on the statistical efficiency of the lms algorithm with nonstationary inputs a fundamental relationship exists between the quality of an adaptive solution and the amount of data used in obtaining it quality is defined here in terms of misadjustment the ratio of the excess mean square error mse in an adaptive solution to the minimum possible mse the higher the misadjustment the lower the quality is the quality of the exact least squares solution is compared with the quality of the solutions obtained by the orthogonalized and the conventional least mean square lms algorithms with stationary and nonstationary input data when adapting with noisy observations a filter trained with a finite data sample using an exact least squares algorithms will have a misadjustment given by m frac n n frac number of weights number of training samples if the same adaptive filter were trained with a steady flow of data using an ideal orthogonalized lms algorithm the misadjustment would be m frac n 4 tau mse frac number of weights number of training samples thus for a given time constant tau mse of the learning process the ideal orthogonalized lms algorithm will have about as low a misadjustment as can be achieved since this algorithm performs essentially as an exact least squares algorithm with exponential data weighting it is well known that when rapid convergence with stationary data is required exact least squares algorithms can in certain cases outperform the conventional widrow hoff lms algorithm it is shown here however that for an important class of nonstationary problems the misadjustment of conventional lms is the same as that of orthogonalized lms which in the stationary case is shown to perform essentially as an exact least squares algorithm

statistical mechanics of interfering links we consider the statistical mechanics of interfering transmissions in a wireless communications protocol in this case a connection between two nodes requires all other nodes within communication distance of the given two nodes to remain quiet on the given channel this leads to an interesting problem of dimers on a lattice with a restriction that no two dimers can overlap or be nearest neighbors we consider both an equilibrium and a nonequilibrium greedy dynamics for the links the equilibrium properties of the model are found to exhibit an interesting spin glass transition at maximum density on certain lattices while the greedy construction is related to the problem of random sequential adsorption

a novel wavelet based generalized sidelobe canceller this paper presents a novel narrow band adaptive beamformer with the generalized sidelobe canceller gsc as the underlying structure the new beamformer employs a wavelet based approach for the design of the blocking matrix of the gsc which is now constituted by a set of regular m band wavelet filters such a construction of the blocking matrix can not only block the desired signals from the lower path as required provided the wavelet filters have sufficiently high regularity but it also encompasses the widely used one with ones and minus ones along the diagonals as a special case in addition it possesses two advantageous features first the eigenvalue spreads of the covariance matrices of the blocking matrix outputs as demonstrated in various scenarios are decreased as compared with those of previous approaches since the popular least mean squares lms algorithm has been notorious for its slow convergence rate the reduction of the eigenvalue spreads can in general accelerate the convergence speed of the succeeding lms algorithm second the new beamformer belongs to a specific type of partially adaptive beamformers wherein only a portion of the available degree of freedom is utilized in the adaptive processing as such the overall computational complexity is substantially reduced when compared to previous works the issues of choosing the parameters involved for superior performance are also addressed simulation results are furnished as well to justify this new approach

stochastic modeling of the transform domain varepsilon rm lms algorithm this paper presents a statistical analysis of the transform domain least mean square tdlms algorithm resulting in a more accurate model than those discussed in the current open literature the motivation to analyze such an algorithm comes from the fact that the tdlms presents a higher convergence speed for correlated input signals as compared with other adaptive algorithms possessing a similar computational complexity such a fact makes it a highly competitive alternative to some applications approximate analytical models for the first and second moments of the filter weight vector are obtained the tdlms algorithm has an orthonormal transformation stage accomplishing a decomposition of the input signal into distinct frequency bands in which the interband samples are practically uncorrelated on the other hand the intraband samples are correlated the larger the number of bands the higher their correlation the model is then derived taking into account such a correlation requiring that a high order hyperelliptic integral be computed in addition to the proposed model an approximate procedure for computing high order hyperelliptic integrals is presented a regularization parameter is also considered in the model expressions permitting to assess its impact on the adaptive algorithm behavior an upper bound for the step size control parameter is also obtained through simulation results the accuracy of the proposed model is assessed

