autocorrelation in meter induction the role of accent structure the performance of autocorrelation based meter induction was tested with two large collections of folk melodies consisting of approximately 13 000 melodies for which the correct meters were available the performance was measured by the proportion of melodies whose meter was correctly classified by a discriminant function furthermore it was examined whether including different melodic accent types would improve the classification performance by determining the components of the autocorrelation functions that were significant in the classification it was found that periodicity in note onset locations was the most important cue for the determination of meter of the melodic accents included thomassen s melodic accent was found to provide the most reliable cues for the determination of meter the discriminant function analyses suggested that periodicities longer than one measure may provide cues for meter determination that are more reliable than shorter periodicities overall the method predicted notated meter with an accuracy reaching 96 for binary classification and 75 for classification into nine categories of meter

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

calculation of a constant q spectral transform the frequencies that have been chosen to make up the scale of western music are geometrically spaced thus the discrete fourier transform dft although extremely efficient in the fast fourier transform implementation yields components which do not map efficiently to musical frequencies this is because the frequency components calculated with the dft are separated by a constant frequency difference and with a constant resolution a calculation similar to a discrete fourier transform but with a constant ratio of center frequency to resolution has been made this is a constant q transform and is equivalent to a 1 24 oct filter bank thus there are two frequency components for each musical note so that two adjacent notes in the musical scale played simultaneously can be resolved anywhere in the musical frequency range this transform against log frequency to obtain a constant pattern in the frequency domain for sounds with harmonic frequency components has been plotted this is compared to the conventio

a high resolution fundamental frequency determination based on phase changes of the fourier transform the constant q transform described recently j c brown and m s puckette an efficient algorithm for the calculation of a constant q transform j acoust soc am 92 2698 2701 1992 has been adapted so that it is suitable for tracking the fundamental frequency of extremely rapid musical passages for this purpose the calculation described previously has been modified so that it is constant frequency resolution rather than constant q for lower frequency bins this modified calculation serves as the input for a fundamental frequency tracker similar to that described by brown j c brown musical fundamental frequency tracking using a pattern recognition method j acoust soc am 92 1394 1402 1992 once the fast fourier transform fft bin corresponding to the fundamental frequency is chosen by the frequency tracker an approximation is used for the phase change in the fft for a time advance of one sample to obtain an extremely precise value for this frequency graphical examples are given for musical passages by a violin executing vibrato and glissando where the fundamental frequency changes are rapid and continuous

structure of void space in polymer solutions the structure of void space in two and three dimensional 3d polymer solutions is studied using voronoi tessellation and percolation theory the polymer molecules are modeled as freely jointed chains of n tangent hard disks two dimensions or spheres three dimensions polymer chains are equilibrated via monte carlo simulations and the pore space in configurations of equilibrated chains is mapped using voronoi tessellation in d dimensions a voronoi vertex is the center of the sphere tangent to the d 1 nearest monomers an edge of the voronoi diagram is the shortest route between two neighboring vertices the edge is considered connected if a monomer can pass through and disconnected otherwise the voronoi construction is used to calculate the percolation threshold of the void space the most interesting result is that the polymer area fraction at the percolation threshold is a nonmonotonic function of n in two dimensions but monotonically reaches a constant value in three dimensions the crossover behavior of the percolation threshold is also observed in pseudo 3d the pore size distribution decreases monotonically with increasing pore size this is markedly different from that in configurations of hard disks monomeric fluid where the pore size distribution is peaked at finite size

voronoi delaunay analysis of voids in systems of nonspherical particles the voronoi network is known to be a useful tool for the structural description of voids in the packings of spheres produced by computer simulations in this article we extend the voronoi delaunay analysis to packings of nonspherical convex objects main properties of the voronoi network which are known for systems of spheres are valid for systems of any convex objects a general numerical algorithm for calculation of the voronoi network in three dimensions is proposed it is based on the calculation of the trajectory of the imaginary empty sphere of variable size moving inside a system the delaunay empty sphere method analysis of voids is presented for an ensemble of random straight lines and for a molecular dynamics model of liquid crystal the spatial distribution of voids and a simple percolation analysis are obtained the distributions of the bottleneck radii and the radii of spheres inscribed in the voids are calculated

new perspectives and improvements on the symmetric extension filter bank for subband wavelet image compression in subband wavelet image coding size limited subband decompositions are ordinarily used to avoid increasing the number of samples that need to be coded to reduce coding distortions that can occur at the borders the symmetric extension filter bank is typically employed this paper introduces some new perspectives and improvements to that decomposition the symmetric extension filter bank is couched in the cyclic frequency domain providing a framework that accommodates fir and iir filters in a natural way all with perfect reconstruction iir filters with both rational and irrational transfer functions can be implemented and in the context of symmetric extension can accommodate iirs that effectively have perfect stopband suppression enhancements to the filter bank at a tree structured system level are also presented and include the application of spectral reversal correction and a transition band normalization approach to designing the constituent filters of the symmetric extension wavelet packet transform

