adaptive bayesian wavelet shrinkage abstract when fitting wavelet based models shrinkage of the empirical wavelet coefficients is an effective tool for denoising the data this article outlines a bayesian approach to shrinkage obtained by placing priors on the wavelet coefficients the prior for each coefficient consists of a mixture of two normal distributions with different standard deviations the simple and intuitive form of prior allows us to propose automatic choices of prior parameters these parameters are chosen adaptively according to the resolution level of the coefficients typically shrinking high resolution frequency coefficients more heavily assuming a good estimate of the background noise level we obtain closed form expressions for the posterior means and variances of the unknown wavelet coefficients the latter may be used to assess uncertainty in the reconstruction several examples are used to illustrate the method and comparisons are made with other shrinkage methods

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

dictionary pair learning on grassmann manifolds for image denoising image denoising is a fundamental problem in computer vision and image processing that holds considerable practical importance for real world applications the traditional patch based and sparse coding driven image denoising methods convert 2d image patches into 1d vectors for further processing thus these methods inevitably break down the inherent 2d geometric structure of natural images to overcome this limitation pertaining to the previous image denoising methods we propose a 2d image denoising model namely the dictionary pair learning dpl model and we design a corresponding algorithm called the dpl on the grassmann manifold dplg algorithm the dplg algorithm first learns an initial dictionary pair i e the left and right dictionaries by employing a subspace partition technique on the grassmann manifold wherein the refined dictionary pair is obtained through a sub dictionary pair merging the dplg obtains a sparse representation by encoding each image patch only with the selected sub dictionary pair the non zero elements of the sparse representation are further smoothed by the graph laplacian operator to remove the noise consequently the dplg algorithm not only preserves the inherent 2d geometric structure of natural images but also performs manifold smoothing in the 2d sparse coding space we demonstrate that the dplg algorithm also improves the structural similarity values of the perceptual visual quality for denoised images using the experimental evaluations on the benchmark images and berkeley segmentation data sets moreover the dplg also produces the competitive peak signal to noise ratio values from popular image denoising algorithms

method of and device for speech signal coding and decoding by subband analysis and vector quantization with dynamic bit allocation according to the coding method the digital speech signal is split into subbands each subband is coded independently of the others the first two subbands undergo an adaptive linear prediction operation yielding a residual normalized with respect to a quantized r m s value the residual samples are quantized and coded by a variable bit number as to the third subband the samples normalized with respect to a quantized gain term are directly quantized and coded by a variable bit number while splitting the subband signals into sample blocks for the first two subbands the coefficient vectors of subband linear prediction filters relevant to each block are also determined by vector quantization and linear prediction inverse filtering operations quantized r m s values are also determined to calculate the numbers of bits permitting subband signals coding the coded signal consists of subband signal quantization level indices of r m s value quantization level indices and of linear prediction filter coefficient vector indices

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

polynomial wavelet regression for images with irregular boundaries in this paper we focus on denoising images for which observations are equally spaced except around the boundaries which are irregular such images are very common in many fields for example in geophysics the advantages of adding a low order polynomial term when implementing a wavelet regression for such images are presented besides removing the classical restriction of having a dyadic of number of observations this strategy reduces the bias at the edges without significantly increasing the risk in addition this method is simple to implement fast and efficient its utility is illustrated with simulation studies and a real example

on the dual tree complex wavelet packet and m band transforms the two band discrete wavelet transform dwt provides an octave band analysis in the frequency domain but this might not be ldquooptimalrdquo for a given signal the discrete wavelet packet transform dwpt provides a dictionary of bases over which one can search for an optimal representation without constraining the analysis to an octave band one for the signal at hand however it is well known that both the dwt and the dwpt are shift varying also when these transforms are extended to 2 d and higher dimensions using tensor products they do not provide a geometrically oriented analysis the dual tree complex wavelet transform introduced by kingsbury is approximately shift invariant and provides directional analysis in 2 d and higher dimensions in this paper we propose a method to implement a dual tree complex wavelet packet transform extending the as the dwpt extends the dwt to find the best complex wavelet packet frame for a given signal we adapt the basis selection algorithm by coifman and wickerhauser providing a solution to the basis selection problem for the lastly we show how to extend the two band to an band provided that using the same method