block adaptive filters with deterministic reference inputs for event related signals blms and brls adaptive estimation of the linear coefficient vector in truncated expansions is considered for the purpose of modeling noisy recurrent signals two different criteria are studied for block wise processing of the signal the mean square error mse and the least squares ls error the block lms blms algorithm being the solution of the steepest descent strategy for minimizing the mse is shown to be steady state unbiased and with a lower variance than the lms algorithm it is demonstrated that blms is equivalent to an exponential averager in the subspace spanned by the truncated set of basis functions the block recursive least squares brls solution is shown to be equivalent to the blms algorithm with a decreasing step size the brls is unbiased at any occurrence number of the signal and has the same steady state variance as the blms but with a lower variance at the transient stage the estimation methods can be interpreted in terms of linear time variant filtering the performance of the methods is studied on an ecg signal and the results show that the performance of the block algorithms is superior to that of the lms algorithm in addition measurements with clinical interest are found to be more robustly estimated in noisy signals

simultaneous structure and texture image inpainting an algorithm for the simultaneous filling in of texture and structure in regions of missing image information is presented in this paper the basic idea is to first decompose the image into the sum of two functions with different basic characteristics and then reconstruct each one of these functions separately with structure and texture filling in algorithms the first function used in the decomposition is of bounded variation representing the underlying image structure while the second function captures the texture and possible noise the region of missing information in the bounded variation image is reconstructed using image inpainting algorithms while the same region in the texture image is filled in with texture synthesis techniques the original image is then reconstructed adding back these two sub images the novel contribution of this paper is then in the combination of these three previously developed components image decomposition with inpainting and texture synthesis which permits the simultaneous use of filling in algorithms that are suited for different image characteristics examples on real images show the advantages of this proposed approach

variable step size lms algorithm for fractal signals this paper presents a novel variable step size lms vslms algorithm for tracking signals from the gaussian 1 fbeta family of fractal signals that are inherently nonstationary the proposed algorithm differs from the existing vslms algorithms in the following ways 1 it deals with a specific class of nonstationary signals 2 it utilizes a nondiagonal step size matrix which is simultaneously diagonalizable with the auto covariance matrix of the input signal 3 in the decoupled weight vector space one of the step size parameters requires time varying constraints for the algorithm to converge to the optimal weights whereas the constraints on the remaining step size parameters are time invariant and 4 it computes the step size matrix by estimating the hurst exponent required to characterize the statistical properties of the signal at the input of the adaptive filter the experimental setup of an adaptive channel equalizer is considered for equalization of fractal signals transmitted over stationary awgn channel the performance of the proposed fractal based variable step size least mean square fb vslms algorithm is compared with the unsigned vslms algorithm and is observed to be better for the class of nonstationary signals considered

an analysis of real fourier domain based adaptive algorithms implemented with the hartley transform using cosine sine symmetries the least mean squared lms algorithm and its variants have been the most often used algorithms in adaptive signal processing however the lms algorithm suffers from a high computational complexity especially with large filter lengths the fourier transform based block normalized lms fbnlms reduces the computation count by using the discrete fourier transform dft and exploiting the fast algorithms for implementing the dft even though the savings achieved with the fbnlms over the direct lms implementation are significant the computational requirements of fbnlms are still very high rendering many real time applications like audio and video estimation infeasible the hartley transform based bnlms hbnlms is found to have a computational complexity much less than and a memory requirement almost of the same order as that of the fbnlms this paper is based on the cosine and sine symmetric implementation of the discrete hartley transform dht which is the key in reducing the computational complexity of the fbnlms by 33 asymptotically with respect to multiplications the parallel implementation of the discrete cosine transform dct in turn can lead to more efficient implementations of the hbnlms

monte carlo simulations of the ising spin glass on lattices with finite connectivity the authors have simulated the ising spin glass model on a random lattice with a finite average coordination number and also on the bethe lattice with various different boundary conditions in particular they have calculated the overlap function p q for two independent samples for the random lattice the results are consistent with a spin glass transition above which p q converges to a dirac delta function for large n number of sites and below which p q has in addition a long tail similar to previous results obtained for the infinite range model for the bethe lattice they obtain results in the interior by discarding the two outer shells of the cayley tree when calculating the thermal averages for fixed uncorrelated boundary conditions p q seems to converge to a delta function even below the spin glass transition whereas on a closed lattice correlated boundary conditions p q has a long tail similar to its behaviour in the random lattice case