computer identification of musical instruments using pattern recognition with cepstral coefficients as features cepstral coefficients based on a constant q transform have been calculated for 28 short 1 2 s oboe sounds and 52 short saxophone sounds these were used as features in a pattern analysis to determine for each of these sounds comprising the test set whether it belongs to the oboe or to the sax class the training set consisted of longer sounds of 1 min or more for each of the instruments a k means algorithm was used to calculate clusters for the training data and gaussian probability density functions were formed from the mean and variance of each of the clusters each member of the test set was then analyzed to determine the probability that it belonged to each of the two classes and a bayes decision rule was invoked to assign it to one of the classes results have been extremely good and are compared to a human perception experiment identifying a subset of these same sounds

frequency warped filter banks and wavelet transforms a discrete time approach via laguerre expansion we introduce a new generation of perfect reconstruction filter banks that can be obtained from classical critically sampled filter banks by means of frequency transformations the novel filters are laguerre type iir filters that can be directly derived and designed from ordinary orthogonal or biorthogonal filter banks generalized downsampling and upsampling operators based on dispersive delay lines are the building blocks of our structures by iterating the filter banks we construct new orthogonal and complete sets of wavelets whose passbands are not octave spaced and may be designed by selecting a single parameter

the least squares invertible constant q spectrogram and its application to phase vocoding this paper discusses the development of a constant q spectrogram representation that is invertible in a least squares sense a good quality inverse is possible because this modified transform method unlike the usual sliding window constant q spectrogram does not discard data samples when performing the variable length discrete fourier transforms on the signal the development of a phase vocoder application using this modified technique is also discussed it is shown that a phase vocoder constructed using the least squares invertible constant q spectrogram lsicqs is not a trivial extension of the regular fft based phase vocoder algorithm and some of the mathematical subtleties related to phase reassignment are addressed

hierarchical image segmentation part i detection of regular curves in a vector graph the problem of edge detection is viewed as a hierarchy of detection problems where the geometric objects to be detected e g edge points curves regions have increasing complexity and spatial extent an early stage of the proposed hierarchy consists in detecting the regular portions of the visible edges the input to this stage is given by a graph whose vertices are tangent vectors representing local and uncertain information about the edges a model relating the input vector graph to the curves to be detected is proposed an algorithm with linear time complexity is described which solves the corresponding detection problem in a worst case scenario the stability of curve reconstruction in the presence of uncertain information and multiple responses to the same edge is analyzed and addressed explicitly by the proposed algorithm

nonlocal sparse model with adaptive structural clustering for feature extraction of aero engine bearings abstract fault information of aero engine bearings presents two particular phenomena i e waveform distortion and impulsive feature frequency band dispersion which leads to a challenging problem for current techniques of bearing fault diagnosis moreover although many progresses of sparse representation theory have been made in feature extraction of fault information the theory also confronts inevitable performance degradation due to the fact that relatively weak fault information has not sufficiently prominent and sparse representations therefore a novel nonlocal sparse model coined nlsm and its algorithm framework has been proposed in this paper which goes beyond simple sparsity by introducing more intrinsic structures of feature information this work adequately exploits the underlying prior information that feature information exhibits nonlocal self similarity through clustering similar signal fragments and stacking them together into groups within this framework the prior information is transformed into a regularization term and a sparse optimization problem which could be solved through block coordinate descent method bcd is formulated additionally the adaptive structural clustering sparse dictionary learning technique which utilizes k nearest neighbor knn clustering and principal component analysis pca learning is adopted to further enable sufficient sparsity of feature information moreover the selection rule of regularization parameter and computational complexity are described in detail the performance of the proposed framework is evaluated through numerical experiment and its superiority with respect to the state of the art method in the field is demonstrated through the vibration signals of experimental rig of aircraft engine bearings

multiresolution analysis of a class of nonstationary processes processing nonstationary signals is an important and challenging problem we focus on the class of nonstationary processes with stationary increments of an arbitrary order and place them in a multiscale framework unlike other related studies we concentrate on the discrete time analysis and derive a number of new results in addition to placing the related existing ones in the same framework we extend the study to various parametric models for which we derive the resulting multiresolution description we show that wide sense stationarity may be achieved by adequately selecting the analysis wavelet after generalizing the study to wavelet packet analysis we show that the latter possesses additional properties which are useful in the presence of other types of nonstationarities

superposition frames for adaptive time frequency analysis and fast reconstruction in this paper we introduce a broad family of adaptive linear time frequency representations termed superposition frames and show that they admit desirable fast overlap add reconstruction properties akin to standard short time fourier techniques this approach stands in contrast to many adaptive time frequency representations in the existing literature which while more flexible than standard fixed resolution approaches typically fail to provide for efficient reconstruction and often lack the regular structure necessary for precise frame theoretic analysis our main technical contributions come through the development of properties which ensure that our superposition construction provides for a numerically stable invertible signal representation our primary algorithmic contributions come via the introduction and discussion of two signal adaptation schemes based on greedy selection and dynamic programming respectively we conclude with two short enhancement examples that serve to highlight potential applications of our approach