wavelet threshold estimators for data with correlated noise wavelet threshold estimators for data with stationary correlated noise are constructed by applying a level dependent soft threshold to the coefficients in the wavelet transform a variety of threshold choices is proposed including one based on an unbiased estimate of mean squared error the practical performance of the method is demonstrated on examples including data from a neurophysiological context the theoretical properties of the estimators are investigated by comparing them with an ideal but unattainable bench mark that can be considered in the wavelet context as the risk obtained by ideal spatial adaptivity and more generally is obtained by the use of an oracle that provides information that is not actually available in the data it is shown that the level dependent threshold estimator performs well relative to the bench mark risk and that its minimax behaviour cannot be improved on in order of magnitude by any other estimator the wavelet domain structure of both short and long range dependent noise is considered and in both cases it is shown that the estimators have near optimal behaviour simultaneously in a wide range of function classes adapting automatically to the regularity properties of the underlying model the proofs of the main results are obtained by considering a more general multivariate normal decision theoretic problem

an adaptive parameterized block based singular value decomposition for image de noising and compression abstract we propose an adaptive parametrized block based singular value decomposition apbsvd for preserving the edge structure and avoiding blurred image after the compressing process we also exploit a proper selection of the peak signal to noise ratio psnr parameter at each block to appropriately eliminate high frequency noise our numerical results show that the proposed methods are promising which effectively remove the noise and preserves the edge information well during the block based svd image compression

calculation of minimal capacity vectors through k minimal paths under budget and time constraints abstract reducing the transmission time is an important issue for a flow network to transmit a given amount of data from the source to the sink the quickest path problem thus arises to find a single path with minimum transmission time more specifically the capacity of each arc is assumed to be deterministic however in many real life networks such as computer networks and telecommunication networks the capacity of each arc is stochastic due to failure maintenance etc hence the minimum transmission time is not a fixed number such a network is named a stochastic flow network in order to reduce the transmission time the network allows the data to be transmitted through k minimal paths simultaneously including the cost attribute this paper evaluates the probability that d units of data can be transmitted under both time threshold t and budget b such a probability is called the system reliability an efficient algorithm is proposed to generate all of lower boundary points for d t b the minimal capacity vectors satisfying the demand time and budget requirements the system reliability can then be computed in terms of such points moreover the optimal combination of k minimal paths with highest system reliability can be obtained

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

restoration by compression in this paper we study the topic of signal restoration using complexity regularization quantifying the compression bit cost of the signal estimate while complexity regularized restoration is an established concept solid practical methods were suggested only for the gaussian denoising task leaving more complicated restoration problems without a generally constructive approach here we present practical methods for complexity regularized restoration of signals accommodating deteriorations caused by a known linear degradation operator of an arbitrary form our iterative procedure obtained using the alternating direction method of multipliers admm approach addresses the restoration task as a sequence of simpler problems involving ell 2 regularized estimations and rate distortion optimizations considering the squared error criterion we replace the rate distortion optimizations with an arbitrary standardized compression technique and thereby restore the signal by leveraging underlying models designed for compression additionally we propose a shift invariant complexity regularizer measuring the bit cost of all the shifted forms of the estimate extending our method to use averaging of decompressed outputs gathered from compression of shifted signals on the theoretical side we present an analysis of complexity regularized restoration of a cyclo stationary gaussian signal from deterioration by a linear shift invariant operator and an additive white gaussian noise the theory shows that optimal complexity regularized restoration relies on an elementary restoration filter and compression spreading reconstruction quality unevenly based on the energy distribution of the degradation filter these ideas are realized also in the proposed practical methods finally we present experiments showing good results for image deblurring and inpainting using the jpeg2000 and hevc compression standards

image coding using wavelet transform a scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed this method involves two steps first a wavelet transform used in order to obtain a set of biorthogonal subclasses of images the original image is decomposed at different scales using a pyramidal algorithm architecture the decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image second according to shannon s rate distortion theory the wavelet coefficients are vector quantized using a multiresolution codebook to encode the wavelet coefficients a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed in order to allow the receiver to recognize a picture as quickly as possible at minimum cost a progressive transmission scheme is presented it is shown that the wavelet transform is particularly well adapted to progressive transmission

