nonlinear wavelet transforms for image coding via lifting we investigate central issues such as invertibility stability synchronization and frequency characteristics for nonlinear wavelet transforms built using the lifting framework the nonlinearity comes from adaptively choosing between a class of linear predictors within the lifting framework we also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood of pixels preliminary compression results for model and real world images demonstrate the promise of our techniques

design of steerable wavelets to detect multifold junctions we propose a framework for the detection of junctions in images although the detection of edges and key points is a well examined and described area the multiscale detection of junction centers especially for odd orders poses a challenge in pattern analysis the goal of this paper is to build optimal junction detectors based on 2d steerable wavelets that are polar separable in the fourier domain the approaches we develop are general and can be used for the detection of arbitrary symmetric and asymmetric junctions the backbone of our construction is a multiscale pyramid with a radial wavelet function where the directional components are represented by circular harmonics and encoded in a shaping matrix we are able to detect m fold junctions in different scales and orientations we provide experimental results on both simulated and real data to demonstrate the effectiveness of the algorithm

sparse geometric image representations with bandelets this paper introduces a new class of bases called bandelet bases which decompose the image along multiscale vectors that are elongated in the direction of a geometric flow this geometric flow indicates directions in which the image gray levels have regular variations the image decomposition in a bandelet basis is implemented with a fast subband filtering algorithm bandelet bases lead to optimal approximation rates for geometrically regular images for image compression and noise removal applications the geometric flow is optimized with fast algorithms so that the resulting bandelet basis produces minimum distortion comparisons are made with wavelet image compression and noise removal algorithms

wideband spectrum sensing based on sub nyquist sampling in this paper we consider the problem of locating multiple active spectrum subbands in a wide range of frequency bands a major challenge associated with such wideband spectrum sensing is that it is either infeasible or too expensive to perform nyquist sampling on the wideband signal in this paper we propose a sensing scheme based on a sub nyquist sampling method called multicoset sampling which is similar to the polyphase implementation of the nyquist sampling but requires less a d converters in contrast to the traditional sub nquist approaches where the wideband signal is first reconstructed from the sub nyquist samples we develop a method that directly estimates the power spectrum of the wideband signal of interest using the sub nyquist samples by exploiting its statistical properties we also characterize the statistical distribution of the proposed power spectrum estimator based on which we obtain a constant false alarm energy detector for the frequency bins simulation results are provided to demonstrate the effectiveness of the proposed multiband spectrum sensing method based on sub nyquist sampling

approximate orientation steerability based on angular gaussians junctions are significant features in images with intensity variation that exhibits multiple orientations this makes the detection and characterization of junctions a challenging problem the characterization of junctions would ideally be given by the response of a filter at every orientation this can be achieved by the principle of steerability that enables the decomposition of a filter into a linear combination of basis functions however current steerability approaches suffer from the consequences of the uncertainty principle in order to achieve high resolution in orientation they need a large number of basis filters increasing thus the computational complexity furthermore these functions have usually a wide support which only accentuates the computational burden we propose a novel alternative to current steerability approaches it is based on utilizing a set of polar separable filters with small support to sample orientation information the orientation signature is then obtained by interpolating orientation samples using gaussian functions with small support compared with current steerability techniques our approach achieves a higher orientation resolution with a lower complexity in addition we build a polar pyramid to characterize junctions of arbitrary inherent orientation scales

directionlets anisotropic multidirectional representation with separable filtering in spite of the success of the standard wavelet transform wt in image processing in recent years the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions one dimensional 1 d discontinuities in images edges and contours that are very important elements in visual perception intersect too many wavelet basis functions and lead to a nonsparse representation to efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions a more complex multidirectional m dir and anisotropic transform is required we present a new lattice based perfect reconstruction and critically sampled anisotropic m dir wt the transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two dimensional wt unlike in the case of some other directional transform constructions e g curvelets contourlets or edgelets the corresponding anisotropic basis functions directionlets have directional vanishing moments along any two directions with rational slopes furthermore we show that this novel transform provides an efficient tool for nonlinear approximation of images achieving the approximation power o n sup 1 55 which while slower than the optimal rate o n sup 2 is much better than o n sup 1 achieved with wavelets but at similar complexity