iterative reweighted least squares design of fir filters develops a new iterative reweighted least squares algorithm for the design of optimal l sub p approximation fir filters the algorithm combines a variable p technique with a newton s method to give excellent robust initial convergence and quadratic final convergence details of the convergence properties when applied to the l sub p optimization problem are given the primary purpose of l sub p approximation for filter design is to allow design with different error criteria in pass and stopband and to design constrained l sub 2 approximation filters the new method can also be applied to the complex chebyshev approximation problem and to the design of 2d fir filters

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

a self orthogonalizing efficient block adaptive filter this paper deals with the development of a unique self orthogonalizing block adaptive filter sobaf algorithm that yields efficient finite impulse response fir adaptive filter structures computationally the sobaf is shown to be superior to the least mean squares lms algorithm the consistent convergence performance which it provides lies between that of the lms and the recursive least squares rls algorithm but unlike the lms is virtually independent of input statistics the block nature of the sobaf exploits the use of efficient circular convolution algorithms such as the fft the rectangular transform rt the fermat number transform fnt and the fast polynomial transform fpt in performance the sobaf achieves the mean squared error mse convergence of a self orthogonalizing structure that is the adaptive filter converges under any input conditions at the same rate as an lms algorithm would under white input conditions furthermore the selection of the step size for the sobaf is straightforward as the range and the optimum value of the step size are independent of the input statistics

convergence analysis of a data echo canceller with a stochastic gradient adaptive fir filter using the sign algorithm under the assumption that the errors at the taps are gaussian distributed a new set of recurrence formulae is derived for calculating theoretical convergence process of a data echo canceller equipped with an fir filter that is adaptively controlled by using the stochastic gradient sign algorithm with a binary and white process as the filter input convergence curves for the mean squared residual echo based on the recurrence formulae show an excellent agreement with those obtained by simulation approximate recurrence formulae that yield a useful though less accurate estimation of the residual echo convergence are also proposed furthermore a closed form solution to the approximate recurrence formulae is derived and finally probability density function of the residual echo is depicted as it changes its shape as the echo canceller converges

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

the block processing ftf adaptive algorithm a new block type adaptive filtering algorithm is presented this new block adaptive filter differs from the frequency domain block adaptive filters of ferrara 1980 and of clark mitra and parker 1980 in that the new method applies a deterministic time domain least squares criteria within each of the data blocks information is carried from block to block via a weighted initial condition this new block fast transversal filters bftf algorithm is a numerically stable algorithm and can also be used to perform efficient least squares system identification on any one data block in which case it shows a moderate computational advantage over the previous most efficient single data block algorithms of morf et al 1977 of marple 1981 and of kalouptsidis manolakis and carayannis 1984 1985 mechanisms for tracking and varying block length from block to block are also presented and evaluated finally we indicate how the new algorithm could be pipelined for maximum throughput with delay proportional to the number of parameters after computation of the sample correlation lags

a unified approach to time and frequency domain realization of fir adaptive digital filters specific implementations of the finite impulse response fir block adaptive filter in the frequency domain are presented and some of their important properties are discussed the time domain block adaptive filter implemented in the frequency domain is shown to be equivalent to the frequency domain adaptive filter derived in the frequency domain provided data sectioning is done properly all of the known time and frequency domain adaptive filters 1 12 16 18 are contained in the set of possible block adaptive filter structures thus the block adaptive filter is generic and its formulation unifies the current theory of time and frequency domain fir adaptive filter structures a detailed analysis of overlap save and overlap add implementations shows that the former is to be preferred for adaptive applications because it requires less computation a fact that is not true for fixed coefficient filters

