image denoising with edge preserving and segmentation based on mask nha in this paper we propose a zero mean white gaussian noise removal method using a high resolution frequency analysis it is difficult to separate an original image component from a noise component when using discrete fourier transform or discrete cosine transform for analysis because sidelobes occur in the results the 2d non harmonic analysis 2d nha is a high resolution frequency analysis technique that improves noise removal accuracy because of its sidelobe reduction feature however spectra generated by nha are distorted because of which the signal of the image is non stationary in this paper we analyze each region with a homogeneous texture in the noisy image non uniform regions that occur due to segmentation are analyzed by an extended 2d nha method called mask nha we conducted an experiment using a simulation image and found that mask nha denoising attains a higher peak signal to noise ratio psnr value than the state of the art methods if a suitable segmentation result can be obtained from the input image even though parameter optimization was incomplete this experimental result exhibits the upper limit on the value of psnr in our mask nha denoising method the performance of mask nha denoising is expected to approach the limit of psnr by improving the segmentation method

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

a revealed preference test for weakly separable utility maximization with incomplete adjustment abstract functional structure is an important issue in many areas of economics we suggest a nonparametric revealed preference test for weakly separable utility maximization that permits category incomplete adjustment within the period under study this test is an extension of the necessary and sufficient condition for weakly separable utility maximization developed by varian 1983 we implement this test and identify a quarterly economic monetary aggregate this is the first implementation that we know about of any revealed preference necessary and sufficient condition for weakly separable utility maximization we also perform sensitivity analyses of the test and find it to be reasonably robust

revealed preference tests for weak separability an integer programming approach we present the revealed preference conditions that characterize the data sets that are consistent with the maximization of a weakly separable utility function we show that verifying these revealed preference conditions is np hard we also present an integer programming approach which is particularly attractive in view of empirical analysis we demonstrate the versatility of this integer programming approach by showing that it allows for testing homothetic separability and weak separability of the indirect utility function we illustrate the practical usefulness of the approach by an empirical application to spanish household consumption data

context aware sparse decomposition for image denoising and super resolution image prior models based on sparse and redundant representations are attracting more and more attention in the field of image restoration the conventional sparsity based methods enforce sparsity prior on small image patches independently unfortunately these works neglected the contextual information between sparse representations of neighboring image patches it limits the modeling capability of sparsity based image prior especially when the major structural information of the source image is lost in the following serious degradation process in this paper we utilize the contextual information of local patches denoted as context aware sparsity prior to enhance the performance of sparsity based restoration method in addition a unified framework based on the markov random fields model is proposed to tune the local prior into a global one to deal with arbitrary size images an iterative numerical solution is presented to solve the joint problem of model parameters estimation and sparse recovery finally the experimental results on image denoising and super resolution demonstrate the effectiveness and robustness of the proposed context aware method

the guaranteed cost control problem of uncertain singularly perturbed systems abstract in this paper we study the algebraic riccati equation corresponding to the guaranteed cost control theory for an uncertain singularly perturbed system the construction of the controller involves solving the full order algebraic riccati equation with small parameter e under control oriented assumptions we first provide the sufficient conditions such that the full order algebraic riccati equation has a positive semi definite stabilizing solution next we propose an iterative algorithm based on the kleinman algorithm to solve the algebraic riccati equation which depends on the parameter e our new idea is to use the solutions of the reduced order algebraic riccati equations for the initial condition by using the iterative algorithm we can easily obtain a required solution of the algebraic riccati equation moreover using the initial conditions without e we show that there exists an e such that the proposed algorithm has quadratic convergence finally in order to show the effectiveness of the proposed algorithm numerical examples are included

tests for the consistency of consumer data abstract the paper develops non parametric tests for the weak separability or the additive separability of a decision maker s utility function given a finite body of price and quantity data the tests generalize some earlier tests proposed by afriat and varian blackorby primont and russell have pointed out that the econometric literature on testing separability hypotheses is seriously deficient since the econometric tests tend to impose unwanted restrictions on the parametric functional form in addition to the particular separability hypothesis being tested hence the non parametric tests in the present paper should serve as useful supplements to the usual econometric tests for separability

multidimensional directional filter banks and surfacelets in 1992 bamberger and smith proposed the directional filter bank dfb for an efficient directional decomposition of 2 d signals due to the nonseparable nature of the system extending the dfb to higher dimensions while still retaining its attractive features is a challenging and previously unsolved problem we propose a new family of filter banks named ndfb that can achieve the directional decomposition of arbitrary n dimensional nges2 signals with a simple and efficient tree structured construction in 3 d the ideal passbands of the proposed ndfb are rectangular based pyramids radiating out from the origin at different orientations and tiling the entire frequency space the proposed ndfb achieves perfect reconstruction via an iterated filter bank with a redundancy factor of n in n d the angular resolution of the proposed ndfb can be iteratively refined by invoking more levels of decomposition through a simple expansion rule by combining the ndfb with a new multiscale pyramid we propose the surfacelet transform which can be used to efficiently capture and represent surface like singularities in multidimensional data

analysis of multiresolution image denoising schemes using generalized gaussian and complexity priors research on universal and minimax wavelet shrinkage and thresholding methods has demonstrated near ideal estimation performance in various asymptotic frameworks however image processing practice has shown that universal thresholding methods are outperformed by simple bayesian estimators assuming independent wavelet coefficients and heavy tailed priors such as generalized gaussian distributions ggds in this paper we investigate various connections between shrinkage methods and maximum a posteriori map estimation using such priors in particular we state a simple condition under which map estimates are sparse we also introduce a new family of complexity priors based upon rissanen s universal prior on integers one particular estimator in this class outperforms conventional estimators based on earlier applications of the minimum description length mdl principle we develop analytical expressions for the shrinkage rules implied by ggd and complexity priors this allows us to show the equivalence between universal hard thresholding map estimation using a very heavy tailed ggd and mdl estimation using one of the new complexity priors theoretical analysis supported by numerous practical experiments shows the robustness of some of these estimates against mis specifications of the prior a basic concern in image processing applications

bm3d frames and variational image deblurring a family of the block matching 3 d bm3d algorithms for various imaging problems has been recently proposed within the framework of nonlocal patchwise image modeling in this paper we construct analysis and synthesis frames formalizing bm3d image modeling and use these frames to develop novel iterative deblurring algorithms we consider two different formulations of the deblurring problem i e one given by the minimization of the single objective function and another based on the generalized nash equilibrium gne balance of two objective functions the latter results in the algorithm where deblurring and denoising operations are decoupled the convergence of the developed algorithms is proved simulation experiments show that the decoupled algorithm derived from the gne formulation demonstrates the best numerical and visual results and shows superiority with respect to the state of the art in the field confirming a valuable potential of bm3d frames as an advanced image modeling tool

the contourlet transform an efficient directional multiresolution image representation the limitations of commonly used separable extensions of one dimensional transforms such as the fourier and wavelet transforms in capturing the geometry of image edges are well known in this paper we pursue a true two dimensional transform that can capture the intrinsic geometrical structure that is key in visual information the main challenge in exploring geometry in images comes from the discrete nature of the data thus unlike other approaches such as curvelets that first develop a transform in the continuous domain and then discretize for sampled data our approach starts with a discrete domain construction and then studies its convergence to an expansion in the continuous domain specifically we construct a discrete domain multiresolution and multidirection expansion using nonseparable filter banks in much the same way that wavelets were derived from filter banks this construction results in a flexible multiresolution local and directional image expansion using contour segments and thus it is named the contourlet transform the discrete contourlet transform has a fast iterated filter bank algorithm that requires an order n operations for n pixel images furthermore we establish a precise link between the developed filter bank and the associated continuous domain contourlet expansion via a directional multiresolution analysis framework we show that with parabolic scaling and sufficient directional vanishing moments contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves finally we show some numerical experiments demonstrating the potential of contourlets in several image processing applications

sparsity preserving projections with applications to face recognition dimensionality reduction methods drs have commonly been used as a principled way to understand the high dimensional data such as face images in this paper we propose a new unsupervised dr method called sparsity preserving projections spp unlike many existing techniques such as local preserving projection lpp and neighborhood preserving embedding npe where local neighborhood information is preserved during the dr procedure spp aims to preserve the sparse reconstructive relationship of the data which is achieved by minimizing a l1 regularization related objective function the obtained projections are invariant to rotations rescalings and translations of the data and more importantly they contain natural discriminating information even if no class labels are provided moreover spp chooses its neighborhood automatically and hence can be more conveniently used in practice compared to lpp and npe the feasibility and effectiveness of the proposed method is verified on three popular face databases yale ar and extended yale b with promising results

h control of linear singularly perturbed systems with small state delay an infinite horizon h state feedback control problem for singularly perturbed linear systems with a small state delay is considered an asymptotic solution of the hybrid system of riccati type algebraic ordinary differential and partial differential equations with deviating arguments associated with this problem is constructed based on this asymptotic solution conditions for the existence of a solution of the original h problem independent of the singular perturbation parameter are derived a simplified controller with parameter independent gain matrices solving the original problem for all sufficiently small values of this parameter is obtained an illustrative example is presented

new iterative algorithm for algebraic riccati equation related to h sub spl infin control problem of singularly perturbed systems we present the solution to the algebraic riccati equation are with indefinite sign quadratic term related to the h sub spl infin control problem for singularly perturbed systems by means of a kleinman type algorithm the resulting algorithm is very efficient from the numerical point of view because the are is solvable even if the quadratic term has an indefinite sign moreover the resulting iterative algorithm is quadratically convergent we also present an algorithm for solving the generalized algebraic lyapunov equation on the basis of the fixed point algorithm

denoising natural images based on a modified sparse coding algorithm this paper proposes a novel image reconstruction method for natural images using a modified sparse coding sc algorithm proposed by us this sc algorithm exploited the maximum kurtosis as the maximizing sparse measure criterion at one time a fixed variance term of sparse coefficients is used to yield a fixed information capacity on the other hand in order to improve the convergence speed we use a determinative basis function which is obtained by a fast fixed point independent component analysis fastica algorithm as the initialization feature basis function of our sparse coding algorithm instead of using a random initialization matrix the experimental results show that by using our sc algorithm the feature basis vectors of natural images can be successfully extracted then exploiting these features the original images can be reconstructed easily furthermore compared with the standard ica method the experimental results show that our sc algorithm is indeed efficient and effective in performing image reconstruction task

llsure local linear sure based edge preserving image filtering in this paper we propose a novel approach for performing high quality edge preserving image filtering based on a local linear model and using the principle of stein s unbiased risk estimate as an estimator for the mean squared error from the noisy image only we derive a simple explicit image filter which can filter out noise while preserving edges and fine scale details moreover this filter has a fast and exact linear time algorithm whose computational complexity is independent of the filtering kernel size thus it can be applied to real time image processing tasks the experimental results demonstrate the effectiveness of the new filter for various computer vision applications including noise reduction detail smoothing and enhancement high dynamic range compression and flash no flash denoising

pointwise shape adaptive dct for high quality denoising and deblocking of grayscale and color images the shape adaptive discrete cosine transform sa dct transform can be computed on a support of arbitrary shape but retains a computational complexity comparable to that of the usual separable block dct b dct despite the near optimal decorrelation and energy compaction properties application of the sa dct has been rather limited targeted nearly exclusively to video compression in this paper we present a novel approach to image filtering based on the sa dct we use the sa dct in conjunction with the anisotropic local polynomial approximation intersection of confidence intervals technique which defines the shape of the transform s support in a pointwise adaptive manner the thresholded or attenuated sa dct coefficients are used to reconstruct a local estimate of the signal within the adaptive shape support since supports corresponding to different points are in general overlapping the local estimates are averaged together using adaptive weights that depend on the region s statistics this approach can be used for various image processing tasks in this paper we consider in particular image denoising and image deblocking and deringing from block dct compression a special structural constraint in luminance chrominance space is also proposed to enable an accurate filtering of color images simulation experiments show a state of the art quality of the final estimate both in terms of objective criteria and visual appearance thanks to the adaptive support reconstructed edges are clean and no unpleasant ringing artifacts are introduced by the fitted transform

quadtree structured image approximation for denoising and interpolation the success of many image restoration algorithms is often due to their ability to sparsely describe the original signal shukla proposed a compression algorithm based on a sparse quadtree decomposition model which could optimally represent piecewise polynomial images in this paper we adapt this model to the image restoration by changing the rate distortion penalty to a description length penalty in addition one of the major drawbacks of this type of approximation is the computational complexity required to find a suitable subspace for each node of the quadtree we address this issue by searching for a suitable subspace much more efficiently using the mathematics of updating matrix factorisations algorithms are developed to tackle denoising and interpolation simulation results indicate that we beat state of the art results when the original signal is in the model e g depth images and are competitive for natural images when the degradation is high