a new shift invariance of discrete time systems and its application to discrete wavelet transform analysis this work is motivated by the search for discrete wavelet transform dwt with near shift invariance after examining the elements of the property we introduce a new notion of shift invariance which is particularly informative for multirate systems that are not shift invariant in the strict sense briefly speaking a discrete time system is mu shift invariant if a shift in input results in the output being shifted as well however the amount of the shift in output is not necessarily identical to that in input a fractional shift is also acceptable and can be properly specified in the fourier domain the mu shift invariance can be interpreted as invariance of magnitude spectrum with linear phase offset of output with respect to shift in input it is stronger than the shiftability in position which is equivalent to insensitivity of energy to shift in input under this generalized notion the expander is always mu shift invariant the m fold decimator is mu shift invariant for input with width of frequency support not more than 2pi m equivalently the output contains no aliasing term in some frequency band with length of 2pi we generalize the transfer function description of linear shift invariant systems for mu shift invariant systems we then perform mu shift invariance analysis of 2 band orthogonal dwt and of the 2 band dual tree complex wavelet transform dt cwt the analysis in each case provides clarifications to early understanding of near shift invariance we show that the dwt is mu shift invariant if and only if the conjugate quadrature filter cqf is analytic or antianalytic for the dt cwt the cqfs must have supports included within 2pi 3 2pi 3 in addition to the well know half sample delay condition at higher levels and the one sample delay condition at the first level

isotropic polyharmonic b splines scaling functions and wavelets in this paper we use polyharmonic b splines to build multidimensional wavelet bases these functions are nonseparable multidimensional basis functions that are localized versions of radial basis functions we show that rabut s elementary polyharmonic b splines do not converge to a gaussian as the order parameter increases as opposed to their separable b spline counterparts therefore we introduce a more isotropic localization operator that guarantees this convergence resulting into the isotropic polyharmonic b splines next we focus on the two dimensional quincunx subsampling scheme this configuration is of particular interest for image processing because it yields a finer scale progression than the standard dyadic approach however up until now the design of appropriate filters for the quincunx scheme has mainly been done using the mcclellan transform in our approach we start from the scaling functions which are the polyharmonic b splines and as such explicitly known and we derive a family of polyharmonic spline wavelets corresponding to different flavors of the semi orthogonal wavelet transform e g orthonormal b spline and dual the filters are automatically specified by the scaling relations satisfied by these functions we prove that the isotropic polyharmonic b spline wavelet converges to a combination of four gabor atoms which are well separated in the frequency domain we also show that these wavelets are nearly isotropic and that they behave as an iterated laplacian operator at low frequencies we describe an efficient fast fourier transform based implementation of the discrete wavelet transform based on polyharmonic b splines

singularity detection and processing with wavelets the mathematical characterization of singularities with lipschitz exponents is reviewed theorems that estimate local lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed it is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their lipschitz exponents the wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately the local frequency of such oscillations is measured from the wavelet transform modulus maxima it has been shown numerically that one and two dimensional signals can be reconstructed with a good approximation from the local maxima of their wavelet transform modulus as an application an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales in two dimensions the wavelet transform maxima indicate the location of edges in images

trace inference curvature consistency and curve detection an approach is described for curve inference that is based on curvature information the inference procedure is divided into two stages a trace inference stage which is the subject of the present work and a curve synthesis stage it is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time and that tangent and curvature information are sufficient these make it possible to specify powerful constraints between estimated tangents to a curve in terms of a neighborhood relationship called cocircularity and between curvature estimates in terms of a curvature consistency relation because all curve information is quantized special care must be taken to obtain accurate estimates of trace points tangents and curvatures this issue is addressed specifically to the introduction of a smoothness constraint and a maximum curvature constraint the procedure is applied to two types of images artificial images designed to evaluate curvature and noise sensitivity and natural images

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

frame theoretic analysis of oversampled filter banks we provide a frame theoretic analysis of oversampled finite impulse response fir and infinite impulse response fir uniform filter banks fbs our analysis is based on a new relationship between the fbs polyphase matrices and the frame operator corresponding to an fb for a given oversampled analysis fb we present a parameterization of all synthesis fbs providing perfect reconstruction we find necessary and sufficient conditions for an oversampled fb to provide a frame expansion a new frame theoretic procedure for the design of paraunitary fbs from given nonparaunitary fbs is formulated we show that the frame bounds of an fb can be obtained by an eigen analysis of the polyphase matrices the relevance of the frame bounds as a characterization of important numerical properties of an fb is assessed by means of a stochastic sensitivity analysis we consider special cases in which the calculation of the frame bounds and synthesis filters is simplified finally simulation results are presented

computer simulations of nearest neighbor distribution functions and related quantities for hard sphere systems one of the fundamental quantities which statistically characterizes a random system of interacting particles is the nearest neighbor distribution function we present computersimulation results for two different types of nearest neighbor distribution functions for random distributions of identical impenetrable hard spheres we also report for such systems computer simulation data for closely related quantities such as the associated cumulative distributions from this information we calculate the mean nearest neighbor distance between particles our computer simulation results are compared to the various sets of theoretical expressions derived recently by torquato lu and rubinstein one of these sets of expressions is shown to be in excellent agreement with the simulation data

on the location error of curved edges in low pass filtered 2 d and 3 d images the authors study the location error of curved edges in two and three dimensional images after analog and digital low pass filtering the zero crossing of a second derivative filter is a well known edge localization criterion the second derivative in gradient direction sdgd produces a predictable bias in edge location towards the centers of curvature while the linear laplace filter produces a shift in the opposite direction their sum called plus plus laplace sdgd leads to an edge detector that finds curved edges one order more accurately than its constituents this argument holds irrespective of the dimension the influence of commonly used low pass filters such as the psf originating from diffraction limited optics using incoherent light 2 d the gaussian filter with variable cutoff point d d and the isotropic uniform filter d d is studied