distribution and reliability evaluation of max flow in dynamic multi state flow networks abstract in this article each arc in multi state flow networks in addition to multi valued capacities and associated operation probabilities is weighted with a transit time as a result the value of max flow from source to sink within specified time horizon is multi valued existing literature evaluates the transit time integrated reliability with a restriction that data is transmitted through k disjoint minimal paths this article considers the same reliability problem however the transmission of data is extended from k disjoint minimal paths to a flow that includes all disjoint and non disjoint minimal paths simultaneously this paper presents an algorithm to evaluate the probability distribution of the values of dynamic max flow the expectation of dynamic max flow as a representation of the distribution can be induced directly the transit time integrated reliability r d t is then computed which is the probability that at least d unit of data can be transmitted from source to sink within time horizon t this study is the first that discusses transit time integrated reliability in terms of flow finally computational experiments are conducted on a benchmark network to explore the properties of the proposed algorithms

nonlinear wavelet image processing variational problems compression and noise removal through wavelet shrinkage this paper examines the relationship between wavelet based image processing algorithms and variational problems algorithms are derived as exact or approximate minimizers of variational problems in particular we show that wavelet shrinkage can be considered the exact minimizer of the following problem given an image f defined on a square i minimize over all g in the besov space b11 l1 i the functional f g l2 i 2 g b11 l1 i we use the theory of nonlinear wavelet image compression in l2 i to derive accurate error bounds for noise removal through wavelet shrinkage applied to images corrupted with i i d mean zero gaussian noise a new signal to noise ratio snr which we claim more accurately reflects the visual perception of noise in images arises in this derivation we present extensive computations that support the hypothesis that near optimal shrinkage parameters can be derived if one knows or can estimate only two parameters about an image f the largest for which f bq lq i 1 q 2 1 2 and the norm f bq lq i both theoretical and experimental results indicate that our choice of shrinkage parameters yields uniformly better results than donoho and johnstone s visushrink procedure an example suggests however that donoho and johnstone s 1994 1995 1996 sureshrink method which uses a different shrinkage parameter for each dyadic level achieves a lower error than our procedure

secure digital speech communication a novel form of waveform coding is used designated a critical point coder cpc it operates by transmitting only those points in a waveform which are significant for defining its overall structure the receiver reconstructs the missing points in the waveform using some sort of approximating interpolation the critical point coder uses a new approach to waveform coding rather than transmitting information about each sample as other waveform coders the critical point coder transmits information for only samples deemed critical to high quality reconstruction the four major functions performed by the critical point coder are 1 detecting which samples are critical called critical points e g those points in the waveform where it is changing direction most rapidly generally the peaks and valleys 2 quantizing the vectors which are formed between successive critical points 3 dealing with the non uniform bit rate since critical points do not occur regularly and 4 reconstructing the waveform between the endpoints of the quantized vectors for stabilizing the bit rate stabilization intervals of fixed duration are divided into equal analysis intervals with logic to select from three modes for quantizing and encoding the vectors during each stabilization interval depending upon the stepsize

fuzzy entropy and its application for enhanced subspace filtering fuzzy entropy fuzzyen which employs the fuzzy probability to characterize the similarity between vectors is a robust nonlinear statistic to quantify the complexity or regularity of nonlinear time series the aim of this study is to investigate the statistical properties of fuzzyen and improve the subspace denoising technique using fuzzyen we first show the asymptotic normality of fuzzyen and derive its variance for finite sample behavior we then analyze the two pending and fundamental issues in subspace denoising i e depending on the so called noise floor and the unaltered noise existing in signal subspace from the point of view of fuzzy logic a fuzzyen assisted subspace iterative soft threshold fesist denoising method which can effectively overcome the deficiency in the existing subspace filtering ssf techniques is presented the effectiveness of the method is first demonstrated on two synthetic chaotic series and then tested on real biological signals the results demonstrate the superiority of the proposed method over existing ssf techniques as well as the empirical mode decomposition and wavelet decomposition approaches

speech enhancement via two stage dual tree complex wavelet packet transform with a speech presence probability estimator in this paper a two stage dual tree complex wavelet packet transform dtcwpt based speech enhancement algorithm has been proposed in which a speech presence probability spp estimator and a generalized minimum mean squared error mmse estimator are developed to overcome the drawback of signal distortions caused by down sampling of wavelet packet transform wpt a two stage analytic decomposition concatenating undecimated wavelet packet transform uwpt and decimated wpt is employed an spp estimator in the dtcwpt domain is derived based on a generalized gamma distribution of speech and gaussian noise assumption the validation results show that the proposed algorithm can obtain enhanced perceptual evaluation of speech quality pesq and segmental signal to noise ratio segsnr at low signal to noise ratio snr nonstationary noise compared with four other state of the art speech enhancement algorithms including optimally modified log spectral amplitude om lsa soft masking using a posteriori snr uncertainty smpo a posteriori spp based mmse estimation mmse spp and adaptive bayesian wavelet thresholding bwt