adaptive iir filtering using parallel form realizations several parallel form adaptive iir infinite impulse response filters are presented including a frequency domain implementation based on the discrete fourier transform and a recursive frequency sampling structure the performance of the frequency domain adaptive iir filter is investigated in a system identification application which includes an analysis of its modeling capabilities and a discussion of the mean square error performance surface computer simulation results are presented to illustrate the robust convergence properties of the adaptive algorithm and to demonstrate the stability of the filter

nonlinear quantization effects in the lms and block lms adaptive algorithms a comparison digital implementations of the least mean square lms and block lms blms algorithms are compared with respect to finite word effects the algorithm stalling phenomenon is studied using gaussian data models and conditional expectation arguments it is shown that the blms algorithm requires 1 2 log sub 2 l k fewer bits for the same stalling behavior l block length and k lies between 0 2 and 1 0 depending on the precise definition of algorithm stalling on the other hand the lms algorithm requires log sub 2 l fewer bits than blms for the same level of saturation behavior transient response at algorithm initialization hence the lms algorithm requires 1 2 log sub 2 l k fewer bits than the blms algorithm for the same saturation and stalling effects

image denoising via sparse and redundant representations over learned dictionaries we address the image denoising problem where zero mean white and homogeneous gaussian additive noise is to be removed from a given image the approach taken is based on sparse and redundant representations over trained dictionaries using the k svd algorithm we obtain a dictionary that describes the image content effectively two training options are considered using the corrupted image itself or training on a corpus of high quality image database since the k svd is limited in handling small image patches we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image we show how such bayesian treatment leads to a simple and effective denoising algorithm this leads to a state of the art denoising performance equivalent and sometimes surpassing recently published leading alternative denoising methods

a fast adaptive filter algorithm using eigenvalue reciprocals as stepsizes it is shown that there exist finite optimum update positions in the gradient direction of the least mean square lms algorithm the optimum stepsizes to reach these positions are in a discrete set on this basis a new adaptive filter adf algorithm is proposed the discrete cosine transform a fairly good approximation of the karhunen loeve transform for a large number of signal classes is used to estimate the optimum stepsizes a block averaging operation is also used for smoothing the gradient estimate computer simulations show that the proposed adf algorithm provides fast convergence rates when the input signal autocorrelation matrix has either large or small eigenvalue spread ratio of the largest to the smallest eigenvalues the number of multiplications required by the new adf is about 11 log sub 2 n 12 which is comparable to the 10 log sub 2 n 8 required by the fast lms algorithm

the application of the frequency domain lms adaptive filter to split array bearing estimation with a sinusoidal signal this paper considers the use of the frequency domain lms adaptive filter in a split array sonar to estimate the bearing of a plane wave acoustic source radiating a sinusoidal signal for such a signal the bearing can be determined from the relative signal phase between split array outputs at the signal frequency in this paper the split array outputs are fast fourier transformed and used as the primary and reference inputs to the frequency domain lms adaptive filter configured as a canceller the signal frequency is estimated based upon the magnitude of the weights and the relative signal phase between split array outputs is estimated as the phase of the frequency domain weight with the largest magnitude the statistics of the magnitude and phase of the frequency domain weights are determined and then mapped to the variance of the bearing estimate computer simulations of the adaptive tracker which verify the analytical results are included

realization of adaptive digital filters using the fermat number transform an efficient realization of the block least mean square adaptive digital filters using fast transforms is discussed the computational complexities of the fermat number transform realization and the fixed point fast fourier transform realization are compared and their convergence properties are studied through the computer simulation of practical applications

block realization of multirate adaptive digital filters in this paper we study multirate transversal adaptive digital filters adf s based on the block least mean square blms algorithms these include an adf with decimation adfd and an adf with interpolation adfi we first formulate these filters based on the block mean squared error bmse criterion and derive blms multi rate weight adjustment algorithms and then study efficient realization of those filters it is shown that the blms adfd can be realized efficiently in the direct form or in the filter bank structure both using the fast fourier transform fft and an appropriate sectioning procedure according to our analysis of computational complexity the fft realization of the blms adfd in the filter bank structure is more efficient than in the direct form and the two structures using the fft become more efficient in comparison to the lms adfd as the number of weights increases unlike the direct form realization the filter bank realization of the blms adfd using the fft becomes more efficient as the decimation ratio increases similar results have been obtained for the blms adfi finally we investigate by computer simulation the effects of different weight adjustment algorithms and several system parameters on the performances of adfd s the results of simulation indicate that as expected the convergence speed of the blms adfd can be significantly improved by self orthogonalization of weight adjustment in the frequency domain furthermore the convergence factor of the self orthogonalizing blms adfd can be chosen such that the steady state performance of the new adfd is the same as that of the existing lms adfd