flexible tree structured signal expansions using time varying wavelet packets addresses the problem of finding the best time varying filter bank tree structured representation for a signal the tree is allowed to vary at regular intervals and the spacing of these changes can be arbitrarily short the question of how to choose tree structured representations of signals based on filter banks is considered wavelets and their adaptive version known as wavelet packets represent one approach that is popular wavelet packets are subband trees where the tree is chosen to match the characteristics of the signal variations where the tree varies over time have been proposed as the double tree and the time frequency tree algorithms time variation adds a further level of adaptivity in all of the approaches proposed so far the tree must be either fixed for the whole duration of the signal or fixed for its dyadic subintervals the solution that we propose as it allows more flexible variation is an advance on the wavelet packet algorithm the double tree algorithm and the recently proposed time frequency tree algorithm our solution is based on casting it in a dynamic programming dp setting focusing on compression applications we use a lagrangian cost of distortion spl lambda spl times rate as the objective function and explain our algorithm in detail pointing out its relation to existing approaches to the problem we demonstrate that the new algorithm indeed searches a larger library of representations than previously possible and that overcoming the constraint of dyadic time segmentations gives a significant improvement in practice

an analytic wavelet transform with a flexible time frequency covering we develop a rational dilation wavelet transform for which the dilation factor the q factor and the redundancy can be easily specified the introduced transform contains hilbert transform pairs of atoms therefore it is also suitable for oscillatory signal processing the transform may be modified to obtain a tight chirplet frame for discrete time signals a fast implementation that makes use of an equivalent filter bank makes the transform suitable for long signals examples on natural signals are provided to demonstrate the utility of the transform

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

using canny s criteria to derive a recursively implemented optimal edge detector a highly efficient recursive algorithm for edge detection is presented using canny s design 1 we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension which can be efficiently implemented by two recursive filters moving in opposite directions in addition to the noise truncature immunity which results the recursive nature of the filtering operations leads with sequential machines to a substantial saving in computational effort five multiplications and five additions for one pixel independent of the size of the neighborhood the extension to the two dimensional case is considered and the resulting filtering structures are implemented as two dimensional recursive filters hence the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm performance measures of this new edge detector are given and compared to canny s filters various experimental results are shown

a four parameter atomic decomposition of chirplets a new four parameter atomic decomposition of chirplets is developed for compact and precise representation of signals with chirp components the four parameter chirplet atom is obtained from the unit gaussian function by successive applications of scaling fractional fourier transform frft and time shift and frequency shift operators the application of the frft operator results in a rotation of the wigner distribution of the gaussian in the time frequency plane by a specified angle the decomposition is realized by using the matching pursuit algorithm for this purpose the four parameter space is discretized to obtain a small but complete subset in the hilbert space a time frequency distribution tfd is developed for clear and readable visualization of the signal components it is observed that the chirplet decomposition and the related tfd provide more compact and precise representation of signal inner structures compared with the commonly used time frequency representations

an orthogonal family of quincunx wavelets with continuously adjustable order we present a new family of two dimensional and three dimensional orthogonal wavelets which uses quincunx sampling the orthogonal refinement filters have a simple analytical expression in the fourier domain as a function of the order spl lambda which may be noninteger we can also prove that they yield wavelet bases of l sub 2 r sup 2 for any spl lambda 0 the wavelets are fractional in the sense that the approximation error at a given scale a decays like o a sup spl lambda they also essentially behave like fractional derivative operators to make our construction practical we propose a fast fourier transform based implementation that turns out to be surprisingly fast in fact our method is almost as efficient as the standard mallat algorithm for separable wavelets

a bayesian multiple hypothesis approach to edge grouping and contour segmentation a contour segmentation algorithm is presented that takes an edge map and extracts continuous curves of arbitrary smoothness correctly handling curve intersections and capable of extrapolating over significant measurement gaps the algorithm incorporates noise models of the edge detection process and limited scene statistics it is based on an explicit contour model and employs a statistical distance measure to quantify the likelihood of each segmentation hypothesis a bayesian multiple hypothesis tree organizes possible segementations making it possible to postpone grouping decisions until a sufficient amount of information is available we have demonstrated its performance on real and synthetic images

equivalence of the void percolation problem for overlapping spheres and a network problem the percolation problem for the complement of the union of randomly located overlapping spheres is shown to be equivalent to a bond percolation problem on the edges of the voronoi tesselation of the sphere centres this result provides a convenient definition of cluster size and therefore of the critical exponents for this problem it also provides an efficient algorithm for monte carlo computation of the percolation threshold and the critical exponents

wigner based formulation of the chirplet transform using the wigner distribution we derive and analyze a matrix formulation for the chirplet transform a signal analysis tool that generalizes the wavelet and short time fourier transforms the formulation expresses the translations scalings and shears of the chirplet transform in terms of affine matrix transformations on the time frequency plane our approach leads naturally to several new signal transforms which we derive analyze and extend