rotated orthogonal transform rot for motion compensation residual coding discrete cosine transform dct is the orthogonal transform that is most commonly used in image and video compression the motion compensation residual mc residual is also compressed with the dct in most video codecs however the mc residual has different characteristics from a nature image in this paper we develop a new orthogonal transform rotated orthogonal transform rot that can perform better on the mc residual than the dct for coding purposes we derive the proposed rot based on orthogonal constrained l1 norm minimization problem for its sparse property using the dct matrix as the starting point a better orthogonal transform matrix is derived in addition by exploring inter frame dependency and local motion activity transmission of substantial side information is avoided the experiment results confirm that with small computation overhead the rot is adaptive to change of local spatial characteristic of mc residual frame and provides higher compression efficiency for the mc residual than dct especially for high and complex motion videos

convergence of the strongly damped nonlinear klein gordon equation in ℝn with radial symmetry on considere l equation de klein gordon fortement amortie dans r 3 dans le cas ou les donnees initiales possedent une symetrie radiale on construit une solution faible globale v de l equation non amortie pour des puissances elevees p qui peuvent etre approchees par les solutions globales fortes de l equation amortie

energy convergence results for strongly damped nonlinear wave equations on considere l equation d onde non lineaire abstraite fortement amortie u tt a 2 u t b 2 u f u ou a et b sont des operateurs auto adjoints positifs sur un espace de hilbert h u u t prend des valeurs dans h pour t non negatif et f est une application localement lipschitz d un bon sous ensemble de h dans h et sont des constantes non negatives soit u une solution on etudie le comportement de u quand o

directionlets using in phase lifting for image representation directionlets allow a construction of perfect reconstruction and critically sampled multidirectional anisotropic basis yet retaining the separable filtering of standard wavelet transform however due to the spatially varying filtering and downsampling direction it is forced to apply spatial segmentation and process each segment independently because of this independent processing of the image segments directionlets suffer from the following two major limitations when applied to say image coding first failure to exploit the correlation across block boundaries degrades the coding performance and also induces blocking artifacts thus making it mandatory to use de blocking filter at low bit rates second spatial scalability i e minimum segment size or the number of levels of the transform is limited due to independent processing of segments we show that with simple modifications in the block boundaries we can overcome these limitations by what we call in phase lifting implementation of directionlets in the context of directionlets using in phase lifting we identify different possible groups of downsampling matrices that would allow the construction of a multilevel transform without forcing independent processing of segments both with and without any modifications in the segment boundary experimental results in image coding show objective and subjective improvements when compared with the directionlets applied independently on each image segment as an application using both the in phase lifting implementation of directionlets and the adaptive directional lifting we have constructed an adaptive directional wavelet transform which has shown improved image coding performance over these adaptive directional wavelet transforms

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

compression limits for random vectors with linearly parameterized second order statistics the class of complex random vectors whose covariance matrix is linearly parameterized by a basis of hermitian toeplitz ht matrices is considered and the maximum compression ratios that preserve all second order information are derived the statistics of the uncompressed vector must be recoverable from a set of linearly compressed observations this kind of vectors typically arises when sampling widesense stationary random processes and features a number of applications in signal and array processing explicit guidelines to design optimal and nearly optimal schemes operating both in a periodic and non periodic fashion are provided by considering two of the most common linear compression schemes non uniform sampling and random sampling it is seen that the maximum compression ratios depend on the structure of the ht subspace where the covariance matrix of the uncompressed observations is known to be contained compression patterns attaining these maximum ratios are found for the case without structure as well as for the cases with circulant or banded structure