efficiency analysis of multihypothesis motion compensated prediction for video coding overlapped block motion compensation or b frames are examples of multihypothesis motion compensation where several motion compensated signals are superimposed to reduce the bit rate of a video codec this paper extends the wide sense stationary theory of motion compensated prediction mcp for hybrid video codecs to multihypothesis motion compensation the power spectrum of the prediction error is related to the displacement error probability density functions pdfs of an arbitrary number of hypotheses in a closed form expression we then study the influence of motion compensation accuracy on the efficiency of multihypothesis motion compensation as well as the influence of the residual noise level and the gain from optimal combination of n hypotheses for the noise free limiting case doubling the number of equally good hypotheses can yield a gain of up to 1 2 bits sample while doubling the accuracy of motion compensation can additionally reduce the bit rate by up to 1 bit sample independent of n for realistic noise levels it is shown that the introduction of b frames or overlapped block motion compensation can provide larger gains than doubling motion compensation accuracy spatial filtering of the motion compensated candidate signals becomes less important if more hypotheses are combined the critical accuracy beyond which the gain due to more accurate motion compensation is small moves to larger displacement error variances with increasing noise and increasing number of hypotheses n hence sub pel accurate motion compensation becomes less important with multihypothesis mcp the theoretical insights are confirmed by experimental results for overlapped block motion compensation b frames and multiframe motion compensated prediction with up to eight hypotheses from ten previous frames

a discriminative approach for wavelet denoising this paper suggests a discriminative approach for wavelet denoising where a set of mapping functions mfs are applied to the transform coefficients in an attempt to produce a noise free image as opposed to the descriptive approaches modeling image or noise priors is not required here and the mfs are learned directly from an ensemble of example images using least squares fitting the suggested scheme generates a novel set of mfs that are essentially different from the traditional soft hard thresholding in the over complete case these mfs are demonstrated to obtain comparable performance to the state of the art denoising approaches additionally this framework enables a seamless customization of the shrinkage operation to a new set of restoration problems that were not addressed previously with shrinkage techniques such as deblurring jpeg artifact removal and various types of additive noise that are not necessarily gaussian white noise

optimum block adaptive filtering algorithms using the preconditioning technique we propose three block adaptive algorithms using the preconditioning technique the toeplitz preconditioned optimum block adaptive toba algorithm employs a preconditioner assumed to be toeplitz the symmetric successive overrelaxation ssor preconditioned optimum block adaptive soba algorithm uses a product of triangular matrices as a preconditioner and the circulant preconditioned oba coba algorithm is based on a circulant preconditioner it is also shown that their tracking properties and convergence rates are superior to those of the oba algorithm the self orthogonizing block adaptive filter sobaf and the normalized frequency domain oba nfoba algorithm

a transform domain circular convolution algorithm for adaptive filtering a new transform domain adaptive digital filter using the common lms adaptation algorithm based on a highly efficient circular convolution algorithm is presented the proposed filter has an easily implementable structure involving only real valued arithmetic it is shown to converge to the wiener solution in the transform domain and has significant advantage in efficiency over the corresponding fft based adaptive digital filters

performance of lms based adaptive filters in tracking a time varying plant the article gives a general analysis of the lms based adaptive filters when used for tracking a class of time varying plants the algorithms covered are the conventional lms the transform domain normalized lms and the lms newton algorithm an important fact that we observe is that in comparing these algorithms better initial convergence does not necessarily mean better tracking a few special cases are presented that show the contrary