independent component analysis for automatic note extraction from musical trills the method of principal component analysis which is based on second order statistics or linear independence has long been used for redundancy reduction of audio data the more recent technique of independent component analysis enforcing much stricter statistical criteria based on higher order statistical independence is introduced and shown to be far superior in separating independent musical sources this theory has been applied to piano trills and a database of trill rates was assembled from experiments with a computer driven piano recordings of a professional pianist and commercially available compact disks the method of independent component analysis has thus been shown to be an outstanding effective means of automatically extracting interesting musical information from a sea of redundant data

shear madness new orthonormal bases and frames using chirp functions the proportional bandwidth and constant bandwidth time frequency signal decompositions of the wavelet gabor and wilson orthonormal bases have attracted substantial interest for representing nonstationary signals however these representations are limited in that they are based on rectangular tessellations of the time frequency plane while much effort has gone into methods for designing nice wavelet and window functions for these frameworks little consideration has been given to methods for constructing orthonormal bases employing nonrectangular time frequency tilings the authors take a first step in this direction by deriving two new families of orthonormal bases and frames employing elements that shear or chirp in the time frequency plane in addition to translate and scale the new scale shear fan bases and shift shear chevron bases are obtained by operating on an existing wavelet gabor 1946 or wilson basis set with two special unitary warping transformations in addition to the theoretical benefit of broadening the class of valid time frequency plane tilings these new bases could possibly also be useful for representing certain types of signals such as chirping and dispersed signals

cluster based probability model and its application to image and texture processing we develop analyze and apply a specific form of mixture modeling for density estimation within the context of image and texture processing the technique captures much of the higher order nonlinear statistical relationships present among vector elements by combining aspects of kernel estimation and cluster analysis experimental results are presented in the following applications image restoration image and texture compression and texture classification

detection of faults in rotating machinery using periodic time frequency sparsity abstract this paper addresses the problem of extracting periodic oscillatory features in vibration signals for detecting faults in rotating machinery to extract the feature we propose an approach in the short time fourier transform stft domain where the periodic oscillatory feature manifests itself as a relatively sparse grid to estimate the sparse grid we formulate an optimization problem using customized binary weights in the regularizer where the weights are formulated to promote periodicity in order to solve the proposed optimization problem we develop an algorithm called augmented lagrangian majorization minimization algorithm which combines the split augmented lagrangian shrinkage algorithm salsa with majorization minimization mm and is guaranteed to converge for both convex and non convex formulation as examples the proposed approach is applied to simulated data and used as a tool for diagnosing faults in bearings and gearboxes for real data and compared to some state of the art methods the results show that the proposed approach can effectively detect and extract the periodical oscillatory features

enhanced b wavelets via mixed composite packets a modified b wavelet construction with enhanced filter characteristics is considered the design comprises a superposition of tessellated integer dilated sister wavelet functions we here propose a cascaded filter bank realization of this wavelet family together with some notable extensions we prove that modifications of low order members exist in the multiresolution subspace spanned by the half translates of the original wavelets and hence that the resulting modified wavelet coefficients can be computed as convolutions of the undecimated original wavelet coefficients finite impulse response filters are thus designed and incorporated into a b wavelet packet architecture such that the mainlobe to sidelobe ratio of the resulting wavelet filter characteristic is improved this is achieved by designing the filters so that zeros are introduced near to the maxima of the harmonics it is shown that the numbers of zeros can be balanced with the length of the corresponding filters by controlling the modification order several constructions are presented we prove that two such constructions satisfy the perfect reconstruction property for all orders the resulting modified wavelets preserve many of the properties of the original b wavelets such as differentiability number of vanishing moments symmetry anti symmetry finite support and the existence of a closed form expression

hilbert transform pairs of orthogonal wavelet bases necessary and sufficient conditions the condition on scaling filters of two orthogonal wavelet bases that render the corresponding wavelets as hilbert transform pairs is re examined in this note without making any pre assumption on the relationship between the two scaling filters the authors derive necessary and sufficient conditions for forming hilbert transform pairs they lead to new magnitude conditions and selesnick s phase condition unique solutions to these conditions are concluded it is shown that orthogonal wavelet bases form hilbert transform pairs if and only if the two scaling filters are offset from one another by half a sample

fast fir algorithms for the continuous wavelet transform from constrained least squares new algorithms for the continuous wavelet transform are developed that are easy to apply each consisting of a single pass finite impulse response fir filter and several times faster than the fastest existing algorithms the single pass filter named wt fir 1 is made possible by applying constraint equations to least squares estimation of filter coefficients which removes the need for separate low pass and high pass filters non dyadic two scale relations are developed and it is shown that filters based on them can work more efficiently than dyadic ones example applications to the mexican hat wavelet are presented

synthesis of musical tones based on the karhunen loeve transform a musical tone synthesis technique based on the karhunen loeve kl transform is introduced currently most additive synthesis methods are based on a truncated fourier series representation the computational load has been reduced considerably compared to that of fourier based additive synthesis by replacing the sinusoids with a smaller set of basis functions derived from kl statistical techniques algorithms are developed for the analysis of tones yielding the basis functions and synthesis parameters energy compression in the kl basis functions is enhanced by a classification procedure applied to the tones to be synthesized a high level of natural quality is achieved in tones synthesized with this method