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

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

compressive wideband power spectrum estimation in several applications such as wideband spectrum sensing for cognitive radio only the power spectrum a k a the power spectral density is of interest and there is no need to recover the original signal itself in addition high rate analog to digital converters adcs are too power hungry for direct wideband spectrum sensing these two facts have motivated us to investigate compressive wideband power spectrum sensing which consists of a compressive sampling procedure and a reconstruction method that is able to recover the unknown power spectrum of a wide sense stationary signal from the obtained sub nyquist rate samples it is different from spectrum blind sampling sbs which aims at reconstructing the original signal instead of the power spectrum in this paper a solution is first presented based on a periodic sampling procedure and a simple least squares reconstruction method we evaluate the reconstruction process both in the time and frequency domain then we examine two possible implementations for the compressive sampling procedure namely complex gaussian sampling and multicoset sampling although we mainly focus on the latter a new type of multicoset sampling is introduced based on the so called minimal sparse ruler problem next we analyze the statistical properties of the estimated power spectrum the computation of the mean and the covariance of the estimates allows us to calculate the analytical normalized mean squared error nmse of the estimated power spectrum further when the received signal is assumed to contain only circular complex zero mean gaussian i i d noise the computed mean and covariance can be used to derive a suitable detection threshold simulation results underline the promising performance of our proposed approach note that all benefits of our method arise without putting any sparsity constraints on the power spectrum

positive definite toeplitz completion in doa estimation for nonuniform linear antenna arrays ii partially augmentable arrays this paper considers the problem of direction of arrival doa estimation for multiple uncorrelated plane waves incident on so called fully augmentable sparse linear arrays in situations where a decision is made on the number of existing signal sources m prior to the estimation stage we investigate the conditions under which doa estimation accuracy is effective in the maximum likelihood sense in the case where m is less than the number of antenna sensors m a new approach called music maximum entropy equalization is proposed to improve doa estimation performance in the preasymptotic region of finite sample size n and signal to noise ratio a full sized positive definite p d toeplitz matrix is constructed from the m spl times m direct data covariance matrix and then alternating projections are applied to find a p d toeplitz matrix with m variate signal eigensubspace signal subspace truncations when m spl ges m cramer rao bound analysis suggests that the minimal useful sample size n is rather large even for arbitrarily strong signals it is demonstrated that the well known direct augmentation approach daa cannot approach the accuracy of the corresponding cramer rao bound even asymptotically as n spl rarr spl infin and therefore needs to be improved we present a new estimation method whereby signal subspace truncation of the daa augmented matrix is used for initialization and is followed by a local maximum likelihood optimization routine the accuracy of this method is demonstrated to be asymptotically optimal for the various superior scenarios m spl ges m presented

image compression using adaptive vector quantization the paper demonstrates the application of adaptive vector quantization techniques to the coding of monochromatic and color pictures codebooks of representative vectors are generated for different portions of the image by means of extensive simulations the performance of the coder for monochrome images is estimated as a function of the various coding parameters vector dimensionality number of representative vectors and degree of adaptivity it is shown that for a vector size of dimension 4 there is a zone of operation ranging from 1 0 to 1 5 bits pixel where adaptive vector quantization is advantageous despite the simplicity of the decoder the performance of the adaptive vector quantizer is found to be comparable with block transform coding schemes for both monochrome and color pictures

steerable wedge filters for local orientation analysis steerable filters have been used to analyze local orientation patterns in imagery such filters are typically based on directional derivatives whose symmetry produces orientation responses that are periodic with period spl pi independent of image structure we present a more general set of steerable filters that alleviate this problem

curved wavelet transform for image coding the conventional two dimensional wavelet transform used in existing image coders is usually performed through one dimensional 1 d filtering in the vertical and horizontal directions which cannot efficiently represent edges and lines in images the curved wavelet transform presented in this paper is carried out by applying 1 d filters along curves rather than being restricted to vertical and horizontal straight lines the curves are determined based on image content and are usually parallel to edges and lines in the image to be coded the pixels along these curves can be well represented by a small number of wavelet coefficients the curved wavelet transform is used to construct a new image coder the code stream syntax of the new coder is the same as that of jpeg2000 except that a new marker segment is added to the tile headers results of image coding and subjective quality assessment show that the new image coder performs better than or as well as jpeg2000 it is particularly efficient for images that contain sharp edges and can provide a psnr gain of up to 1 67 db for natural images compared with jpeg2000