stochastic flow networks via multiple paths under time threshold and budget constraint this paper extends the quickest path problem to a stochastic flow network in which the capacity of each arc is variable we mainly evaluate the system reliability that d units of data can be sent from the source to the sink under both time threshold t and budget b in particular the data are transmitted through multiple disjoint minimal paths simultaneously in order to reduce the transmission time a simple algorithm is proposed to generate all lower boundary points for d t b and the system reliability can then be computed in terms of such points by utilizing a union of subsets computational complexity in both worst case and average cases show that the proposed algorithm can be executed efficiently

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

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

analytic wavelet packets combining the dual tree approach with wavelet packets for signal analysis and filtering real wavelets or real basis functions in general suffer from two major disadvantages shift variance and oscillating coefficients this paper provides a review of these problems as well as the undecimated wavelet transform which solves the problem of shift variance however undecimated transforms have very high computational costs and still have oscillating coefficients the work of kingsbury is summarized afterwards they have presented a dual tree complex wavelet transform dtcwt which is nearly shift invariant and has smooth coefficients subsequently a filter swapping scheme is developed in order to create complex wavelet packets with analytic basis functions finally the effectiveness of the proposed method is demonstrated by five examples

internet packet routing application of a k quickest path algorithm this paper describes a study on the application of an algorithm to rank the k quickest paths to the routing of data packets in internet networks for this purpose an experimental framework was developed by considering two types of random generated networks to simulate values of the ip packet sizes a truncated pareto distribution was defined having in mind to reflect a key feature of internet traffic namely its self similar stochastic nature results concerning the average cpu times of the algorithm for the different sets of experiments will be presented and discussed

nonlinear wavelet shrinkage with bayes rules and bayes factors abstract wavelet shrinkage the method proposed by the seminal work of donoho and johnstone is a disarmingly simple and efficient way of denoising data shrinking wavelet coefficients was proposed from several optimality criteria in this article a wavelet shrinkage by coherent bayesian inference in the wavelet domain is proposed the methods are tested on standard donoho johnstone test functions

noise level estimation for natural images based on scale invariant kurtosis and piecewise stationarity noise level estimation is crucial in many image processing applications such as blind image denoising in this paper we propose a novel noise level estimation approach for natural images by jointly exploiting the piecewise stationarity and a regular property of the kurtosis in bandpass domains we design a k means based algorithm to adaptively partition an image into a series of non overlapping regions each of whose clean versions is assumed to be associated with a constant but unknown kurtosis throughout scales the noise level estimation is then cast into a problem to optimally fit this new kurtosis model in addition we develop a rectification scheme to further reduce the estimation bias through noise injection mechanism extensive experimental results show that our method can reliably estimate the noise level for a variety of noise types and outperforms some state of the art techniques especially for non gaussian noises

bayesian wavelet based image denoising using the gauss hermite expansion the probability density functions pdfs of the wavelet coefficients play a key role in many wavelet based image processing algorithms such as denoising the conventional pdfs usually have a limited number of parameters that are calculated from the first few moments only consequently such pdfs cannot be made to fit very well with the empirical pdf of the wavelet coefficients of an image as a result the shrinkage function utilizing any of these density functions provides a substandard denoising performance in order for the probabilistic model of the image wavelet coefficients to be able to incorporate an appropriate number of parameters that are dependent on the higher order moments a pdf using a series expansion in terms of the hermite polynomials that are orthogonal with respect to the standard gaussian weight function is introduced a modification in the series function is introduced so that only a finite number of terms can be used to model the image wavelet coefficients ensuring at the same time the resulting pdf to be non negative it is shown that the proposed pdf matches the empirical one better than some of the standard ones such as the generalized gaussian or bessel k form pdf a bayesian image denoising technique is then proposed wherein the new pdf is exploited to statistically model the subband as well as the local neighboring image wavelet coefficients experimental results on several test images demonstrate that the proposed denoising method both in the subband adaptive and locally adaptive conditions provides a performance better than that of most of the methods that use pdfs with limited number of parameters