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

asymptotic expansions for game theoretic riccati equations and stabilization with disturbance attenuation for singularly perturbed systems abstract if the systems to be controlled are singularly perturbed then the riccati equations which appear in h problems are difficult to solve due to the presence of the small parameter the present paper describes and validates asymptotic expansions showing how they may be used in h control furthermore we construct a composite controller based on the solution of slow and fast problems which guarantees a desired achievable performance level for the full order plant as e approaches zero

asymptotic properties of input output operators norm associated with singularly perturbed systems with multiplicative white noise in this paper we study the problem of the asymptotic property of the norm of input output operators related to a class of singularly perturbed stochastic linear systems the system is under perturbation of multiplicative white noise by using reduction order and boundary layer techniques it is shown that the norm of the operator of the perturbed system is less than a given number gamma when the small perturbation varepsilon tends to zero if both the related norms of the reduced subsystem and the boundary layer subsystem are less than gamma furthermore a stabilizing robust controller is designed which is independent of perturbation varepsilon

brief paper h control for fast sampling discrete time singularly perturbed systems this paper is concerned with the h control problem via state feedback for fast sampling discrete time singularly perturbed systems a new h controller design method is given in terms of solutions to linear matrix inequalities lmis which eliminates the regularity restrictions attached to the riccati based solution a method for evaluating the upper bound of singular perturbation parameter e with meeting a prescribed h performance bound requirement is also given furthermore the results are extended to robust controller design for fast sampling discrete time singularly perturbed systems with polytopic uncertainties numerical examples are given to illustrate the validity of the proposed methods

robust stabilization of two time scale systems with respect to the normalized coprime factorization the present paper has two main purposes the first is to provide an explicit state space solution of the robust stabilization problem with respect to the nlcf for two time scale systems in this construction only the solutions of the control and of the filtering riccati equations associated with the slow and with the fast dynamics of the nominal plant are used these solutions do not depend upon the singular perturbation and therefore all computations are well conditioned the second purpose of the paper is to investigate the case when an k independent robust controller can be used for the robust stabilization of a two time scale nominal system two constructions of such controllers are developed under some additional assumptions numerical examples illustrate the theoretical developments

the lifting factorization and construction of wavelet bi frames with arbitrary generators and scaling in this paper we present the lifting factorization and construction of wavelet bi frames with arbitrary generators and scaling we show that an arbitrary polyphase matrix of a wavelet bi frame can be factorized into a series of lifting steps based on the proposed factorization we present a general construction of bi frames especially we give an explicit formula to construct the bi frames of two scaling and two generators with symmetry and one vanishing moment this paper does not involve many theories of wavelet frames in mathematics but focuses on the algebraic issues related to laurent polynomials which are efficient expressions in redundant filter banks associated with wavelet frames as an extension of the classical two channel filter bank the redundant filter bank is more complicated but also more flexible furthermore we present an algorithm to increase the number of vanishing moments to arbitrary order by lifting which is iterated and is straightforward in implementation

directional multiscale modeling of images using the contourlet transform the contourlet transform is a new two dimensional extension of the wavelet transform using multiscale and directional filter banks the contourlet expansion is composed of basis images oriented at various directions in multiple scales with flexible aspect ratios given this rich set of basis images the contourlet transform effectively captures smooth contours that are the dominant feature in natural images we begin with a detailed study on the statistics of the contourlet coefficients of natural images using histograms to estimate the marginal and joint distributions and mutual information to measure the dependencies between coefficients this study reveals the highly non gaussian marginal statistics and strong interlocation interscale and interdirection dependencies of contourlet coefficients we also find that conditioned on the magnitudes of their generalized neighborhood coefficients contourlet coefficients can be approximately modeled as gaussian random variables based on these findings we model contourlet coefficients using a hidden markov tree hmt model with gaussian mixtures that can capture all interscale interdirection and interlocation dependencies we present experimental results using this model in image denoising and texture retrieval applications in denoising the contourlet hmt outperforms other wavelet methods in terms of visual quality especially around edges in texture retrieval it shows improvements in performance for various oriented textures

technical communique a revised kleinman algorithm to solve algebraic riccati equation of singularly perturbed systems in this paper we show that the kleinman algorithm can be used well to solve the algebraic riccati equation are of singularly perturbed systems where the quadratic term of the are may be indefinite the quadratic convergence property of the kleinman algorithm is proved by using the newton kantorovich theorem when the initial condition is chosen appropriately in addition the numerical method to solve the generalized algebraic lyapunov equation gale appearing in the kleinman algorithm is given

the curvelet transform for image denoising we describe approximate digital implementations of two new mathematical transforms namely the ridgelet transform and the curvelet transform our implementations offer exact reconstruction stability against perturbations ease of implementation and low computational complexity a central tool is fourier domain computation of an approximate digital radon transform we introduce a very simple interpolation in the fourier space which takes cartesian samples and yields samples on a rectopolar grid which is a pseudo polar sampling set based on a concentric squares geometry despite the crudeness of our interpolation the visual performance is surprisingly good our ridgelet transform applies to the radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain our curvelet transform uses our ridgelet transform as a component step and implements curvelet subbands using a filter bank of a spl grave trous wavelet filters our philosophy throughout is that transforms should be overcomplete rather than critically sampled we apply these digital transforms to the denoising of some standard images embedded in white noise in the tests reported here simple thresholding of the curvelet coefficients is very competitive with state of the art techniques based on wavelets including thresholding of decimated or undecimated wavelet transforms and also including tree based bayesian posterior mean methods moreover the curvelet reconstructions exhibit higher perceptual quality than wavelet based reconstructions offering visually sharper images and in particular higher quality recovery of edges and of faint linear and curvilinear features existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems the empirical results reported here are in encouraging agreement

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

linear worst case estimators for denoising quantization noise in transform coded images transform coded images exhibit distortions that fall outside of the assumptions of traditional denoising techniques in this paper we use tools from robust signal processing to construct linear worst case estimators for the denoising of transform compressed images we show that while standard denoising is fundamentally determined by statistical models for images alone the distortions induced by transform coding are heavily dependent on the structure of the transform used our method thus uses simple models for the image and for the quantization error with the latter capturing the transform dependency based on these models we derive optimal linear estimators of the original image that are optimal in the mean squared error sense for the worst case cross correlation between the original and the quantization error our construction is transform agnostic and is applicable to transforms from block discrete cosine transforms to wavelets furthermore our approach is applicable to different types of image statistics and can also serve as an optimization tool for the design of transforms quantizers through the interaction of the source and quantizer models our work provides useful insights and is instrumental in identifying and removing quantization artifacts from general signals coded with general transforms as we decouple the modeling and processing steps we allow for the construction of many different types of estimators depending on the desired sophistication and available computational complexity in the low end of this spectrum our lookup table based estimator which can be deployed in low complexity environments provides competitive psnr values with some of the best results in the literature

the lifting scheme for wavelet bi frames theory structure and algorithm in this paper we present the lifting scheme of wavelet bi frames along with theory analysis structure and algorithm we show how any wavelet bi frame can be decomposed into a finite sequence of simple filtering steps this decomposition corresponds to a factorization of a polyphase matrix of a wavelet bi frame based on this concept we present a new idea for constructing wavelet bi frames for the construction of symmetric bi frames we use generalized bernstein basis functions which enable us to design symmetric prediction and update filters the construction allows more efficient implementation and provides tools for custom design of wavelet bi frames by combining the different designed filters for the prediction and update steps we can devise practically unlimited forms of wavelet bi frames moreover we present an algorithm of increasing the number of vanishing moments of bi framelets to arbitrary order via the presented lifting scheme which adopts an iterative algorithm and ensures the shortest lifting scheme several construction examples are given to illustrate the results

a descriptor system approach to singular perturbation of linear regulators the relationship between the regulator problem for a singularly perturbed system and the analogous one for a descriptor system is investigated meanwhile a decomposition approach is provided for solution of the linear quadratic regulator problem for singularly perturbed systems this approach is a significant advance over the two stage method

on the importance of combining wavelet based nonlinear approximation with coding strategies this paper provides a mathematical analysis of transform compression in its relationship to linear and nonlinear approximation theory contrasting linear and nonlinear approximation spaces we show that there are interesting classes of functions random processes which are much more compactly represented by wavelet based nonlinear approximation these classes include locally smooth signals that have singularities and provide a model for many signals encountered in practice in particular for images however we also show that nonlinear approximation results do not always translate to efficient compress on strategies in a rate distortion sense based on this observation we construct compression techniques and formulate the family of functions stochastic processes for which they provide efficient descriptions in a rate distortion sense we show that this family invariably leads to besov spaces yielding a natural relationship among besov smoothness linear nonlinear approximation order and compression performance in a rate distortion sense the designed compression techniques show similarities to modern high performance transform codecs allowing us to establish relevant rate distortion estimates and identify performance limits

h sup spl infin optimal control for singularly perturbed systems ii imperfect state measurements for pt i see ibid vol 29 no 2 p 401 423 1993 in this paper we study the h sup spl infin optimal control of singularly perturbed linear systems under general imperfect measurements for both finite and infinite horizon formulations using a differential game theoretic approach we first show that as the singular perturbation parameter say spl epsiv 0 approaches zero the optimal disturbance attenuation level for the full order system under a quadratic performance index converges to a value that is bounded above by and in some cases equal to the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate slow and fast quadratic cost functions with the bound being computable independently of e and knowing only the slow and fast dynamics of the system we then construct a controller based on the slow subsystem only and obtain conditions under which it delivers a desired performance level even though the fast dynamics are completely neglected the ultimate performance level achieved by this slow controller can be uniformly improved upon however by a composite controller that uses some feedback from the output of the fast subsystem we construct one such controller via a two step sequential procedure which uses static feedback from the fast output and dynamic feedback from an appropriate slow output each one obtained by solving appropriate spl epsiv independent lower dimensional h sup spl infin optimal control problems under some informational constraints we provide a detailed analysis of the performance achieved by this lower dimensional spl epsiv independent composite controller when applied to the full order system and illustrate the theory with some numerical results on some prototype systems

brief robust h minimum entropy static output feedback control of singularly perturbed systems the problem of designing static output feedback e independent controllers for linear time invariant singularly perturbed systems is considered the controller is required to satisfy a prescribed h norm bound and to minimize the closed loop entropy at s for all small enough e the optimal controller gain is designed on the basis of generalized riccati and lyapunov equations with symmetric block 2 2 that are coupled via a projection this gain is either purely fast purely slow or a composite one depending on the structure of the output coupling matrix a well posed problem with a finite value of entropy for e 0 is obtained by assuming that the entropy of the fast subproblem is zero or by scaling the matrices of the system in the first case the optimal controller is the one that minimizes the entropy of the corresponding descriptor system

on the bias in flexible functional forms and an essentially unbiased form the fourier flexible form abstract the fourier flexible form and its derived expenditure system are introduced subject to smoothness conditions on the consumer s true indirect utility function the consumer s true expenditure system must be of the fourier form over the region of interest in an empirical investigation arbitrarily accurate finite parameter approximations of the consumer s true expenditure system are obtained by dropping all high order terms of the fourier expenditure system past an appropriate truncation point the resulting finite parametersystem is tractable in empirical studies the reader who is primarily interested in applications need only read the second and fifth sections the remainder of the article is concerned with the verification of these claims and an investigation of some aspects of the bias in translog specifications

from local kernel to nonlocal multiple model image denoising we review the evolution of the nonparametric regression modeling in imaging from the local nadaraya watson kernel estimate to the nonlocal means and further to transform domain filtering based on nonlocal block matching the considered methods are classified mainly according to two main features local nonlocal and pointwise multipoint here nonlocal is an alternative to local and multipoint is an alternative to pointwise these alternatives though obvious simplifications allow to impose a fruitful and transparent classification of the basic ideas in the advanced techniques within this framework we introduce a novel single and multiple model transform domain nonlocal approach the block matching and 3 d filtering bm3d algorithm which is currently one of the best performing denoising algorithms is treated as a special case of the latter approach

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

why simple shrinkage is still relevant for redundant representations shrinkage is a well known and appealing denoising technique introduced originally by donoho and johnstone in 1994 the use of shrinkage for denoising is known to be optimal for gaussian white noise provided that the sparsity on the signal s representation is enforced using a unitary transform still shrinkage is also practiced with nonunitary and even redundant representations typically leading to very satisfactory results in this correspondence we shed some light on this behavior the main argument in this work is that such simple shrinkage could be interpreted as the first iteration of an algorithm that solves the basis pursuit denoising bpdn problem while the desired solution of bpdn is hard to obtain in general we develop a simple iterative procedure for the bpdn minimization that amounts to stepwise shrinkage we demonstrate how the simple shrinkage emerges as the first iteration of this novel algorithm furthermore we show how shrinkage can be iterated turning into an effective algorithm that minimizes the bpdn via simple shrinkage steps in order to further strengthen the denoising effect

weighted averaging for denoising with overcomplete dictionaries we consider the scenario where additive independent and identically distributed i i d noise in an image is removed using an overcomplete set of linear transforms and thresholding rather than the standard approach where one obtains the denoised signal by ad hoc averaging of the denoised estimates provided by denoising with each of the transforms we formulate the optimal combination as a conditional linear estimation problem and solve it for optimal estimates our approach is independent of the utilized transforms and the thresholding scheme and as we illustrate using oracle based denoisers it extends established work by exploiting a separate degree of freedom that is in general not reachable using previous techniques our derivation of the optimal estimates specifically relies on the assumption that the utilized transforms provide sparse decompositions at the same time our work is robust as it does not require any assumptions about image statistics beyond sparsity unlike existing work which tries to devise ever more sophisticated transforms and thresholding algorithms to deal with the myriad types of image singularities our work uses basic tools to obtain very high performance on singularities by taking better advantage of the sparsity that surrounds them with well established transforms we obtain results that are competitive with state of the art methods

automatic design of high sensitivity color filter arrays with panchromatic pixels in most of existing digital cameras color images have to be reconstructed from raw images which only have one color sensed at each pixel as their imaging sensors are covered by color filter arrays cfas at each pixel a cfa usually allows only a portion of the light spectrum to pass through and thereby reduces the light sensitivity of pixels to address this issue previous works have explored adding panchromatic pixels into cfas however almost all existing methods assign panchromatic pixels empirically making the designed cfas prone to aliasing artifacts in this paper based on a mathematical model we propose a fully automatic approach to designing high sensitivity cfas using panchromatic pixels by the frequency structure representation of cfas we formulate high sensitivity cfa design as a continuous multi objective optimization problem where robustness to aliasing artifacts and percentage of panchromatic pixels are simultaneously maximized we analyze the characteristics of our new formulation according to the analysis we develop a new method to propose frequency structure candidates which can produce cfas that reach a desired percentage of panchromatic pixels then for each candidate we optimize parameters to obtain the final cfa which is an appropriately balanced solution to the multi objective optimization problem we formulate the two design procedures as constrained optimization problems and solve them using the alternating direction method extensive experiments confirm the advantage of the proposed method in both low light and normal light conditions

adaptive directional lifting based wavelet transform for image coding we present a novel 2 d wavelet transform scheme of adaptive directional lifting adl in image coding instead of alternately applying horizontal and vertical lifting as in present practice adl performs lifting based prediction in local windows in the direction of high pixel correlation hence it adapts far better to the image orientation features in local windows the adl transform is achieved by existing 1 d wavelets and is seamlessly integrated into the global wavelet transform the predicting and updating signals of adl can be derived even at the fractional pixel precision level to achieve high directional resolution while still maintaining perfect reconstruction to enhance the adl performance a rate distortion optimized directional segmentation scheme is also proposed to form and code a hierarchical image partition adapting to local features experimental results show that the proposed adl based image coding technique outperforms jpeg 2000 in both psnr and visual quality with the improvement up to 2 0 db on images with rich orientation features

bivariate shrinkage functions for wavelet based denoising exploiting interscale dependency most simple nonlinear thresholding rules for wavelet based denoising assume that the wavelet coefficients are independent however wavelet coefficients of natural images have significant dependencies we only consider the dependencies between the coefficients and their parents in detail for this purpose new non gaussian bivariate distributions are proposed and corresponding nonlinear threshold functions shrinkage functions are derived from the models using bayesian estimation theory the new shrinkage functions do not assume the independence of wavelet coefficients we show three image denoising examples in order to show the performance of these new bivariate shrinkage rules in the second example a simple subband dependent data driven image denoising system is described and compared with effective data driven techniques in the literature namely visushrink sureshrink bayesshrink and hidden markov models in the third example the same idea is applied to the dual tree complex wavelet coefficients

lapb locally adaptive patch based wavelet domain edge preserving image denoising abstract image denoising is one of the most diversified research areas in the field of image processing and computer vision it is highly desirable for a denoising technique to preserve important image features such as edges corners and other sharp structures of an image after denoising wavelet transforms show excellent proficiency in providing efficient edge preserving image denoising due to their capability of suppressing noisy signals from an image this paper presents a novel edge preserving image denoising technique based on wavelet transforms the multi level decomposition of the noisy image is carried out to transform the data into the wavelet domain a locally adaptive patch based lapb thresholding scheme is used to effectively reduce noise while preserving relevant features of the original image experimental results on benchmark test images demonstrate that the proposed method achieves competitive denoising performance in comparison to various state of the art algorithms

the idude framework for grayscale image denoising we present an extension of the discrete universal denoiser dude specialized for the denoising of grayscale images the original dude is a low complexity algorithm aimed at recovering discrete sequences corrupted by discrete memoryless noise of known statistical characteristics it is universal in the sense of asymptotically achieving without access to any information on the statistics of the clean sequence the same performance as the best denoiser that does have access to such information the dude however is not effective on grayscale images of practical size the difficulty lies in the fact that one of the dude s key components is the determination of conditional empirical probability distributions of image samples given the sample values in their neighborhood when the alphabet is relatively large as is the case with grayscale images even for a small sized neighborhood the required distributions would be estimated from a large collection of sparse statistics resulting in poor estimates that would not enable effective denoising the present work enhances the basic dude scheme by incorporating statistical modeling tools that have proven successful in addressing similar issues in lossless image compression instantiations of the enhanced framework which is referred to as idude are described for examples of additive and nonadditive noise the resulting denoisers significantly surpass the state of the art in the case of salt and pepper s p and ary symmetric noise and perform well for gaussian noise

h optimal control for singularly perturbed systems part i perfect state measurements we study the h optimal control of singularly perturbed linear systems under perfect state measurements for both finite and infinite horizons using a differential game theoretic approach we show that as the singular perturbation parameter approaches zero the optimal disturbance attenuation level for the full order system under a quadratic performance index converges to a value that is bounded above by the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate slow and fast quadratic cost functions furthermore we construct a composite controller based on the solution of the slow and fast games which guarantees a desired achievable performance level for the full order plant as approaches zero a slow controller however is not generally robust in this sense but still under some conditions which are delineated in the paper the fast dynamics can be totally ignored the paper also studies optimality when the controller includes a feedforward term in the disturbance and presents some numerical examples to illustrate the theoretical results

asymptotic h sub spl infin control of singularly perturbed systems with parametric uncertainties this paper deals with the problem of control of singularly perturbed linear continuous time systems the authors attention is focused on the design of a composite linear controller based on the slow and fast problems such that both stability and a prescribed h sub spl infin performance for the full order system are achieved the asymptotic behavior of the composite controller is studied which is independent of the singular perturbation spl epsiv when spl epsiv is sufficiently small furthermore the problem of robust control for the above system with parameter uncertainty is also investigated

image denoising using a tight frame we present a general mathematical theory for lifting frames that allows us to modify existing filters to construct new ones that form parseval frames we apply our theory to design nonseparable parseval frames from separable tensor products of a piecewise linear spline tight frame these new frame systems incorporate the weighted average operator the sobel operator and the laplacian operator in directions that are integer multiples of 45 spl deg a new image denoising algorithm is then proposed tailored to the specific properties of these new frame filters we demonstrate the performance of our algorithm on a diverse set of images with very encouraging results

spatially adaptive wavelet thresholding with context modeling for image denoising the method of wavelet thresholding for removing noise or denoising has been researched extensively due to its effectiveness and simplicity much of the literature has focused on developing the best uniform threshold or best basis selection however not much has been done to make the threshold values adaptive to the spatially changing statistics of images such adaptivity can improve the wavelet thresholding performance because it allows additional local information of the image such as the identification of smooth or edge regions to be incorporated into the algorithm this work proposes a spatially adaptive wavelet thresholding method based on context modeling a common technique used in image compression to adapt the coder to changing image characteristics each wavelet coefficient is modeled as a random variable of a generalized gaussian distribution with an unknown parameter context modeling is used to estimate the parameter for each coefficient which is then used to adapt the thresholding strategy this spatially adaptive thresholding is extended to the overcomplete wavelet expansion which yields better results than the orthogonal transform experimental results show that spatially adaptive wavelet thresholding yields significantly superior image quality and lower mse than the best uniform thresholding with the original image assumed known

frequency scale decomposition of h disk problems time and frequency scale decomposition methods have been used extensively for the sim plification of automatic control problems this paper considers the problem of parametrizing all functions in a specified h infty function disk over the unit ball in h infty this problem arises in the design of stabilizing feedback compensators to minimize a weighted sensitivity matrix in the h infty norm sense it is shown that an h infty disk problem whose data has two frequency scale behavior can be broken down into slow and fast subproblems if solutions can be found for both subproblems then the solutions can be combined to give an approximate solution for the original problem

spatial sparsity induced prediction sip for images and video a simple way to reject structured interference we propose a prediction technique that is geared toward forming successful estimates of a signal based on a correlated anchor signal that is contaminated with complex interference the corruption in the anchor signal involves intensity modulations linear distortions structured interference clutter and noise just to name a few the proposed setup reflects nontrivial prediction scenarios involving images and video frames where statistically related data is rendered ineffective for traditional methods due to cross fades blends clutter brightness variations focus changes and other complex transitions rather than trying to solve a difficult estimation problem involving nonstationary signal statistics we obtain simple predictors in linear transform domain where the underlying signals are assumed to be sparse we show that these simple predictors achieve surprisingly good performance and seamlessly allow successful predictions even under complicated cases none of the interference parameters are estimated as our algorithm provides completely blind and automated operation we provide a general formulation that allows for nonlinearities in the prediction loop and we consider prediction optimal decompositions beyond an extensive set of results on prediction and registration the proposed method is also implemented to operate inside a state of the art compression codec and results show significant improvements on scenes that are difficult to encode using traditional prediction techniques

the estimation of laplace random vectors in additive white gaussian noise this paper develops and compares the maximum a posteriori map and minimum mean square error mmse estimators for spherically contoured multivariate laplace random vectors in additive white gaussian noise the mmse estimator is expressed in closed form using the generalized incomplete gamma function we also find a computationally efficient yet accurate approximation for the mmse estimator in addition this paper develops an expression for the mse for any estimator of spherically contoured multivariate laplace random vectors in additive white gaussian noise awgn the development of which again depends on the generalized incomplete gamma function the estimators are motivated and tested on the problem of wavelet based image denoising

a nonparametric test of weak separability and consumer preferences abstract two stochastic nonparametric procedures are developed to evaluate the significance of violations of weak separability when the data have measurement error we show that the necessary and sufficient weak separability conditions of varian varian h 1983 nonparametric tests of consumer behavior review of economic studies 50 99 110 must also satisfy the afriat inequalities the tests detect weak separability with high probability for weakly separable data in addition the procedures correctly reject weak separability for both nonseparable and random utility simulated data sets the tests also fail to reject weak separability for a monetary and consumption data set which suggests that measurement error may be the source of the observed violations

brief paper h control for singularly perturbed systems this paper derives a set of e independent sufficient and necessary conditions for the h control problem for singularly perturbed systems in a different approach from previous ones a sub optimal controller is explicitly constructed we observe that the controller is also singularly perturbed with its fast slow part being an h sub optimal controller for the fast slow sub system of the original system respectively e independent h controller design is also considered the main contribution of this paper is that our results apply to both standard and non standard singularly perturbed systems

adaptive sequential prediction of multidimensional signals with applications to lossless image coding we investigate the problem of designing adaptive sequential linear predictors for the class of piecewise autoregressive multidimensional signals and adopt an approach of minimum description length mdl to determine the order of the predictor and the support on which the predictor operates the design objective is to strike a balance between the bias and variance of the prediction errors in the mdl criterion the predictor design problem is particularly interesting and challenging for multidimensional signals e g images and videos because of the increased degree of freedom in choosing the predictor support our main result is a new technique of sequentializing a multidimensional signal into a sequence of nested contexts of increasing order to facilitate the mdl search for the order and the support shape of the predictor and the sequentialization is made adaptive on a sample by sample basis the proposed mdl based adaptive predictor is applied to lossless image coding and its performance is empirically established to be the best among all the results that have been published till present

the nonsubsampled contourlet transform theory design and applications in this paper we develop the nonsubsampled contourlet transform nsct and study its applications the construction proposed in this paper is based on a nonsubsampled pyramid structure and nonsubsampled directional filter banks the result is a flexible multiscale multidirection and shift invariant image decomposition that can be efficiently implemented via the a trous algorithm at the core of the proposed scheme is the nonseparable two channel nonsubsampled filter bank nsfb we exploit the less stringent design condition of the nsfb to design filters that lead to a nsct with better frequency selectivity and regularity when compared to the contourlet transform we propose a design framework based on the mapping approach that allows for a fast implementation based on a lifting or ladder structure and only uses one dimensional filtering in some cases in addition our design ensures that the corresponding frame elements are regular symmetric and the frame is close to a tight one we assess the performance of the nsct in image denoising and enhancement applications in both applications the nsct compares favorably to other existing methods in the literature

multiresolution direction filterbanks theory design and applications this paper presents new developments of directional filterbanks dfbs the motivation for the paper is the existence of multiresolution and multidirection orthogonal transform for two dimensional 2 d discrete signals based on the frequency supports of the ideal transform a new uniformly maximally decimated dfb with six highpass directional subbands and two lowpass subands is introduced the uniform dfb udfb can be implemented by a binary tree structure of two channel filterbanks the filterbank employed in the tree is shown to be alias free decimation and permissible the udfb is then extended to a nonuniform case nudfb which is still maximally decimated by combining the two lowpass subbands the nudfb yields nonuniform frequency division which composes of one lowpass filter with a decimation factor of one fourth and six highpass directional filters with a decimation factor of one eighth the new dfbs offer alternative image decompositions which overcome the limited directional selectivity of the separable wavelets and the limited multiresolution of the conventional dfb the lowpass subband of the nudfb can be used to obtain a multiresolution representation by simply reiterating the same nudfb decomposition on the other hand the directional subbands can also be further refined by simply applying a two channel conventional dfb at each highpass component a simple design method yielding near orthogonal uniform and nonuniform multidimensional filterbanks is presented finally the performances of the newly proposed nudfb are compared with other conventional transforms in nonlinear approximation image denoising and texture classification to demonstrate its potential

robust locally linear embedding in the past few years some nonlinear dimensionality reduction nldr or nonlinear manifold learning methods have aroused a great deal of interest in the machine learning community these methods are promising in that they can automatically discover the low dimensional nonlinear manifold in a high dimensional data space and then embed the data points into a low dimensional embedding space using tractable linear algebraic techniques that are easy to implement and are not prone to local minima despite their appealing properties these nldr methods are not robust against outliers in the data yet so far very little has been done to address the robustness problem in this paper we address this problem in the context of an nldr method called locally linear embedding lle based on robust estimation techniques we propose an approach to make lle more robust we refer to this approach as robust locally linear embedding rlle we also present several specific methods for realizing this general rlle approach experimental results on both synthetic and real world data show that rlle is very robust against outliers

direction adaptive discrete wavelet transform for image compression we propose a direction adaptive dwt da dwt that locally adapts the filtering directions to image content based on directional lifting with the adaptive transform energy compaction is improved for sharp image features a mathematical analysis based on an anisotropic statistical image model is presented to quantify the theoretical gain achieved by adapting the filtering directions the analysis indicates that the proposed da dwt is more effective than other lifting based approaches experimental results report a gain of up to 2 5 db in psnr over the conventional dwt for typical test images subjectively the reconstruction from the da dwt better represents the structure in the image and is visually more pleasing

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

wavelet based statistical signal processing using hidden markov models wavelet based statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly gaussian these models are unrealistic for many real world signals we develop a new framework for statistical signal processing based on wavelet domain hidden markov models hmms that concisely models the statistical dependencies and non gaussian statistics encountered in real world signals wavelet domain hmms are designed with the intrinsic properties of the wavelet transform in mind and provide powerful yet tractable probabilistic signal models efficient expectation maximization algorithms are developed for fitting the hmms to observational signal data the new framework is suitable for a wide range of applications including signal estimation detection classification prediction and even synthesis to demonstrate the utility of wavelet domain hmms we develop novel algorithms for signal denoising classification and detection

adaptive wavelet thresholding for image denoising and compression the first part of this paper proposes an adaptive data driven threshold for image denoising via wavelet soft thresholding the threshold is derived in a bayesian framework and the prior used on the wavelet coefficients is the generalized gaussian distribution ggd widely used in image processing applications the proposed threshold is simple and closed form and it is adaptive to each subband because it depends on data driven estimates of the parameters experimental results show that the proposed method called bayesshrink is typically within 5 of the mse of the best soft thresholding benchmark with the image assumed known it also outperforms sureshrink donoho and johnstone 1994 1995 donoho 1995 most of the time the second part of the paper attempts to further validate claims that lossy compression can be used for denoising the bayesshrink threshold can aid in the parameter selection of a coder designed with the intention of denoising and thus achieving simultaneous denoising and compression specifically the zero zone in the quantization step of compression is analogous to the threshold value in the thresholding function the remaining coder design parameters are chosen based on a criterion derived from rissanen s minimum description length mdl principle experiments show that this compression method does indeed remove noise significantly especially for large noise power however it introduces quantization noise and should be used only if bitrate were an additional concern to denoising

reliable h control of multiple time scales singularly perturbed systems with sensor failure this paper studies the reliable h control for linear time invariant multiparameter singularly perturbed systems against sensor failures by time scale decomposition the full order system is decomposed into slow and fast subsystems after designing a reliable h controller for the global system three reduced reliable h sub controllers based on the slow and fast problems are obtained through the manipulation of the algebraic riccati equations the resulting control systems are reliable in that they provide guaranteed asymptotic stability and h performance when all control components are operational as well as when sensor failures occur

translation invariant directional framelet transform combined with gabor filters for image denoising this paper is devoted to the study of a directional lifting transform for wavelet frames a nonsubsampled lifting structure is developed to maintain the translation invariance as it is an important property in image denoising then the directionality of the lifting based tight frame is explicitly discussed followed by a specific translation invariant directional framelet transform tidft the tidft has two framelets 1 2 with vanishing moments of order two and one respectively which are able to detect singularities in a given direction set it provides an efficient and sparse representation for images containing rich textures along with properties of fast implementation and perfect reconstruction in addition an adaptive block wise orientation estimation method based on gabor filters is presented instead of the conventional minimization of residuals furthermore the tidft is utilized to exploit the capability of image denoising incorporating the map estimator for multivariate exponential distribution consequently the tidft is able to eliminate the noise effectively while preserving the textures simultaneously experimental results show that the tidft outperforms some other frame based denoising methods such as contourlet and shearlet and is competitive to the state of the art denoising approaches

the discrete shearlet transform a new directional transform and compactly supported shearlet frames it is now widely acknowledged that analyzing the intrinsic geometrical features of the underlying image is essential in many applications including image processing in order to achieve this several directional image representation schemes have been proposed in this paper we develop the discrete shearlet transform dst which provides efficient multiscale directional representation and show that the implementation of the transform is built in the discrete framework based on a multiresolution analysis mra we assess the performance of the dst in image denoising and approximation applications in image approximations our approximation scheme using the dst outperforms the discrete wavelet transform dwt while the computational cost of our scheme is comparable to the dwt also in image denoising the dst compares favorably with other existing transforms in the literature

data compression and harmonic analysis in this paper we review some recent interactions between harmonic analysis and data compression the story goes back of course to shannon s r d theory in the case of gaussian stationary processes which says that transforming into a fourier basis followed by block coding gives an optimal lossy compression technique practical developments like transform based image compression have been inspired by this result in this paper we also discuss connections perhaps less familiar to the information theory community growing out of the field of harmonic analysis recent harmonic analysis constructions such as wavelet transforms and gabor transforms are essentially optimal transforms for transform coding in certain settings some of these transforms are under consideration for future compression standards we discuss some of the lessons of harmonic analysis in this century typically the problems and achievements of this field have involved goals that were not obviously related to practical data compression and have used a language not immediately accessible to outsiders nevertheless through an extensive generalization of what shannon called the sampling theorem harmonic analysis has succeeded in developing new forms of functional representation which turn out to have significant data compression interpretations we explain why harmonic analysis has interacted with data compression and we describe some interesting recent ideas in the field that may affect data compression in the future

local sparse structure denoising for low light level image sparse and redundant representations perform well in image denoising however sparsity based methods fail to denoise low light level lll images because of heavy and complex noise they consider sparsity on image patches independently and tend to lose the texture structures to suppress noises and maintain textures simultaneously it is necessary to embed noise invariant features into the sparse decomposition process we therefore used a local structure preserving sparse coding lspsc formulation to explore the local sparse structures both the sparsity and local structure in image it was found that with the introduction of spatial local structure constraint into the general sparse coding algorithm lspsc could improve the robustness of sparse representation for patches in serious noise we further used a kernel lspsc k lspsc formulation which extends lspsc into the kernel space to weaken the influence of linear structure constraint in nonlinear data based on the robust lspsc and k lspsc algorithms we constructed a local sparse structure denoising lssd model for lll images which was demonstrated to give high performance in the natural lll images denoising indicating that both the lspsc and k lspsc based lssd models have the stable property of noise inhibition and texture details preservation

brief paper new results on h control of discrete singularly perturbed systems this paper studies the problem of h control of discrete time singularly perturbed systems a new sufficient condition which ensures the existence of state feedback controllers such that the resulting closed loop system is asymptotically stable while satisfying a prescribed h norm bound is obtained this condition is in terms of a linear matrix inequality which is independent of the singular perturbation parameter furthermore a new condition on searching for the allowable upper bound of the singular perturbation parameter is proposed under which the discrete time singularly perturbed system is asymptotically stable with an h norm bound when the singular perturbation parameter is lower than this upper bound in these derived conditions the upper bound of the singular perturbation parameter is not required to be smaller than one the reduced conservatism of our results is demonstrated via a numerical example

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

translation invariant contourlet transform and its application to image denoising most subsampled filter banks lack the feature of translation invariance which is an important characteristic in denoising applications in this paper we study and develop new methods to convert a general multichannel multidimensional filter bank to a corresponding translation invariant ti framework in particular we propose a generalized algorithme agrave trous which is an extension of the algorithme agrave trous introduced for 1 d wavelet transforms using the proposed algorithm as well as incorporating modified versions of directional filter banks we construct the ti contourlet transform tict to reduce the high redundancy and complexity of the tict we also introduce semi translation invariant contourlet transform stict then we employ an adapted bivariate shrinkage scheme to the stict to achieve an efficient image denoising approach our experimental results demonstrate the benefits and potential of the proposed denoising approach complexity analysis and efficient realization of the proposed ti schemes are also presented

weighted adaptive lifting based wavelet transform for image coding in this paper a new weighted adaptive lifting wal based wavelet transform is presented the proposed wal approach is designed to solve the problems existing in the previous adaptive directional lifting adl approach such as mismatch between the predict and update steps interpolation favoring only horizontal or vertical direction and invariant interpolation filter coefficients for all images the main contribution of the proposed approach consists of two parts one is the improved weighted lifting which maintains the consistency between the predict and update steps as far as possible and preserves the perfect reconstruction at the same time another is the directional adaptive interpolation which improves the orientation property of the interpolated image and adapts to statistical property of each image experimental results show that the proposed wal based wavelet transform for image coding outperforms the conventional lifting based wavelet transform up to 3 06 db in psnr and significant improvement in subjective quality is also observed compared with the adl based wavelet transform up to 1 22 db improvement in psnr is reported