a note on finite time blowup for dissipative klein gordon equation abstract this is a continuation of the study on an arbitrarily positive initial energy finite time blowup result of the solution to the initial value problem of strongly damped klein gordon equation based on an adapted concavity method both the conclusions and arguments of the present paper are not bounded by the coefficients of dissipative damping terms

analysis of superimposed oriented patterns estimation of local orientation in images may be posed as the problem of finding the minimum gray level variance axis in a local neighborhood in bivariate images the solution is given by the eigenvector corresponding to the smaller eigenvalue of a 2times2 tensor for an ideal single orientation the tensor is rank deficient i e the smaller eigenvalue vanishes a large minimal eigenvalue signals the presence of more than one local orientation what may be caused by non opaque additive or opaque occluding objects crossings bifurcations or corners we describe a framework for estimating such superimposed orientations our analysis is based on the eigensystem analysis of suitably extended tensors for both additive and occluding superpositions unlike in the single orientation case the eigensystem analysis does not directly yield the orientations rather it provides so called mixed orientation parameters mops we therefore show how to decompose the mops into the individual orientations we also show how to use tensor invariants to increase efficiency and derive a new feature for describing local neighborhoods which is invariant to rigid transformations applications are e g in texture analysis directional filtering and interpolation feature extraction for corners and crossings tracking and signal separation

multidimensional orientation estimation with applications to texture analysis and optical flow the problem of detection of orientation in finite dimensional euclidean spaces is solved in the least squares sense the theory is developed for the case when such orientation computations are necessary at all local neighborhoods of the n dimensional euclidean space detection of orientation is shown to correspond to fitting an axis or a plane to the fourier transform of an n dimensional structure the solution of this problem is related to the solution of a well known matrix eigenvalue problem the computations can be performed in the spatial domain without actually doing a fourier transformation along with the orientation estimate a certainty measure based on the error of the fit is proposed two applications in image analysis are considered texture segmentation and optical flow the theory is verified by experiments which confirm accurate orientation estimates and reliable certainty measures in the presence of noise the comparative results indicate that the theory produces algorithms computing robust texture features as well as optical flow

1 d transforms for the motion compensation residual transforms used in image coding are also commonly used to compress prediction residuals in video coding prediction residuals have different spatial characteristics from images and it is useful to develop transforms that are adapted to prediction residuals in this paper we explore the differences between the characteristics of images and motion compensated prediction residuals by analyzing their local anisotropic characteristics and develop transforms adapted to the local anisotropic characteristics of these residuals the analysis indicates that many regions of motion compensated prediction residuals have 1 d anisotropic characteristics and we propose to use 1 d directional transforms for these regions we present experimental results with one example set of such transforms within the h 264 avc codec and the results indicate that the proposed transforms can improve the compression efficiency of motion compensated prediction residuals over conventional transforms

nonlinear second order equations with applications to partial differential equations where a and b are usually unbounded linear operators in a banach space these problems arise often in the study of partial differential equations as is usual we control a nonlinear perturbation possibly involving spatial derivatives by the linear terms which contain higher order spatial derivatives but contrary to the usual method of reducing the problem to a first order system in some energy norm space as in 9 5 we use the factoring method of lo this method allows the equation to be written as an integral equation containing a double integral involving the nonlinearity reflecting the fact that the equation is second order there are several advantages to this approach which will be illustrated fully in the examples first we show that the equation is locally well posed if loosely the nonlinearity satisfies the local lipschitz condition

a singular perturbation problem for nonlinear damped hyperbolic equations on considere des equations hyperboliques non lineaires amorties u tt au t au a 2 u g u 0 ou a est un operateur positif et g est la derivee de gateaux d une fonctionnelle convexe on etudie le comportement asymptotique des solutions et la convergence des solutions fortes quand o