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

reliability evaluation of a revised stochastic flow network with uncertain minimum time abstract this paper constructs a revised stochastic flow network to model a realistic computer network in which each arc has a lead time and a stochastic capacity the minimum time to send a specified amount of data through the network is thus uncertain hence this paper mainly proposes an approach for evaluating the system reliability that d units of data can be transmitted through k minimal paths simultaneously within the time threshold t the idea of lower boundary points for d t the minimal system states satisfying the demand d within the time threshold t is proposed firstly all system states meeting the time and demand requirements can be represented as the union of subsets generated from all lower boundary points for d t and thus the system reliability is computed quickly

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

multiple shrinkage and subset selection in wavelets this paper discusses bayesian methods for multiple shrinkage estimation in wavelets wavelets are used in applications for data denoising via shrinkage of the coefficients towards zero and for data compression by shrinkage and setting small coefficients to zero we approach wavelet shrinkage by using bayesian hierarchical models assigning a positive prior probability to the wavelet coefficients being zero the resulting estimator for the wavelet coefficients is a multiple shrinkage estimator that exhibits a wide variety of nonlinear patterns we discuss fast computational implementations with a focus on easy to compute analytic approximations as well as importance sampling and markov chain monte carlo methods multiple shrinkage estimators prove to have excellent mean squared error performance in reconstructing standard test functions we demonstrate this in simulated test examples comparing various implementations of multiple shrinkage to commonly used shrinkage rules finally we illustrate our approach with an application to the so called glint data

compressive estimation and imaging based on autoregressive models compressed sensing cs is a fast and efficient way to obtain compact signal representations oftentimes one wishes to extract some information from the available compressed signal since cs signal recovery is typically expensive from a computational point of view it is inconvenient to first recover the signal and then extract the information a much more effective approach consists in estimating the information directly from the signal s linear measurements in this paper we propose a novel framework for compressive estimation of autoregressive ar process parameters based on ad hoc sensing matrix construction more in detail we introduce a compressive least square estimator for ar p parameters and a specific ar 1 compressive bayesian estimator we exploit the proposed techniques to address two important practical problems the first is compressive covariance estimation for toeplitz structured covariance matrices where we tackle the problem with a novel parametric approach based on the estimated ar parameters the second is a block based compressive imaging system where we introduce an algorithm that adaptively calculates the number of measurements to be acquired for each block from a set of initial measurements based on its degree of compressibility we show that the proposed techniques outperform the state of the art methods for these two problems

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 shrinkage asymptopia much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects curves densities spectral densities images from noisy data a now rich and complex body of work develops nearly or exactly minimax estimators for an array of interesting problems unfortunately the results have rarely moved into practice for a variety of reasons among them being similarity to known methods computational intractability and lack of spatial adaptivity we discuss a method for curve estimation based on n noisy data translate the empirical wavelet coefficients towards the origin by an amount 2 log n n the proposal differs from those in current use is computationally practical and is spatially adaptive it thus avoids several of the previous objections further the method is nearly minimax both for a wide variety of loss functions pointwise error global error measured in l p norms pointwise and global error in estimation of derivatives and for a wide range of smoothness classes including standard holder and sobolev classes and bounded variation this is a much broader near optimality than anything previously proposed we draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves finally the theory underlying the method is interesting as it exploits a correspondence between statistical questions and questions of optimal recovery and information based complexity

time version of the shortest path problem in a stochastic flow network many studies on hardware framework and routing policy are devoted to reducing the transmission time for a flow network a time version of the shortest path problem thus arises to find a quickest path which sends a given amount of data from the unique source to the unique sink with minimum transmission time more specifically the capacity of each arc in the flow network is assumed to be deterministic however in many real life networks such as computer systems telecommunication systems etc the capacity of each arc should be stochastic due to failure maintenance etc such a network is named a stochastic flow network hence the minimum transmission time is not a fixed number we extend the quickest path problem to evaluating the probability that d units of data can be sent under the time constraint t such a probability is named the system reliability in particular the data are transmitted through two minimal paths simultaneously in order to reduce the transmission time a simple algorithm is proposed to generate all d t mps and the system reliability can then be computed in terms of d t mps moreover the optimal pair of minimal paths with highest system reliability could be obtained

