image denoising in steerable pyramid domain based on a local laplace prior this paper presents a new image denoising algorithm based on the modeling of coefficients in each subband of steerable pyramid employing a laplacian probability density function pdf with local variance this pdf is able to model the heavy tailed nature of steerable pyramid coefficients and the empirically observed correlation between the coefficient amplitudes within this framework we describe a novel method for image denoising based on designing both maximum a posteriori map and minimum mean squared error mmse estimators which relies on the zero mean laplacian random variables with high local correlation despite the simplicity of our spatially adaptive denoising method both in its concern and implementation our denoising results achieves better performance than several published methods such as bayes least squared gaussian scale mixture bls gsm technique that is a state of the art denoising technique

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

an orientation selective orthogonal lapped transform a novel critically sampled orientation selective orthogonal lapped transform called the lapped hartley transform lht is derived in a first step overlapping basis functions are generated by modulating basis functions of a 2 d block hartley transform by a cosine wave to achieve invertibility and orthogonality an iterative filter is applied as prefilter in the analysis and as postfilter in the synthesis operation respectively alternatively filtering can be restricted to analysis or synthesis ending up with a biorthogonal transform lht pr lht po a statistical analysis based on a 4000 image data base shows that the lht and lht po have better redundancy removal properties than other block or lapped transforms finally image compression and noise removal examples are given showing the advantages of the lht especially in images containing oriented textures

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

image denoising in mixed poisson gaussian noise we propose a general methodology pure let to design and optimize a wide class of transform domain thresholding algorithms for denoising images corrupted by mixed poisson gaussian noise we express the denoising process as a linear expansion of thresholds let that we optimize by relying on a purely data adaptive unbiased estimate of the mean squared error mse derived in a non bayesian framework pure poisson gaussian unbiased risk estimate we provide a practical approximation of this theoretical mse estimate for the tractable optimization of arbitrary transform domain thresholding we then propose a pointwise estimator for undecimated filterbank transforms which consists of subband adaptive thresholding functions with signal dependent thresholds that are globally optimized in the image domain we finally demonstrate the potential of the proposed approach through extensive comparisons with state of the art techniques that are specifically tailored to the estimation of poisson intensities we also present denoising results obtained on real images of low count fluorescence microscopy

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

a new sure approach to image denoising interscale orthonormal wavelet thresholding this paper introduces a new approach to orthonormal wavelet image denoising instead of postulating a statistical model for the wavelet coefficients we directly parametrize the denoising process as a sum of elementary nonlinear processes with unknown weights we then minimize an estimate of the mean square error between the clean image and the denoised one the key point is that we have at our disposal a very accurate statistically unbiased mse estimate stein s unbiased risk estimate that depends on the noisy image alone not on the clean one like the mse this estimate is quadratic in the unknown weights and its minimization amounts to solving a linear system of equations the existence of this a priori estimate makes it unnecessary to devise a specific statistical model for the wavelet coefficients instead and contrary to the custom in the literature these coefficients are not considered random any more we describe an interscale orthonormal wavelet thresholding algorithm based on this new approach and show its near optimal performance both regarding quality and cpu requirement by comparing it with the results of three state of the art nonredundant denoising algorithms on a large set of test images an interesting fallout of this study is the development of a new group delay based parent child prediction in a wavelet dyadic tree

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

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

single image super resolution using local geometric duality and non local similarity super resolution sr from a single image plays an important role in many computer vision applications it aims to estimate a high resolution hr image from an input low resolution lr image to ensure a reliable and robust estimation of the hr image we propose a novel single image sr method that exploits both the local geometric duality gd and the non local similarity of images the main principle is to formulate these two typically existing features of images as effective priors to constrain the super resolved results in consideration of this principle the robust soft decision interpolation method is generalized as an outstanding adaptive gd agd based local prior to adaptively design weights for the agd prior a local non smoothness detection method and a directional standard deviation based weights selection method are proposed after that the agd prior is combined with a variational framework based non local prior furthermore the proposed algorithm is speeded up by a fast gd matrices construction method which primarily relies on the selective pixel processing the extensive experimental results verify the effectiveness of the proposed method compared with several state of the art sr algorithms