three dimensional subband coding with motion compensation three dimensional 3 d frequency coding is an alternative approach to hybrid coding concepts used in today s standards the first part of this paper presents a study on concepts for temporal axis frequency decomposition along the motion trajectory in video sequences it is shown that if a two band split is used it is possible to overcome the problem of spatial inhomogeneity in the motion vector field mvf which occurs at the positions of uncovered and covered areas in these cases original pixel values from one frame are placed into the lowpass band signal while displaced frame difference values are embedded into the highpass band this technique is applicable with arbitrary mvf s examples with block matching and interpolative motion compensation are given derivations are first performed for the example of two tap quadrature mirror filters qmf s and then generalized to any linear phase qmf s with two band analysis and synthesis stages arranged as cascade structures higher resolution frequency decompositions are realizable in the second part of the paper encoding of the temporal axis subband signals is discussed a parallel filterbank scheme was used for spatial subband decomposition and adaptive lattice vector quantization was employed to approach the entropy rate of the 3 d subband samples coding results suggest that high motion video sequences can be encoded at significantly lower rates than those achievable with conventional hybrid coders main advantages are the high energy compaction capability and the nonrecursive decoder structure in the conclusion the scheme is interpreted more generally viewed as a motion compensated short time spectral analysis of video sequences which can adapt to the quickness of changes although a 3 d multiresolution representation of the picture information is produced a true multiresolution representation of motion information based on spatio temporal decimation and interpolation of the mvf is regarded as the still missing part

design of signal adapted multidimensional lifting scheme for lossy coding this paper proposes a new method for the design of lifting filters to compute a multidimensional nonseparable wavelet transform our approach is stated in the general case and is illustrated for the 2 d separable and for the quincunx images results are shown for the jpeg2000 database and for satellite images acquired on a quincunx sampling grid the design of efficient quincunx filters is a difficult challenge which has already been addressed for specific cases our approach enables the design of less expensive filters adapted to the signal statistics to enhance the compression efficiency in a more general case it is based on a two step lifting scheme and joins the lifting theory with wiener s optimization the prediction step is designed in order to minimize the variance of the signal and the update step is designed in order to minimize a reconstruction error application for lossy compression shows the performances of the method

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

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

analysis of multiple orientations estimation of local orientations in multivariate signals is an important problem in image processing and computer vision this general problem formulation also covers optical flow estimation which can be regarded as orientation estimation in space time volumes modelling a signal using only a single orientation however is often too restrictive since occlusions and transparencies occur frequently thus necessitating the modelling and analysis of multiple orientations we therefore develop a unifying mathematical model for multiple orientations beyond describing an arbitrary number of orientations in scalar and vector valued image data such as color image sequences it allows the unified treatment of additively and occludingly superimposed oriented structures as well as of combinations of these based on this model we describe estimation schemes for an arbitrary number of additively or occludingly superimposed orientations in images we confirm the performance of our framework on both synthetic and real image data

design of steerable filters for feature detection using canny like criteria we propose a general approach for the design of 2d feature detectors from a class of steerable functions based on the optimization of a canny like criterion in contrast with previous computational designs our approach is truly 2d and provides filters that have closed form expressions it also yields operators that have a better orientation selectivity than the classical gradient or hessian based detectors we illustrate the method with the design of operators for edge and ridge detection we present some experimental results that demonstrate the performance improvement of these new feature detectors we propose computationally efficient local optimization algorithms for the estimation of feature orientation we also introduce the notion of shape adaptable feature detection and use it for the detection of image corners