region competition unifying snakes region growing and bayes mdl for multiband image segmentation we present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition this algorithm is derived by minimizing a generalized bayes minimum description length mdl criterion using the variational principle the algorithm is guaranteed to converge to a local minimum and combines aspects of snakes balloons and region growing the classic snakes balloons and region growing algorithms can be directly derived from our approach we provide theoretical analysis of region competition including accuracy of boundary location criteria for initial conditions and the relationship to edge detection using filters it is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images color images and texture images the novel color model allows us to eliminate intensity gradients and shadows thereby obtaining segmentation based on the albedos of objects it also helps detect highlight regions

wavelet transform with tunable q factor this paper describes a discrete time wavelet transform for which the q factor is easily specified hence the transform can be tuned according to the oscillatory behavior of the signal to which it is applied the transform is based on a real valued scaling factor dilation factor and is implemented using a perfect reconstruction over sampled filter bank with real valued sampling factors two forms of the transform are presented the first form is defined for discrete time signals defined on all of z the second form is defined for discrete time signals of finite length and can be implemented efficiently with ffts the transform is parameterized by its q factor and its oversampling rate redundancy with modest oversampling rates e g three to four times overcomplete being sufficient for the analysis synthesis functions to be well localized

overcomplete discrete wavelet transforms with rational dilation factors this paper develops an overcomplete discrete wavelet transform dwt based on rational dilation factors for discrete time signals the proposed overcomplete rational dwt is implemented using self inverting fir filter banks is approximately shift invariant and can provide a dense sampling of the time frequency plane a straightforward algorithm is described for the construction of minimal length perfect reconstruction filters with a specified number of vanishing moments whereas in the nonredundant rational case no such algorithm is available the algorithm is based on matrix spectral factorization the analysis synthesis functions discrete time wavelets can be very smooth and can be designed to closely approximate the derivatives of the gaussian function

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

perfect reconstruction filter banks with rational sampling factors an open problem namely how to construct perfect reconstruction filter banks with rational sampling factors is solved such filter banks have n branches each one having a sampling factor of p i qi and their sum equals one in this way the well known theory of filter banks with uniform band splitting is extended to allow for nonuniform divisions of the spectrum this can be very useful in the analysis of speech and music the theory relies on two transforms the first transform leads to uniform filter banks having polyphase components as individual filters the other results in a uniform filter bank containing shifted versions of same filters this in turn introduces dependencies in design and is left for future work as an illustration several design examples for the 2 3 1 3 case are given filter banks are then classified according to the possible ways in which they can be built it is shown that some cases cannot be solved even with ideal filters with real coefficients

an efficient algorithm for the calculation of a constant q transform an efficient method of transforming a discrete fourier transform dft into a constant q transform where q is the ratio of center frequency to bandwidth has been devised this method involves the calculation of kernels that are then applied to each subsequent dft only a few multiples are involved in the calculation of each component of the constant q transform so this transformation adds a small amount to the computation in effect this method makes it possible to take full advantage of the computational efficiency of the fast fourier transform fft graphical examples of the application of this calculation to musical signals are given for sounds produced by a clarinet and a violin

an efficient and provably correct algorithm for the multiscale estimation of image contours by means of polygonal lines a large portion of image contours is characterized by local properties such as sharp variations of the image intensity across the contour the integration of local image descriptors estimated by using these local properties into curvilinear descriptors is a difficult problem from a theoretical viewpoint because of the combinatorially large number of possible curvilinear descriptors to deal with this difficulty the notion of compressible graphs is introduced and a contour data model is defined leading to an efficient linear time algorithm which provably recovers contours with an upper bound on the approximation error

the chirplet transform physical considerations we consider a multidimensional parameter space formed by inner products of a parameterizable family of chirp functions with a signal under analysis we propose the use of quadratic chirp functions which we will call q chirps for short giving rise to a parameter space that includes both the time frequency plane and the time scale plane as 2 d subspaces the parameter space contains a time frequency scale volume and thus encompasses both the short time fourier transform as a slice along the time and frequency axes and the wavelet transform as a slice along the time and scale axes in addition to time frequency and scale there are two other coordinate axes within this transform space shear in time obtained through convolution with a q chirp and shear in frequency obtained through multiplication by a q chirp signals in this multidimensional space can be obtained by a new transform which we call the q chirplet transform or simply the chirplet transform the proposed chirplets are generalizations of wavelets related to each other by 2 d affine coordinate transformations translations dilations rotations and shears in the time frequency plane as opposed to wavelets which are related to each other by 1 d affine coordinate transformations translations and dilations in the time domain only

iterated filter banks with rational rate changes connection with discrete wavelet transforms some properties of two band filter banks with rational rate changes rational filter banks are first reviewed focusing then on iterated rational filter banks compactly supported limit functions are obtained in the same manner as previously done for dyadic schemes allowing a characterization of such filter banks these functions are carefully studied and the properties they share with the dyadic case are highlighted they are experimentally observed to verify a shift property strictly verified in the dyadic ease up to an error which can be made arbitrarily small when their regularity increases in this case the high pass outputs of an iterated filter bank can be very close to samples of a discrete wavelet transform with the same rational dilation factor straightforward extension of the formalism of multiresolution analysis is also made finally it is shown that if one is ready to put up with the loss of the shift property rational iterated filter banks can be used in the same manner as if they were dyadic filter banks with the advantage that rational dilation factors can be chosen closer to 1