a nonlinear stein based estimator for multichannel image denoising the use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions however the observed images are often corrupted by an additive gaussian noise in this paper we are interested in multichannel image denoising based on a multiscale representation of the images a multivariate statistical approach is adopted to take into account both the spatial and the intercomponent correlations existing between the different wavelet subbands more precisely we propose a new parametric nonlinear estimator which generalizes many reported denoising methods the derivation of the optimal parameters is achieved by applying stein s principle in the multivariate case experiments performed on multispectral remote sensing images clearly indicate that our method outperforms conventional wavelet denoising techniques

the sure let approach to image denoising we propose a new approach to image denoising based on the image domain minimization of an estimate of the mean squared error stein s unbiased risk estimate sure unlike most existing denoising algorithms using the sure makes it needless to hypothesize a statistical model for the noiseless image a key point of our approach is that although the nonlinear processing is performed in a transformed domain typically an undecimated discrete wavelet transform but we also address nonorthonormal transforms this minimization is performed in the image domain indeed we demonstrate that when the transform is a ldquotightrdquo frame an undecimated wavelet transform using orthonormal filters separate subband minimization yields substantially worse results in order for our approach to be viable we add another principle that the denoising process can be expressed as a linear combination of elementary denoising processes linear expansion of thresholds let armed with the sure and let principles we show that a denoising algorithm merely amounts to solving a linear system of equations which is obviously fast and efficient quite remarkably the very competitive results obtained by performing a simple threshold image domain sure optimized on the undecimated haar wavelet coefficients show that the sure let principle has a huge potential

randomizing quantum states constructions and applications the construction of a perfectly secure private quantum channel in dimension d is known to require 2 log d shared random key bits between the sender and receiver we show that if only near perfect security is required the size of the key can be reduced by a factor of two more specifically we show that there exists a set of roughly d log d unitary operators whose average effect on every input pure state is almost perfectly randomizing as compared to the d2 operators required to randomize perfectly aside from the private quantum channel variations of this construction can be applied to many other tasks in quantum information processing we show for instance that it can be used to construct locc data hiding schemes for bits and qubits that are much more efficient than any others known allowing roughly log d qubits to be hidden in 2 log d qubits the method can also be used to exhibit the existence of quantum states with locked classical correlations an arbitrarily large amplification of the correlation being accomplished by sending a negligibly small classical key our construction also provides the basic building block for a method of remotely preparing arbitrary d dimensional pure quantum states using approximately log d bits of communication and log d ebits of entanglement

rtni a symbolic integrator for haar random tensor networks we provide a computer algebra package called random tensor network integrator rtni it allows to compute averages of tensor networks containing multiple haar distributed random unitary matrices and deterministic symbolic tensors such tensor networks are represented as multigraphs with vertices corresponding to tensors or random unitaries and edges corresponding to tensor contractions input and output spaces of random unitaries may be subdivided into arbitrary tensor factors with dimensions treated symbolically the algorithm implements the graphical weingarten calculus and produces a weighted sum of tensor networks representing the average over the unitary group we illustrate the use of this algorithmic tool on some examples from quantum information theory including entropy calculations for random tensor network states as considered in toy models for holographic duality mathematica and python implementations are supplied

finite element techniques for removing the mixture of gaussian and impulsive noise the finite element method has become a very powerful and popular tool to solve boundary value problems coming from science and engineering here we consider a scattered data fitting method based on the finite element method and apply the method to remove the mixture of gaussian and impulsive noise from an image numerical results show the performance of the approach

better subset regression using the nonnegative garrote a new method called the nonnegative nn garrote is proposed for doing subset regression it both shrinks and zeroes coefficients in tests on real and simulated data it produces lower prediction error than ordinary subset selection it is also compared to ridge regression if the regression equations generated by a procedure do not change drastically with small changes in the data the procedure is called stable subset selection is unstable ridge is very stable and the nn garrote is intermediate simulation results illustrate the effects of instability on prediction error