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

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

a 2 d orientation adaptive prediction filter in lifting structures for image coding lifting style implementations of wavelets are widely used in image coders a two dimensional 2 d edge adaptive lifting structure which is similar to daubechies 5 3 wavelet is presented the 2 d prediction filter predicts the value of the next polyphase component according to an edge orientation estimator of the image consequently the prediction domain is allowed to rotate spl plusmn 45 spl deg in regions with diagonal gradient the gradient estimator is computationally inexpensive with additional costs of only six subtractions per lifting instruction and no multiplications are required

directional lapped transforms for image coding in this paper we present the design of directional lapped transforms for image coding a lapped transform which can be implemented by a prefilter followed by a discrete cosine transform dct can be factorized into elementary operators the corresponding directional lapped transform is generated by applying each elementary operator along a given direction the proposed directional lapped transforms are not only nonredundant and perfectly reconstructed but they can also provide a basis along an arbitrary direction these properties along with the advantages of lapped transforms make the proposed transforms appealing for image coding a block based directional transform scheme is also presented and integrated into hd phtoto one of the state of the art image coding systems to verify the effectiveness of the proposed transforms

convergence properties of the strongly damped nonlinear klein gordon equation abstract we consider the nonlinear klein gordon equation u tt u i m 2 u u p 1 u 0 over a domain in r 3 in 2 aviles and sandefur established global existence of strong solutions when 0 for p 3 for each 0 let u be such a solution in this paper we show that if is a bounded domain with smooth boundary then there exists a sequence k and a global weak solution v of the undamped equation where 0 such that lim k 0 u k v in l 2 uniformly on any finite interval 0 t with t 0 we also show that if u is a strong local solution with 0 then for smooth enough initial data there exists an interval 0 t such that lim 0 u u uniformly in a much stronger norm we conclude by noting a connection between these two results and by discussing the difficulty of extending the first result to the case r 3 we also note in section 2 a natural extension of theorem 1 1 to bounded domains in r n n 3

wideband spectrum sensing from compressed measurements using spectral prior information wideband spectrum sensing wss encompasses a collection of techniques intended to estimate or to decide over the occupancy parameters of a wide frequency band however broad bands require expensive acquisition systems thus motivating the use of compressive schemes in this context previous works in compressive wss have already realized that great compression rates can be achieved if only second order statistics are of interest in spectrum sensing in this paper we go a step further by exploiting spectral prior information that is typically available in practice in order to reduce the sampling rate even more the signal model assumes that the acquisition is done by means of an analog to information converter a2i the input signal is the linear combination of a number of signals whose second order statistics are known and the goal is to estimate decide over the coefficients of this combination the problem is thus a particular instance of the well known structured covariance estimation problem unfortunately the algorithms used in this area are extremely complex for inexpensive spectrum sensors so that alternative techniques need to be devised exploiting the fact that the basis matrices are toeplitz we use the asymptotic theory of circulant matrices to propose a dimensionality reduction technique that simplifies existing structured covariance estimation algorithms achieving a similar performance at a much lower computational cost

orientation adaptive subband coding of images in the subband coding of images directionality of image features has thus far been exploited very little the proposed subband coding scheme utilizes orientation of local image features to avoid the highly objectionable gibbs like phenomena observed at reconstructed image edges with conventional subband schemes at low bit rates at comparable bit rates the subjective image quality obtained by our orientation adaptive scheme is considerably enhanced over a conventional separable subband coding scheme as well as other separable approaches such as the jpeg compression standard

template free wavelet based detection of local symmetries our goal is to detect and group different kinds of local symmetries in images in a scale and rotation invariant way we propose an efficient wavelet based method to determine the order of local symmetry at each location our algorithm relies on circular harmonic wavelets which are used to generate steerable wavelet channels corresponding to different symmetry orders to give a measure of local symmetry we use the f test to examine the distribution of the energy across different channels we provide experimental results on synthetic images biological micrographs and electron microscopy images to demonstrate the performance of the algorithm

nested arrays a novel approach to array processing with enhanced degrees of freedom a new array geometry which is capable of significantly increasing the degrees of freedom of linear arrays is proposed this structure is obtained by systematically nesting two or more uniform linear arrays and can provide o n2 degrees of freedom using only n physical sensors when the second order statistics of the received data is used the concept of nesting is shown to be easily extensible to multiple stages and the structure of the optimally nested array is found analytically it is possible to provide closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors this cannot be done for existing classes of arrays like minimum redundancy arrays which have been used earlier for detecting more sources than the number of physical sensors in minimum input minimum output mimo radar the degrees of freedom are increased by constructing a longer virtual array through active sensing the method proposed here however does not require active sensing and is capable of providing increased degrees of freedom in a completely passive setting to utilize the degrees of freedom of the nested co array a novel spatial smoothing based approach to doa estimation is also proposed which does not require the inherent assumptions of the traditional techniques based on fourth order cumulants or quasi stationary signals as another potential application of the nested array a new approach to beamforming based on a nonlinear preprocessing is also introduced which can effectively utilize the degrees of freedom offered by the nested arrays the usefulness of all the proposed methods is verified through extensive computer simulations

efficient steerable circular harmonic functions two dimensional 2d filtering and pattern matching applications often involve processing of images using a set sf which includes several transformed e g rotated scaled warped versions of the same 2d function f depending on the application f may correspond to a filter kernel or a pattern in general image processing using all functions in sf poses a computational burden steerability offers a solution to the problem specifically each function in sf can be exactly expressed or closely approximated by a linear combination of a few basis or steering functions in such cases processing images by employing steering functions and obtaining linear combinations of the associated responses may be preferable over utilizing all functions in sf however employing the steering functions is still a computationally expensive process this paper presents a method to significantly improve the computational efficiency of circular harmonic functions which are the steering functions when rotation is the transformation of interest the method is presented mainly in the context of image filtering yet 2d pattern matching is also discussed the advantages of the proposed technique in relation to other techniques are presented and its efficiency is demonstrated in terms of execution time and number of operations an extension of the technique to more general cases where sf includes rotated but also otherwise transformed versions of f is also discussed highlightsvery efficient circular harmonic function chf steerable filter technique presented chf implementation several times faster than direct convolution and fft conditionally technique provides exact results as direct convolution comparisons presented for pattern matching orientation analysis and denoising

a flexible new technique for camera calibration we propose a flexible technique to easily calibrate a camera it only requires the camera to observe a planar pattern shown at a few at least two different orientations either the camera or the planar pattern can be freely moved the motion need not be known radial lens distortion is modeled the proposed procedure consists of a closed form solution followed by a nonlinear refinement based on the maximum likelihood criterion both computer simulation and real data have been used to test the proposed technique and very good results have been obtained compared with classical techniques which use expensive equipment such as two or three orthogonal planes the proposed technique is easy to use and flexible it advances 3d computer vision one more step from laboratory environments to real world use

design and implementation of multisteerable matched filters image analysis problems such as feature tracking edge detection image enhancement or texture analysis require the detection of multi oriented patterns which can appear at arbitrary orientations direct rotated matched filtering for feature detection is computationally expensive but can be sped up with steerable filters so far steerable filter approaches were limited to only one direction many important low level image features are however characterized by more than a single orientation we therefore present here a framework for efficiently detecting specific multi oriented patterns with arbitrary orientations in grayscale images the core idea is to construct multisteerable filters by appropriate combinations of single steerable filters we exploit that steerable filters are closed under addition and multiplication this allows to derive a design guide for multisteerable filters by means of multivariate polynomials furthermore we describe an efficient implementation scheme and discuss the use of weighting functions to reduce angular oscillations applications in camera calibration junction analysis of images from plant roots and the discrimination of l t and x junctions demonstrate the potential of this approach

lossless image compression based on optimal prediction adaptive lifting and conditional arithmetic coding the optimal predictors of a lifting scheme in the general n dimensional case are obtained and applied for the lossless compression of still images using first quincunx sampling and then simple row column sampling in each case the efficiency of the linear predictors is enhanced nonlinearly directional postprocessing is used in the quincunx case and adaptive length postprocessing in the row column case both methods are seen to perform well the resulting nonlinear interpolation schemes achieve extremely efficient image decorrelation we further investigate context modeling and adaptive arithmetic coding of wavelet coefficients in a lossless compression framework special attention is given to the modeling contexts and the adaptation of the arithmetic coder to the actual data experimental evaluation shows that the best of the resulting coders produces better results than other known algorithms for multiresolution based lossless image coding