constructing simple stable descriptions for image partitioning a new formulation of the image partitioning problem is presented construct a complete and stable description of an image in terms of a specified descriptive language that is simplest in the sense of being shortest we show that a descriptive language limited to a low order polynomial description of the intensity variation within each region and a chain code like description of the region boundaries yields intuitively satisfying partitions for a wide class of images the advantage of this formulation is that it can be extended to deal with subsequent steps of the image understanding problem or to deal with other attributes such as texture in a natural way by augmenting the descriptive language experiments performed on a variety of both real and synthetic images demonstrate the superior performance of this approach over partitioning techniques based on clustering vectors of local image attributes and standard edge detection techniques

modeling and estimation of multiresolution stochastic processes an overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing a natural framework for developing such a theory is the study of stochastic processes indexed by nodes on lattices or trees in which different depths in the tree or lattice correspond to different spatial scales in representing a signal or image in particular it is shown how the wavelet transform directly suggests such a modeling paradigm this perspective then leads directly to the investigation of several classes of dynamic models and related notions of multiscale stationarity in which scale plays the role of a time like variable the investigation of models on homogeneous trees is emphasized the framework examined here allows for consideration in a very natural way of the fusion of data from sensors with differing resolutions also thanks to the fact that wavelet transforms do an excellent job of compressing large classes of covariance kernels it is seen that these modeling paradigms appear to have promise in a far broader context than one might expect

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

shiftable multiscale transforms one of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance the content of wavelet subbands is unstable under translations of the input signal wavelet transforms are also unstable with respect to dilations of the input signal and in two dimensions rotations of the input signal the authors formalize these problems by defining a type of translation invariance called shiftability in the spatial domain shiftability corresponds to a lack of aliasing thus the conditions under which the property holds are specified by the sampling theorem shiftability may also be applied in the context of other domains particularly orientation and scale jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored two examples of jointly shiftable transforms are designed and implemented a 1 d transform that is jointly shiftable in position and scale and a 2 d transform that is jointly shiftable in position and orientation the usefulness of these image representations for scale space analysis stereo disparity measurement and image enhancement is demonstrated

line search and trust region strategies for canonical decomposition of semi nonnegative semi symmetric 3rd order tensors numerical solutions are proposed to fit the candecomp parafac cp model of real three way arrays when the latter are both nonnegative and symmetric in two modes in other words a semi nonnegative indscal analysis is performed the nonnegativity constraint is circumvented by means of changes of variable into squares leading to an unconstrained problem in addition two globalization strategies are studied namely line search and trust region regarding the former a global plane search scheme is considered it consists in computing for a given direction one or two optimal stepsizes depending on whether the same stepsize is used in various updating rules moreover we provide a compact matrix form for the derivatives of the objective func tion this allows for a direct implementation of several iterative algorithms such as conjugate gradient levenberg marquardt and newton like methods in matrix programming environments like matlab our numerical results show the advantage of our optimization strategies when combined with a priori information such as partial symmetry

theory implementation and applications of nonstationary gabor frames signal analysis with classical gabor frames leads to a fixed time frequency resolution over the whole time frequency plane to overcome the limitations imposed by this rigidity we propose an extension of gabor theory that leads to the construction of frames with time frequency resolution changing over time or frequency we describe the construction of the resulting nonstationary gabor frames and give the explicit formula for the canonical dual frame for a particular case the painless case we show that wavelet transforms constant q transforms and more general filter banks may be modeled in the framework of nonstationary gabor frames further we present the results in the finite dimensional case which provides a method for implementing the above mentioned transforms with perfect reconstruction finally we elaborate on two applications of nonstationary gabor frames in audio signal processing namely a method for automatic adaptation to transients and an algorithm for an invertible constant q transform

design of two band critically sampled rational rate filter banks with multiple regularity orders and associated discrete wavelet transforms an approach for designing two band rational rate critically sampled nonorthogonal filter banks with perfect reconstruction and multiple regularity orders is proposed this approach relies on an updated result on the relationship between the filters in the filter bank to achieve all the desired properties filter responses are optimized to approximate ideal brick wall responses subject to linear and nonlinear constraints derived from regularity and perfect reconstruction conditions respectively the obtained designs are approximately shift invariant as a result of strong frequency selectivity and multiple regularity orders two methods for solving the nonconvex optimization design problem are presented and the results from the proposed approach are compared against existing designs in the literature

weighted low rank sparse model via nuclear norm minimization for bearing fault detection abstract it is a fundamental task in the machine fault diagnosis community to detect impulsive signatures generated by the localized faults of bearings the main goal of this paper is to exploit the low rank physical structure of periodic impulsive features and further establish a weighted low rank sparse model for bearing fault detection the proposed model mainly consists of three basic components an adaptive partition window a nuclear norm regularization and a weighted sequence firstly due to the periodic repetition mechanism of impulsive feature an adaptive partition window could be designed to transform the impulsive feature into a data matrix the highlight of partition window is to accumulate all local feature information and align them then all columns of the data matrix share similar waveforms and a core physical phenomenon arises i e these singular values of the data matrix demonstrates a sparse distribution pattern therefore a nuclear norm regularization is enforced to capture that sparse prior however the nuclear norm regularization treats all singular values equally and thus ignores one basic fact that larger singular values have more information volume of impulsive features and should be preserved as much as possible therefore a weighted sequence with adaptively tuning weights inversely proportional to singular amplitude is adopted to guarantee the distribution consistence of large singular values on the other hand the proposed model is difficult to solve due to its non convexity and thus a new algorithm is developed to search one satisfying stationary solution through alternatively implementing one proximal operator operation and least square fitting moreover the sensitivity analysis and selection principles of algorithmic parameters are comprehensively investigated through a set of numerical experiments which shows that the proposed method is robust and only has a few adjustable parameters lastly the proposed model is applied to the wind turbine wt bearing fault detection and its effectiveness is sufficiently verified compared with the current popular bearing fault diagnosis techniques wavelet analysis and spectral kurtosis our model achieves a higher diagnostic accuracy