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

patch based near optimal image denoising in this paper we propose a denoising method motivated by our previous analysis of the performance bounds for image denoising insights from that study are used here to derive a high performance practical denoising algorithm we propose a patch based wiener filter that exploits patch redundancy for image denoising our framework uses both geometrically and photometrically similar patches to estimate the different filter parameters we describe how these parameters can be accurately estimated directly from the input noisy image our denoising approach designed for near optimal performance in the mean squared error sense has a sound statistical foundation that is analyzed in detail the performance of our approach is experimentally verified on a variety of images and noise levels the results presented here demonstrate that our proposed method is on par or exceeding the current state of the art both visually and quantitatively

behavioral analysis of anisotropic diffusion in image processing in this paper we analyze the behavior of the anisotropic diffusion model of perona and malik 1990 the main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem so its behavior can be analyzed based on the shape of the corresponding energy surface we show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem it is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space we give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima the mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator and the other that flows normally to the edges and thus acts as an enhancement operator

generalized sure for exponential families applications to regularization stein s unbiased risk estimate sure was proposed by stein for the independent identically distributed i i d gaussian model in order to derive estimates that dominate least squares ls recently the sure criterion has been employed in a variety of denoising problems for choosing regularization parameters that minimize an estimate of the mean squared error mse however its use has been limited to the i i d case which precludes many important applications in this paper we begin by deriving a sure counterpart for general not necessarily i i d distributions from the exponential family this enables extending the sure design technique to a much broader class of problems based on this generalization we suggest a new method for choosing regularization parameters in penalized ls estimators we then demonstrate its superior performance over the conventional generalized cross validation and discrepancy approaches in the context of image deblurring and deconvolution the sure technique can also be used to design estimates without predefining their structure however allowing for too many free parameters impairs the estimate s performance to address this inherent tradeoff we propose a regularized sure objective and demonstrate its use in the context of wavelet denoising

principal neighborhood dictionaries for nonlocal means image denoising we present an in depth analysis of a variation of the nonlocal means nlm image denoising algorithm that uses principal component analysis pca to achieve a higher accuracy while reducing computational load image neighborhood vectors are first projected onto a lower dimensional subspace using pca the dimensionality of this subspace is chosen automatically using parallel analysis consequently neighborhood similarity weights for denoising are computed using distances in this subspace rather than the full space the resulting algorithm is referred to as principal neighborhood dictionary pnd nonlocal means we investigate pnd s accuracy as a function of the dimensionality of the projection subspace and demonstrate that denoising accuracy peaks at a relatively low number of dimensions the accuracy of nlm and pnd are also examined with respect to the choice of image neighborhood and search window sizes finally we present a quantitative and qualitative comparison of pnd versus nlm and another image neighborhood pca based state of the art image denoising algorithm

no reference image quality assessment in the spatial domain we propose a natural scene statistic based distortion generic blind no reference nr image quality assessment iqa model that operates in the spatial domain the new model dubbed blind referenceless image spatial quality evaluator brisque does not compute distortion specific features such as ringing blur or blocking but instead uses scene statistics of locally normalized luminance coefficients to quantify possible losses of naturalness in the image due to the presence of distortions thereby leading to a holistic measure of quality the underlying features used derive from the empirical distribution of locally normalized luminances and products of locally normalized luminances under a spatial natural scene statistic model no transformation to another coordinate frame dct wavelet etc is required distinguishing it from prior nr iqa approaches despite its simplicity we are able to show that brisque is statistically better than the full reference peak signal to noise ratio and the structural similarity index and is highly competitive with respect to all present day distortion generic nr iqa algorithms brisque has very low computational complexity making it well suited for real time applications brisque features may be used for distortion identification as well to illustrate a new practical application of brisque we describe how a nonblind image denoising algorithm can be augmented with brisque in order to perform blind image denoising results show that brisque augmentation leads to performance improvements over state of the art methods a software release of brisque is available online http live ece utexas edu research quality brisque release zip for public use and evaluation

a sure approach for digital signal image deconvolution problems in this paper we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white gaussian noise the originality of the proposed approach is twofold first we formulate the restoration problem as a nonlinear estimation problem leading to the minimization of a criterion derived from stein s unbiased quadratic risk estimate secondly the deconvolution procedure is performed using any analysis and synthesis frames that can be overcomplete or not new theoretical results concerning the calculation of the variance of the stein s risk estimate are also provided in this work simulations carried out on natural images show the good performance of our method with respect to conventional wavelet based restoration methods

image denoising using svm classification in nonsubsampled contourlet transform domain for image denoising the main challenge is how to preserve the information bearing structures such as edges and textures to get satisfactory visual quality when improving the signal to noise ratio snr edge preserving image denoising has become a very intensive research topic in this paper we propose an image denoising using support vector machine svm classification in nonsubsampled contourlet transform nsct domain firstly the noisy image is decomposed into different subbands of frequency and orientation responses using the nsct secondly the feature vector for a pixel in a noisy image is formed by the spatial regularity in nsct domain and the least squares support vector machine ls m model is obtained by training then the nsct detail coefficients are divided into two classes edge related coefficients and noise related ones by ls svm training model finally the detail subbands of nsct coefficients are denoised by using shrink method in which the adaptive bayesian threshold is utilized extensive experimental results demonstrate that our method can obtain better performances in terms of both subjective and objective evaluations than those state of the art denoising techniques especially the proposed method can preserve edges very well while removing noise

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

asymptotic values of vector measure games in honor of l s shapley s eightieth birthday the asymptotic value introduced by kannai in 1966 is an asymptotic approach to the notion of the shapley value for games with infinitely many players a vector measure game is a gamev where the worthv s of a coalitions is a functionf of s where is a vector measure special classes of vector measure games are the weighted majority games and the two house weighted majority games where a two house weighted majority game is a game in which a coalition is winning if and only if it is winning in two given weighted majority games all weighted majority games have an asymptotic value however not all two house weighted majority games have an asymptotic value in this paper we prove that the existence of infinitely many atoms with sufficient variety suffice for the existence of the asymptotic value in a general class of nonsmooth vector measure games that includes in particular two house weighted majority games

integration with respect to the haar measure on unitary orthogonal and symplectic group we revisit the work of the first named author and using simpler algebraic arguments we calculate integrals of polynomial functions with respect to the haar measure on the unitary group u d the previous result provided exact formulas only for 2d bigger than the degree of the integrated polynomial and we show that these formulas remain valid for all values of d also we consider the integrals of polynomial functions on the orthogonal group o d and the symplectic group sp d we obtain an exact character expansion and the asymptotic behavior for large d thus we can show the asymptotic freeness of haar distributed orthogonal and symplectic random matrices as well as the convergence of integrals of the itzykson zuber type

novel speed up strategies for non local means denoising with patch and edge patch based dictionaries in this paper a novel technique to speed up a non local means nlm filter is proposed in the original nlm filter most of its computational time is spent on finding distances for all the patches in the search window here we build a dictionary in which patches with similar photometric structures are clustered together dictionary is built only once with high resolution images belonging to different scenes since the dictionary is well organized in terms of indexing its entries it is used to search similar patches very quickly for efficient nlm denoising we achieve a substantial reduction in computational cost compared with the original nlm method especially when the search window of nlm is large without much affecting the psnr second we show that by building a dictionary for edge patches as opposed to intensity patches it is possible to reduce the dictionary size thus further improving the computational speed and memory requirement the proposed method preclassifies similar patches with the same distance measure as used by nlm method the proposed algorithm is shown to outperform other prefiltering based fast nlm algorithms computationally as well as qualitatively

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

multiresolution bilateral filtering for image denoising the bilateral filter is a nonlinear filter that does spatial averaging without smoothing edges it has shown to be an effective image denoising technique an important issue with the application of the bilateral filter is the selection of the filter parameters which affect the results significantly there are two main contributions of this paper the first contribution is an empirical study of the optimal bilateral filter parameter selection in image denoising applications the second contribution is an extension of the bilateral filter multiresolution bilateral filter where bilateral filtering is applied to the approximation low frequency subbands of a signal decomposed using a wavelet filter bank the multiresolution bilateral filter is combined with wavelet thresholding to form a new image denoising framework which turns out to be very effective in eliminating noise in real noisy images experimental results with both simulated and real data are provided

image denoising via bandwise adaptive modeling and regularization exploiting nonlocal similarity this paper proposes a new image denoising algorithm based on adaptive signal modeling and regularization it improves the quality of images by regularizing each image patch using bandwise distribution modeling in transform domain instead of using a global model for all the patches in an image it employs content dependent adaptive models to address the non stationarity of image signals and also the diversity among different transform bands the distribution model is adaptively estimated for each patch individually it varies from one patch location to another and also varies for different bands in particular we consider the estimated distribution to have non zero expectation to estimate the expectation and variance parameters for every band of a particular patch we exploit the nonlocal correlation in image to collect a set of highly similar patches as the data samples to form the distribution irrelevant patches are excluded so that such adaptively learned model is more accurate than a global one the image is ultimately restored via bandwise adaptive soft thresholding based on a laplacian approximation of the distribution of similar patch group transform coefficients experimental results demonstrate that the proposed scheme outperforms several state of the art denoising methods in both the objective and the perceptual qualities

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

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

pure let image deconvolution we propose a non iterative image deconvolution algorithm for data corrupted by poisson or mixed poisson gaussian noise many applications involve such a problem ranging from astronomical to biological imaging we parameterize the deconvolution process as a linear combination of elementary functions termed as linear expansion of thresholds this parameterization is then optimized by minimizing a robust estimate of the true mean squared error the poisson unbiased risk estimate each elementary function consists of a wiener filtering followed by a pointwise thresholding of undecimated haar wavelet coefficients in contrast to existing approaches the proposed algorithm merely amounts to solving a linear system of equations which has a fast and exact solution simulation experiments over different types of convolution kernels and various noise levels indicate that the proposed method outperforms the state of the art techniques in terms of both restoration quality and computational complexity finally we present some results on real confocal fluorescence microscopy images and demonstrate the potential applicability of the proposed method for improving the quality of these images

on the selection of optimum savitzky golay filters savitzky golay s g filters are finite impulse response lowpass filters obtained while smoothing data using a local least squares ls polynomial approximation savitzky and golay proved in their hallmark paper that local ls fitting of polynomials and their evaluation at the mid point of the approximation interval is equivalent to filtering with a fixed impulse response the problem that we address here is how to choose a pointwise minimum mean squared error mmse s g filter length or order for smoothing while preserving the temporal structure of a time varying signal we solve the bias variance tradeoff involved in the mmse optimization using stein s unbiased risk estimator sure we observe that the 3 db cutoff frequency of the sure optimal s g filter is higher where the signal varies fast locally and vice versa essentially enabling us to suitably trade off the bias and variance thereby resulting in near mmse performance at low signal to noise ratios snrs it is seen that the adaptive filter length algorithm performance improves by incorporating a regularization term in the sure objective function we consider the algorithm performance on real world electrocardiogram ecg signals the results exhibit considerable snr improvement noise performance analysis shows that the proposed algorithms are comparable and in some cases better than some standard denoising techniques available in the literature

monte carlo sure a black box optimization of regularization parameters for general denoising algorithms we consider the problem of optimizing the parameters of a given denoising algorithm for restoration of a signal corrupted by white gaussian noise to achieve this we propose to minimize stein s unbiased risk estimate sure which provides a means of assessing the true mean squared error mse purely from the measured data without need for any knowledge about the noise free signal specifically we present a novel monte carlo technique which enables the user to calculate sure for an arbitrary denoising algorithm characterized by some specific parameter setting our method is a black box approach which solely uses the response of the denoising operator to additional input noise and does not ask for any information about its functional form this therefore permits the use of sure for optimization of a wide variety of denoising algorithms we justify our claims by presenting experimental results for sure based optimization of a series of popular image denoising algorithms such as total variation denoising wavelet soft thresholding and wiener filtering smoothing splines in the process we also compare the performance of these methods we demonstrate numerically that sure computed using the new approach accurately predicts the true mse for all the considered algorithms we also show that sure uncovers the optimal values of the parameters in all cases

image denoising using trivariate shrinkage filter in the wavelet domain and joint bilateral filter in the spatial domain this correspondence proposes an efficient algorithm for removing gaussian noise from corrupted image by incorporating a wavelet based trivariate shrinkage filter with a spatial based joint bilateral filter in the wavelet domain the wavelet coefficients are modeled as trivariate gaussian distribution taking into account the statistical dependencies among intrascale wavelet coefficients and then a trivariate shrinkage filter is derived by using the maximum a posteriori map estimator although wavelet based methods are efficient in image denoising they are prone to producing salient artifacts such as low frequency noise and edge ringing which relate to the structure of the underlying wavelet on the other hand most spatial based algorithms output much higher quality denoising image with less artifacts however they are usually too computationally demanding in order to reduce the computational cost we develop an efficient joint bilateral filter by using the wavelet denoising result rather than directly processing the noisy image in the spatial domain this filter could suppress the noise while preserve image details with small computational cost extension to color image denoising is also presented we compare our denoising algorithm with other denoising techniques in terms of psnr and visual quality the experimental results indicate that our algorithm is competitive with other denoising techniques

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

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

counterexamples to additivity of minimum output p renyi entropy for p close to 0 complementing recent progress on the additivity conjecture of quantum information theory showing that the minimum output p renyi entropies of channels are not generally additive for p 1 we demonstrate here by a careful random selection argument that also at p 0 and consequently for sufficiently small p there exist counterexamples

weighted majority games have asymptotic value the asymptotic value of a game v with a continuum set of players i is defined whenever all the sequences of the shapley values of finite games that approximate v have the same limit a weighted majority game is a game of the form f where is a positive measure and fx 1 if x q and fx 0 otherwise and q is a real number 0 q i in this paper we prove that all weighted majority games have asymptotic values this result is then used further to show that if v is of the form v f where is a probability measure and f is a function of bounded variation on 0 1 that is continuous at 0 and at 1 then v has an asymptotic value this bad previously been known only when f is absolutely continuous or when has at most finitely many atoms or when is purely atomic thus the essential novelty is that even when has countably many atoms and a nonatomic part f has an asymptotic value we also show that f does not necessarily have an asymptotic value when is a signed measure

shearlet based deconvolution in this paper a new type of deconvolution algorithm is proposed that is based on estimating the image from a shearlet decomposition shearlets provide a multidirectional and multiscale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets constructions such as curvelets and contourlets share similar properties yet their implementations are significantly different from that of shearlets taking advantage of unique properties of a new m channel implementation of the shearlet transform we develop an algorithm that allows for the approximation inversion operator to be controlled on a multiscale and multidirectional basis a key improvement over closely related approaches such as forward is the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation gcv various tests show that this method can perform significantly better than many competitive deconvolution algorithms

on covering single points by randomly ordered intervals a strictly increasing pure jump process with stationary independent increments hits a single point r 0 with probability 0 adapting a method of proof due to carleson we obtain a similar result for processes with exchangeable increments this enables us to solve a regularity problem from game theory concerning probabilities of covering single points by randomly ordered intervals

bayesian estimation for continuous time sparse stochastic processes we consider continuous time sparse stochastic processes from which we have only a finite number of noisy noiseless samples our goal is to estimate the noiseless samples denoising and the signal in between interpolation problem by relying on tools from the theory of splines we derive the joint a priori distribution of the samples and show how this probability density function can be factorized the factorization enables us to tractably implement the maximum a posteriori and minimum mean square error mmse criteria as two statistical approaches for estimating the unknowns we compare the derived statistical methods with well known techniques for the recovery of sparse signals such as the l1 norm and log l1 l0 relaxation regularization methods the simulation results show that under certain conditions the performance of the regularization techniques can be very close to that of the mmse estimator

building robust wavelet estimators for multicomponent images using stein s principle multichannel imaging systems provide several observations of the same scene which are often corrupted by noise in this paper we are interested in multispectral image denoising in the wavelet domain we adopt a multivariate statistical approach in order to exploit the correlations existing between the different spectral components our main contribution is the application of stein s principle to build a new estimator for arbitrary multichannel images embedded in additive gaussian noise simulation tests carried out on optical satellite images show that the proposed method outperforms conventional wavelet shrinkage techniques

optimal denoising in redundant representations image denoising methods are often designed to minimize mean squared error mse within the subbands of a multiscale decomposition however most high quality denoising results have been obtained with overcomplete representations for which minimization of mse in the subband domain does not guarantee optimal mse performance in the image domain we prove that despite this suboptimality the expected image domain mse resulting from applying estimators to subbands that are made redundant through spatial replication of basis functions e g cycle spinning is always less than or equal to that resulting from applying the same estimators to the original nonredundant representation in addition we show that it is possible to further exploit overcompleteness by jointly optimizing the subband estimators for image domain mse we develop an extended version of stein s unbiased risk estimate sure that allows us to perform this optimization adaptively for each observed noisy image we demonstrate this methodology using a new class of estimator formed from linear combinations of localized ldquobumprdquo functions that are applied either pointwise or on local neighborhoods of subband coefficients we show through simulations that the performance of these estimators applied to overcomplete subbands and optimized for image domain mse is substantially better than that obtained when they are optimized within each subband this performance is in turn substantially better than that obtained when they are optimized for use on a nonredundant representation

nonlocal means with dimensionality reduction and sure based parameter selection nonlocal means nlm is an effective denoising method that applies adaptive averaging based on similarity between neighborhoods in the image an attractive way to both improve and speed up nlm is by first performing a linear projection of the neighborhood one particular example is to use principal components analysis pca to perform dimensionality reduction here we derive stein s unbiased risk estimate sure for nlm with linear projection of the neighborhoods the sure can then be used to optimize the parameters by a search algorithm or we can consider a linear expansion of multiple nlms each with a fixed parameter set for which the optimal weights can be found by solving a linear system of equations the experimental results demonstrate the accuracy of the sure and its successful application to tune the parameters for nlm

dictionary learning algorithms for sparse representation algorithms for data driven learning of domain specific overcomplete dictionaries are developed to obtain maximum likelihood and maximum a posteriori dictionary estimates based on the use of bayesian models with concave schur concave csc negative log priors such priors are appropriate for obtaining sparse representations of environmental signals within an appropriately chosen environmentally matched dictionary the elements of the dictionary can be interpreted as concepts features or words capable of succinct expression of events encountered in the environment the source of the measured signals this is a generalization of vector quantization in that one is interested in a description involving a few dictionary entries the proverbial 25 words or less but not necessarily as succinct as one entry to learn an environmentally adapted dictionary capable of concise expression of signals generated by the environment we develop algorithms that iterate between a representative set of sparse representations found by variants of focuss and an update of the dictionary using these sparse representations experiments were performed using synthetic data and natural images for complete dictionaries we demonstrate that our algorithms have improved performance over other independent component analysis ica methods measured in terms of signal to noise ratios of separated sources in the overcomplete case we show that the true underlying dictionary and sparse sources can be accurately recovered in tests with natural images learned overcomplete dictionaries are shown to have higher coding efficiency than complete dictionaries that is images encoded with an overcomplete dictionary have both higher compression fewer bits per pixel and higher accuracy lower mean square error

regularization parameter selection for nonlinear iterative image restoration and mri reconstruction using gcv and sure based methods regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values we focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive possibly complex gaussian noise generalized cross validation gcv and weighted mean squared error mse approaches based on stein s unbiased risk estimate sure need the jacobian matrix of the nonlinear reconstruction operator representative of the iterative algorithm with respect to the data we derive the desired jacobian matrix for two types of nonlinear iterative algorithms a fast variant of the standard iterative reweighted least squares method and the contemporary split bregman algorithm both of which can accommodate a wide variety of analysis and synthesis type regularizers the proposed approach iteratively computes two weighted sure type measures predicted sure and projected sure which require knowledge of noise variance 2 and gcv which does not need 2 for these algorithms we apply the methods to image restoration and to magnetic resonance image mri reconstruction using total variation and an analysis type l1 regularization we demonstrate through simulations and experiments with real data that minimizing predicted sure and projected sure consistently lead to near mse optimal reconstructions we also observe that minimizing gcv yields reconstruction results that are near mse optimal for image restoration and slightly suboptimal for mri theoretical derivations in this paper related to jacobian matrix evaluations can be extended in principle to other types of regularizers and reconstruction algorithms

wavelet based image denoising using a markov random field a priori model this paper describes a new method for the suppression of noise in images via the wavelet transform the method relies on two measures the first is a classic measure of smoothness of the image and is based on an approximation of the local holder exponent via the wavelet coefficients the second novel measure takes into account geometrical constraints which are generally valid for natural images the smoothness measure and the constraints are combined in a bayesian probabilistic formulation and are implemented as a markov random field mrf image model the manipulation of the wavelet coefficients is consequently based on the obtained probabilities a comparison of quantitative and qualitative results for test images demonstrates the improved noise suppression performance with respect to previous wavelet based image denoising methods

wavelet thresholding via a bayesian approach we discuss a bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression a prior distribution is imposed on the wavelet coefficients of the unknown response function designed to capture the sparseness of wavelet expansion that is common to most applications for the prior specified the posterior median yields a thresholding procedure our prior model for the underlying function can be adjusted to give functions falling in any specific besov space we establish a relationship between the hyperparameters of the prior model and the parameters of those besov spaces within which realizations from the prior will fall such a relationship gives insight into the meaning of the besov space parameters moreover the relationship established makes it possible in principle to incorporate prior knowledge about the function s regularity properties into the prior model for its wavelet coefficients however prior knowledge about a function s regularity properties might be difficult to elicit with this in mind we propose a standard choice of prior hyperparameters that works well in our examples several simulated examples are used to illustrate our method and comparisons are made with other thresholding methods we also present an application to a data set that was collected in an anaesthesiological study

counterexamples to the maximal p norm multiplicativity conjecture for all p 1 for all p 1 we demonstrate the existence of quantum channels with non multiplicative maximal output p norms equivalently for all p 1 the minimum output renyi entropy of order p of a quantum channel is not additive the violations found are large in all cases the minimum output renyi entropy of order p for a product channel need not be significantly greater than the minimum output entropy of its individual factors since p 1 corresponds to the von neumann entropy these counterexamples demonstrate that if the additivity conjecture of quantum information theory is true it cannot be proved as a consequence of any channel independent guarantee of maximal p norm multiplicativity we also show that a class of channels previously studied in the context of approximate encryption lead to counterexamples for all p 2