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

image subband coding using context based classification and adaptive quantization adaptive compression methods have been a key component of many proposed subband or wavelet image coding techniques this paper deals with a particular type of adaptive subband image coding where we focus on the image coder s ability to adjust itself on the fly to the spatially varying statistical nature of image contents this backward adaptation is distinguished from more frequently used forward adaptation in that forward adaptation selects the best operating parameters from a predesigned set and thus uses considerable amount of side information in order for the encoder and the decoder to operate with the same parameters specifically we present backward adaptive quantization using a new context based classification technique which classifies each subband coefficient based on the surrounding quantized coefficients we couple this classification with online parametric adaptation of the quantizer applied to each class a simple uniform threshold quantizer is employed as the baseline quantizer for which adaptation is achieved our subband image coder based on the proposed adaptive classification quantization idea exhibits excellent rate distortion performance in particular at very low rates for popular test images it is comparable or superior to most of the state of the art coders in the literature

filtering random noise from deterministic signals via data compression we present a novel technique for the design of filters for random noise leading to a class of filters called occam filters the essence of the technique is that when a lossy data compression algorithm is applied to a noisy signal with the allowed loss set equal to the noise strength the loss and the noise tend to cancel rather than add we give two illustrative applications of the technique to univariate signals we also prove asymptotic convergence bounds on the effectiveness of occam filters

system reliability for quickest path problems under time threshold and budget many studies on hardware framework and routing policy are devoted to reducing the transmission time for a computer network the quickest path problem thus arises to find a path which sends a given amount of data from the source to the sink such that the transmission time is minimized more specifically the capacity of each arc in the network is assumed to be deterministic however in many real life networks such as computer systems telecommunication systems etc the capacity of each arc is stochastic due to failure maintenance etc such a network is named stochastic flow network hence the minimum transmission time is not a fixed number we extend the quickest path problem to evaluating the probability that d units of data can be sent from the source to the sink under both time threshold t and budget b such a probability is named system reliability a simple algorithm is proposed to generate all lower boundary points for d t b and the system reliability can then be computed in terms of such points

depth first algebraic codebook search for fast coding of speech a codebook is searched in view of encoding a sound signal this codebook consists of a set of codevectors each of 40 positions and comprising n non zero amplitude pulses assignable to predetermined valid positions to reduce the search complexity a depth first search is used which involves a tree structure with levels ordered from 1 through m a path building operation takes place at each level whereby a candidate path from the previous level is extended by choosing a predetermined number of new pulses and selecting valid positions for said new pulses in accordance with a given pulse order rule and a given selection criterion a path originated at the first level and extended by the path building operations of subsequent levels determines the respective positions of the n non zero amplitude pulse of a candidate codevector use of a signal based pulse position likelihood estimate during the first few levels enable initial pulse screening to start the search on favorable conditions a selection criterion based on maximizing a ratio is used to assess the progress and to choose the best one among competing candidate codevectors

function estimation via wavelet shrinkage for long memory data in this article we study function estimation via wavelet shrinkage for data with long range dependence we propose a fractional gaussian noise model to approximate nonparametric regression with long range dependence and establish asymptotics for minimax risks because of long range dependence the minimax risk and the minimax linear risk converge to 0 at rates that differ from those for data with independence or short range dependence wavelet estimates with best selection of resolution leveldependent threshold achieve minimax rates over a wide range of spaces cross validation for dependent data is proposed to select the optimal threshold the wavelet estimates significantly outperform linear estimates the key to proving the asymptotic results is a wavelet vaguelette decomposition which decorrelates fractional gaussian noise such wavelet vaguelette decomposition is also very useful in fractal signal processing

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

speckle suppression in sar images using the 2 d garch model a novel bayesian based speckle suppression method for synthetic aperture radar sar images is presented that preserves the structural features and textural information of the scene first the logarithmic transform of the original image is analyzed into the multiscale wavelet domain we show that the wavelet coefficients of sar images have significantly non gaussian statistics that are best described by the 2 d garch model by using the 2 d garch model on the wavelet coefficients we are capable of taking into account important characteristics of wavelet coefficients such as heavy tailed marginal distribution and the dependencies between the coefficients furthermore we use a maximum a posteriori map estimator for estimating the clean image wavelet coefficients finally we compare our proposed method with various speckle suppression methods applied on synthetic and actual sar images and we verify the performance improvement in utilizing the new strategy

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed