged as the standard approach to ill posed inverse problems in the past few decades these methods produce excellent results but can be challenging to deploy in practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyperparameter selection the starting point of this paper is the observation that unrolled iterative methods have the form of a cnn filtering followed by pointwise non linearity when the normal operator h h where h is the adjoint of the forward imaging operator h of the forward model is a convolution based on this observation we propose using direct inversion followed by a cnn to solve normal convolutional inverse problems the direct inversion encapsulates the physical model of the system but leads to artifacts when the problem is ill posed the cnn combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure we demonstrate the performance of the proposed network in sparse view reconstruction down to 50 views on parallel beam x ray computed tomography in synthetic phantoms as well as in real experimental sinograms the proposed network outperforms total variation regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a 512 times 512 image on the gpu

polynomial filtering for fast convergence in distributed consensus in the past few years the problem of distributed consensus has received a lot of attention particularly in the framework of ad hoc sensor networks most methods proposed in the literature address the consensus averaging problem by distributed linear iterative algorithms with asymptotic convergence of the consensus solution the convergence rate of such distributed algorithms typically depends on the network topology and the weights given to the edges between neighboring sensors as described by the network matrix in this paper we propose to accelerate the convergence rate for given network matrices by the use of polynomial filtering algorithms the main idea of the proposed methodology is to apply a polynomial filter on the network matrix that will shape its spectrum in order to increase the convergence rate such an algorithm is equivalent to periodic updates in each of the sensors by aggregating a few of its previous estimates we formulate the computation of the coefficients of the optimal polynomial as a semidefinite program that can be efficiently and globally solved for both static and dynamic network topologies we finally provide simulation results that demonstrate the effectiveness of the proposed solutions in accelerating the convergence of distributed consensus averaging problems

estimating the probability of the presence of a signal of interest in multiresolution single and multiband image denoising we develop three novel wavelet domain denoising methods for subband adaptive spatially adaptive and multivalued image denoising the core of our approach is the estimation of the probability that a given coefficient contains a significant noise free component which we call signal of interest in this respect we analyze cases where the probability of signal presence is 1 fixed per subband 2 conditioned on a local spatial context and 3 conditioned on information from multiple image bands all the probabilities are estimated assuming a generalized laplacian prior for noise free subband data and additive white gaussian noise the results demonstrate that the new subband adaptive shrinkage function outperforms bayesian thresholding approaches in terms of mean squared error the spatially adaptive version of the proposed method yields better results than the existing spatially adaptive ones of similar and higher complexity the performance on color and on multispectral images is superior with respect to recent multiband wavelet thresholding

fields of experts we develop a framework for learning generic expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks the approach provides a practical method for learning high order markov random field mrf models with potential functions that extend over large pixel neighborhoods these clique potentials are modeled using the product of experts framework that uses non linear functions of many linear filter responses in contrast to previous mrf approaches all parameters including the linear filters themselves are learned from training data we demonstrate the capabilities of this field of experts model with two example applications image denoising and image inpainting which are implemented using a simple approximate inference scheme while the model is trained on a generic image database and is not tuned toward a specific application we obtain results that compete with specialized techniques

stereo matching using belief propagation in this paper we formulate the stereo matching problem as a markov network and solve it using bayesian belief propagation the stereo markov network consists of three coupled markov random fields that model the following a smooth field for depth disparity a line process for depth discontinuity and a binary process for occlusion after eliminating the line process and the binary process by introducing two robust functions we apply the belief propagation algorithm to obtain the maximum a posteriori map estimation in the markov network other low level visual cues e g image segmentation can also be easily incorporated in our stereo model to obtain better stereo results experiments demonstrate that our methods are comparable to the state of the art stereo algorithms for many test cases

a generalization of kharitonov s four polynomial concept for robust stability problems with linearly dependent coefficient perturbations kharitonov s four polynomial concept is generalized to the case of linearly dependent coefficient perturbations and more general zero location regions to this end a specially constructed scalar function of a scalar variable is instrumental to the robustness analysis the present work is motivated by two fundamental limitations of kharitonov s theorem namely 1 the theorem only applies to polynomials with independent coefficient perturbations and 2 it only applies to zeros in the left hand plane

training products of experts by minimizing contrastive divergence it is possible to combine multiple latent variable models of the same data by multiplying their probability distributions together and then renormalizing this way of combining individual expert models makes it hard to generate samples from the combined model but easy to infer the values of the latent variables of each expert because the combination rule ensures that the latent variables of different experts are conditionally independent when given the data a product of experts poe is therefore an interesting candidate for a perceptual system in which rapid inference is vital and generation is unnecessary training a poe by maximizing the likelihood of the data is difficult because it is hard even to approximate the derivatives of the renormalization term in the combination rule fortunately a poe can be trained using a different objective function called contrastive divergence whose derivatives with regard to the parameters can be approximated accurately and efficiently examples are presented of contrastive divergence learning using several types of expert on several types of data

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

some discrete time counterparts to kharitonov s stability criterion for uncertain systems in 1 kharitonov gave an elegant and simple stability criterion for continuous time systems this note reports on similar results for discrete time systems

analysis of accelerated gossip algorithms gossiping is a distributed process whose purpose is to enable the members of a group of n 1 autonomous agents to asymptotically determine in a decentralized manner the average of the initial values of their scalar gossip variables this paper analyzes the accelerated gossip algorithms first proposed in cao spielman and yeh 2006 in which local memory is exploited by installing shift registers at each agent for the two register case the existence of the desired convergence is established under a symmetry assumption by separately studying the convergence in expectation and in mean square in particular the optimal rate of convergence in expectation is derived which is faster than that of the standard gossip algorithm and a sufficient condition on the adjustable parameter for the convergence in mean square is provided these theoretical results are validated for some classes of networks by comparison with existing empirical data more general multi register cases are also discussed

estimating the wrong graphical model benefits in the computation limited setting consider the problem of joint parameter estimation and prediction in a markov random field that is the model parameters are estimated on the basis of an initial set of data and then the fitted model is used to perform prediction e g smoothing denoising interpolation on a new noisy observation working under the restriction of limited computation we analyze a joint method in which the same convex variational relaxation is used to construct an m estimator for fitting parameters and to perform approximate marginalization for the prediction step the key result of this paper is that in the computation limited setting using an inconsistent parameter estimator i e an estimator that returns the wrong model even in the infinite data limit is provably beneficial since the resulting errors can partially compensate for errors made by using an approximate prediction technique en route to this result we analyze the asymptotic properties of m estimators based on convex variational relaxations and establish a lipschitz stability property that holds for a broad class of convex variational methods this stability result provides additional incentive apart from the obvious benefit of unique global optima for using message passing methods based on convex variational relaxations we show that joint estimation prediction based on the reweighted sum product algorithm substantially outperforms a commonly used heuristic based on ordinary sum product

filters random fields and maximum entropy frame towards a unified theory for texture modeling this article presents a statistical theory for texture modeling this theory combines filtering theory and markov random field modeling through the maximum entropy principle and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view our theory characterizes the ensemble of images i with the same texture appearance by a probability distribution f i on a random field and the objective of texture modeling is to make inference about f i given a set of observed texture examples in our theory texture modeling consists of two steps 1 a set of filters is selected from a general filter bank to capture features of the texture these filters are applied to observed texture images and the histograms of the filtered images are extracted these histograms are estimates of the marginal distributions of f i this step is called feature extraction 2 the maximum entropy principle is employed to derive a distribution p i which is restricted to have the same marginal distributions as those in 1 this p i is considered as an estimate of f i this step is called feature fusion a stepwise algorithm is proposed to choose filters from a general filter bank the resulting model called frame filters random fields and maximum entropy is a markov random field mrf model but with a much enriched vocabulary and hence much stronger descriptive ability than the previous mrf models used for texture modeling gibbs sampler is adopted to synthesize texture images by drawing typical samples from p i thus the model is verified by seeing whether the synthesized texture images have similar visual appearances to the texture images being modeled experiments on a variety of 1d and 2d textures are described to illustrate our theory and to show the performance of our algorithms these experiments demonstrate that many textures which are previously considered as from different categories can be modeled and synthesized in a common framework

adding a single state memory optimally accelerates symmetric linear maps previous papers have proposed to add memory registers to the dynamics of discrete time linear systems in order to accelerate their convergence in particular it has been proved that adding one memory slot per agent allows faster convergence towards average consensus we here prove that this situation cannot be improved by adding more memory slots when the knowledge about the self adjoint linear map to be accelerated reduces to bounds on its extreme eigenvalues

limits as p of p laplacian problems with a superdiffusive power type nonlinearity positive and sign changing solutions abstract we investigate the asymptotic behaviour as p of sequences of solutions of the equation p u u q p 2 u in u 0 on where 0 and q p p with lim p q p p q 1 we are interested in the characterization of such limits as viscosity solutions of a pde problem both positive and sign changing solutions are considered

rao blackwellisation of sampling schemes summary this paper proposes a post simulation improvement for two common monte carlo methods the accept reject and metropolis algorithms the improvement is based on a rao blackwellisation method that integrates over the uniform random variables involved in the algorithms and thus post processes the standard estimators we show how the rao blackwellised versions of these algorithms can be implemented and through examples illustrate the improvement in variance brought by these new procedures we also compare the improved version of the metropolis algorithm with ordinary and rao blackwellised importance sampling procedures for independent and general metropolis set ups

separable markov random field model and its applications in low level vision this brief proposes a continuously valued markov random field mrf model with separable filter bank denoted as mrfsepa which significantly reduces the computational complexity in the mrf modeling in this framework we design a novel gradient based discriminative learning method to learn the potential functions and separable filter banks we learn mrfsepa models with 2 d and 3 d separable filter banks for the applications of gray scale color image denoising and color image demosaicing by implementing mrfsepa model on graphics processing unit we achieve real time image denoising and fast image demosaicing with high quality results

training an active random field for real time image denoising many computer vision problems can be formulated in a bayesian framework based on markov random fields mrf or conditional random fields crf generally the mrf crf model is learned independently of the inference algorithm that is used to obtain the final result in this paper we observe considerable gains in speed and accuracy by training the mrf crf model together with a fast and suboptimal inference algorithm an active random field arf is defined as a combination of a mrf crf based model and a fast inference algorithm for the mrf crf model this combination is trained through an optimization of a loss function and a training set consisting of pairs of input images and desired outputs we apply the arf concept to image denoising using the fields of experts mrf together with a 1 4 iteration gradient descent algorithm for inference experimental validation on unseen data shows that the arf approach obtains an improved benchmark performance as well as a 1000 3000 times speedup compared to the fields of experts mrf using the arf approach image denoising can be performed in real time at 8 fps on a single cpu for a 256times256 image sequence with close to state of the art accuracy