musical fundamental frequency tracking using a pattern recognition method in a recent article j c brown calculation of a constant q spectral transform j acoust soc am 89 425 434 1991 the calculation of a constant q spectral transform that gives a constant pattern in the log frequency domain for sounds with harmonic frequency components has been described this property has been utilized in calculating the cross correlation function of spectra of sounds produced by musical instruments with the ideal pattern which consists of one s at the positions of harmonic frequency components therefore the position of the best approximation to the ideal pattern for the spectra produced by these instruments has been determined and in so doing the fundamental frequency for that sound has been obtained results are presented for scales produced by the piano flute and violin as well as for arpeggios played by a wide variety of instruments

a new design algorithm for two band orthonormal rational filter banks and orthonormal rational wavelets we present a new algorithm for the design of orthonormal two band rational filter banks owing to the connection between iterated rational filter banks and rational wavelets this is also a design algorithm for orthonormal rational wavelets it is basically a simple iterative procedure which explains its exponential convergence and adaptability under various linear constraints e g regularity although the filters obtained from this algorithm are suboptimally designed they show excellent frequency selectivity after an in depth account of the algorithm we discuss the properties of the rational wavelets generated by some designed filters in particular we stress the possibility to design almost shift error free wavelets which allows the implementation of a rational wavelet transform

a dual tree rational dilation complex wavelet transform in this correspondence we introduce a dual tree rational dilation complex wavelet transform for oscillatory signal processing like the short time fourier transform and the dyadic dual tree complex wavelet transform the introduced transform employs quadrature pairs of time frequency atoms which allow to work with the analytic signal the introduced wavelet transform is a constant q transform a property lacked by the short time fourier transform which in turn makes the introduced transform more suitable for models that depend on scale also the frequency resolution can be as high as desired a property lacked by the dyadic dual tree complex wavelet transform which makes the introduced transform more suitable for processing oscillatory signals like speech audio and various biomedical signals

estimation of frequency for am fm models using the phase vocoder framework this paper proposes an extension of the applicability of phase vocoder based frequency estimators for generalized sinusoidal models which include phase and amplitude modulations a first approach called phase corrected vocoder pcv takes into account the modification of the fourier phases resulting from these modulations another approach is based on an adaptation of the principles of the time frequency reassignment and is referred to as the reassigned vocoder rv the robustness of the estimation against noise is studied both theoretically and experimentally and the performance is assessed in comparison with two state of the art algorithms an unmodified version of the reassignment method and a quadratically interpolated fast fourier transform method qifft

frequency domain design of overcomplete rational dilation wavelet transforms the dyadic wavelet transform is an effective tool for processing piecewise smooth signals however its poor frequency resolution its low q factor limits its effectiveness for processing oscillatory signals like speech eeg and vibration measurements etc this paper develops a more flexible family of wavelet transforms for which the frequency resolution can be varied the new wavelet transform can attain higher q factors desirable for processing oscillatory signals or the same low q factor of the dyadic wavelet transform the new wavelet transform is modestly overcomplete and based on rational dilations like the dyadic wavelet transform it is an easily invertible constant q discrete transform implemented using iterated filter banks and can likewise be associated with a wavelet frame for l2 r the wavelet can be made to resemble a gabor function and can hence have good concentration in the time frequency plane the construction of the new wavelet transform depends on the judicious use of both the transform s redundancy and the flexibility allowed by frequency domain filter design

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics

localization of the complex spectrum the s transform the s transform which is introduced in the present correspondence is an extension of the ideas of the continuous wavelet transform cwt and is based on a moving and scalable localizing gaussian window it is shown to have some desirable characteristics that are absent in the continuous wavelet transform the s transform is unique in that it provides frequency dependent resolution while maintaining a direct relationship with the fourier spectrum these advantages of the s transform are due to the fact that the modulating sinusoids are fixed with respect to the time axis whereas the localizing scalable gaussian window dilates and translates

fast matching pursuit with a multiscale dictionary of gaussian chirps we introduce a modified matching pursuit algorithm called fast ridge pursuit to approximate n dimensional signals with m gaussian chirps at a computational cost o mn instead of the expected o mn sup 2 logn at each iteration of the pursuit the best gabor atom is first selected and then its scale and chirp rate are locally optimized so as to get a good chirp atom i e one for which the correlation with the residual is locally maximized a ridge theorem of the gaussian chirp dictionary is proved from which an estimate of the locally optimal scale and chirp is built the procedure is restricted to a sub dictionary of local maxima of the gaussian gabor dictionary to accelerate the pursuit further the efficiency and speed of the method is demonstrated on a sound signal