generalized sliding fft and its application to implementation of block lms adaptive filters this paper has two contributions first the concept of the generalized sliding fast fourier transform gsfft as an efficient implementation of the hopping fft is introduced application of the gsfft is broad and not limited to what has been considered in this paper the frequency domain block lms fblms adaptive filters are then revised and their implementations for block lengths less than the length of the adaptive filter are studied the gsfft and the available pruned ffts are used to give an efficient implementation of these filters in the particular case of the block length equal to one where the fblms algorithm reduces to the frequency domain lms flms algorithm it is shown that the latter can be implemented with the order of m complexity where m is the length of the adaptive filter

wavelet transform domain adaptive fir filtering this paper presents and studies two new wavelet transform domain least mean square lms algorithms the algorithms exploit the special sparse structure of the wavelet transform of wide classes of correlation matrices and their cholesky factors in order to compute a whitening transformation of the input data in the wavelet domain and minimize computational complexity the procedures differ in the exact estimates they use and in the way they identify the data dependent whitening transformation the first approach explicitly computes a sparse estimate of the wavelet domain correlation matrix of the input process it then computes the cholesky factor of that matrix and uses its inverse to whiten the input the complexity of this first approach is o n log sup 2 n in contrast the second approach computes a sparse estimate of the cholesky factor of the wavelet domain correlation matrix of the input process directly this second approach has a computational complexity of o n log n floating point operations however it requires a more complex bookkeeping procedure both algorithms have a convergence rate that is faster than that of time domain lms and discrete fourier transform dft or discrete cosine transform dct based lms procedures the paper compares the two procedures and analyzes their mean and mean square performance

on the interrelationships among a class of convolutions in this paper some interrelationships among a class of circular operations are investigated based on matrix formulation it is shown that a class of convolutions representing forward backward and convolution correlation of two periodic sequences may be related to each other in terms of discrete transforms having the circular convolution property the results obtained are useful in efficient realization of adaptive digital filters using fast transforms

wedgelets nearly minimax estimation of edges we study a simple horizon model for the problem of recovering an image from noisy data in this model the image has an edge with fi holder regularity adopting the viewpoint of computational harmonic analysis we develop an overcomplete collection of atoms called wedgelets dyadically organized indicator functions with a variety of locations scales and orientations the wedgelet representation provides nearly optimal representations of objects in the horizon model as measured by minimax description length we show how to rapidly compute a wedgelet approximation to noisy data by flnding a special edgelet decorated recursive partition which minimizes a complexity penalized sum of squares this estimate using su cient sub pixel resolution achieves nearly the minimax mean squared error in the horizon model in fact the method is adaptive in the sense that it achieves nearly the minimax risk for any value of the unknown degree of regularity of the horizon 1 fi 2 wedgelet analysis and de noising may be used successfully outside the horizon model we study images modelled as indicators of star shaped sets with smooth bound aries and show that complexity penalized wedgelet partitioning achieves nearly the minimax risk in that setting also

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

image denoising using scale mixtures of gaussians in the wavelet domain we describe a method for removing noise from digital images based on a statistical model of the coefficients of an overcomplete multiscale oriented basis neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables a gaussian vector and a hidden positive scalar multiplier the latter modulates the local variance of the coefficients in the neighborhood and is thus able to account for the empirically observed correlation between the coefficient amplitudes under this model the bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable we demonstrate through simulations with images contaminated by additive white gaussian noise that the performance of this method substantially surpasses that of previously published methods both visually and in terms of mean squared error

adaptive filtering in subbands using a weighted criterion transform domain adaptive algorithms have been proposed to reduce the eigenvalue spread of the matrix governing their convergence thus improving the convergence rate however a classical problem arises from the conflicting requirements between algorithm improvement requiring rather long transforms and the need to keep the input output delay as small as possible thus imposing short transforms this dilemma has been alleviated by the so called short block transform domain algorithms but is still apparent this paper proposes an adaptive algorithm compatible with the use of rectangular orthogonal transforms e g critically subsampled lossless perfect reconstruction filter banks thus allowing better tradeoffs between algorithm improvement arithmetic complexity and input output delay the method proposed makes a direct connection between the minimization of a specific weighted least squares criterion and the convergence rate of the corresponding stochastic gradient algorithm this method leads to improvements in the convergence rate compared with both lms and classical frequency domain algorithms

a step by step quasi newton algorithm in the frequency domain and its application to adaptive channel equalization in this paper a new efficient adaptive filtering algorithm belonging to the quasi newton qn family is proposed in the new algorithm the involved inverse hessian matrix is approximated by a proper expansion consisting of powers of a toeplitz matrix due to this formulation the algorithm can be implemented in the frequency domain fd using the fast fourier transform fft efficient recursive relations for the frequency domain quantities updated on a step by step basis have been derived the proposed algorithm turns out to be particularly suitable for adaptive channel equalization in wireless burst transmission systems based on this approach new adaptive linear equalization le and decision feedback equalization dfe algorithms have been developed these algorithms enjoy the combined advantages of qn formulation and fd implementation exhibiting faster convergence rate than their stochastic gradient counterparts and less computational complexity as compared with other newton type algorithms

the comparison of the constrained and unconstrained frequency domain block lms adaptive algorithms convergence properties of the constrained and the unconstrained frequency domain block lms algorithms are analyzed comparisons based on both a theoretical analysis and computer simulation are given it is shown that the unconstrained algorithm has a slower convergence rate and smaller stable range of step size than that of the constrained algorithm

rate distortion optimized tree structured compression algorithms for piecewise polynomial images this paper presents novel coding algorithms based on tree structured segmentation which achieve the correct asymptotic rate distortion r d behavior for a simple class of signals known as piecewise polynomials by using an r d based prune and join scheme for the one dimensional case our scheme is based on binary tree segmentation of the signal this scheme approximates the signal segments using polynomial models and utilizes an r d optimal bit allocation strategy among the different signal segments the scheme further encodes similar neighbors jointly to achieve the correct exponentially decaying r d behavior d r spl sim c sub 0 2 sup c1r thus improving over classic wavelet schemes we also prove that the computational complexity of the scheme is of o nlogn we then show the extension of this scheme to the two dimensional case using a quadtree this quadtree coding scheme also achieves an exponentially decaying r d behavior for the polygonal image model composed of a white polygon shaped object against a uniform black background with low computational cost of o nlogn again the key is an r d optimized prune and join strategy finally we conclude with numerical results which show that the proposed quadtree coding scheme outperforms jpeg2000 by about 1 db for real images like cameraman at low rates of around 0 15 bpp

performance of transform domain lms adaptive digital filters in this paper we analyze the performance particularly the convergence behavior of the transform domain least mean square lms adaptive digital filter adf using the discrete fourier transform and discrete orthogonal transforms such as discrete cosine and sine transforms we first obtain the optimum wiener solution and the minimum mean squared error mse in the transform domain it is shown that the two minimum mse s in the time and transform domains are identical independently of the transforms used we then study the convergence conditions and the steady state excess mse s of the transform domain lms trlms algorithms both for the cases of having a constant and a time varying convergence factors when a constant convergence factor is used the convergence behaviors of the lms and trlms adf s appear to be almost identical provided that each has an appropriate value of the convergence factor depending on the transform used also based on the concept of a self orthogonalizing algorithm in the transform domain it is shown that the convergence speed of the trlms adf can be improved significantly for the same excess mse as that of the lms adf in addition we compare the computational complexities of the lms and trlms adf s finally we investigate by computer simulation the effects of system parameter values and different transforms on the convergence behavior of the trlms adf

transform domain lms algorithm the concept of transform domain adaptive filtering is introduced in certain applications filtering in the transform domain results in great improvements in convergence rate over the conventional time domain adaptive filtering the relationship between several existing frequency domain adaptive filtering algorithms is established applications of the discrete fourier transform dft and the discrete cosine transform dct domain adaptive filtering algorithms in the areas of speech processing and adaptive line enhancers are discussed

transient and tracking performance bounds of the sign sign algorithm the paper provides a rigorous tracking analysis of the sign sign algorithm when used in the identification of a time varying plant with a white gaussian input the plant parameters vary according to a random walk model the assumptions allow nonstationarity of the plant input plant noise and increments of the plant parameters upper bounds are derived for the long term averages of the mean of the weight misalignment norm mean absolute error mean square weight misalignment and mean square error these bounds hold for all values of the algorithm step size all initial filter weight settings and all degrees of nonstationarity of the plant input plant noise and plant parameter increments lower bounds of the mean square weight misalignment and mean square error are also derived the step sizes that minimize the above bounds are derived a transient analysis of the algorithm is done in the case of a time invariant plant a tight lower bound of the convergence time is derived the above analytical results are supported by computer simulations

stability and convergence analysis of transform domain lms adaptive filters with second order autoregressive process in this paper the stability and convergence properties of the class of transform domain least mean square lms adaptive filters with second order autoregressive ar process are investigated it is well known that this class of adaptive filters improve convergence property of the standard lms adaptive filters by applying the fixed data independent orthogonal transforms and power normalization however the convergence performance of this class of adaptive filters can be quite different for various input processes and it has not been fully explored in this paper we first discuss the mean square stability and steady state performance of this class of adaptive filters we then analyze the effects of the transforms and power normalization performed in the various adaptive filters for both first order and second order ar processes we derive the input asymptotic eigenvalue distributions and make comparisons on their convergence performance finally computer simulations on ar process as well as moving average ma process and autoregressive moving average arma process are demonstrated for the support of the analytical results

a weighted normalized frequency domain lms adaptive algorithm a general filtering scheme is presented for obtaining an input power estimate for setting the convergence parameter mu separately in each frequency bin of a frequency domain lms adaptive filter fdaf algorithm a linear filtering operation is performed on the magnitude square of the input data and incorporated directly into the algorithm as a data dependent time varying stochastic mu n the mean performance of the weighted normalized frequency domain lms algorithm wnfdaf is analyzed using independent and identically distributed gaussian data and the results are validated by the monte carlo simulations of the algorithm the simulations are also used to study the weight transient behavior the simulations suggest that sort smoothing times are sufficient for rapid weight convergence without large fluctuations in the power estimates significantly affecting transient weight behavior

analysis of the partitioned frequency domain block lms pfblms algorithm in this paper we present a new analysis of the partitioned frequency domain block least mean square pfblms algorithm we analyze the matrices that control the convergence rates of the various forms of the pfblms algorithm and evaluate their eigenvalues for both white and colored input processes because of the complexity of the problem the detailed analyses are only given for the case where the filter input is a first order autoregressive process ar 1 however the results are then generalized to arbitrary processes in a heuristic way by looking into a set of numerical examples an interesting finding that is consistent with earlier publications is that the unconstrained pfblms algorithm suffers from slow modes of convergence which the fblms algorithm does not fortunately however these modes are not present in the constrained pfblms algorithm a simplified version of the constrained pfblms algorithm which is known as the schedule constrained pfblms algorithm is also discussed and the reason for its similar behavior to that of its fully constrained version is explained

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

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

adaptive filtering using hartley transform and overlap save method a novel method of implementing fir finite impulse response adaptive filters using the discrete hartley transform dht and the overlap save method is proposed it not only has the advantage of fast convergence for highly correlated input signals but also provides a significant reduction in computation over the conventional time domain and frequency domain least mean square lms adaptive filters compared with the previously proposed unconstrained frequency domain flms algorithm the convergence performance is similar but an approximate saving of 30 in computation can be obtained for the usual filter length

analysis of the frequency domain block lms algorithm we present a new analysis of the frequency domain block least mean square fblms algorithm an earlier analysis uses a mapping of the frequency domain information to the time domain before proceeding with the analysis of the algorithm we present a direct analysis of the fblms algorithm in the frequency domain as compared with the previous analysis the new analysis is easier to follow it is also more rigorous than the previous works and gives a better insight to the effect of various processing components in the algorithm structure on its convergence behavior in particular we show how the transformation of input samples to the frequency domain combined with the effect of the involved windowing matrices and step normalization affect the convergence behavior of both constrained and unconstrained versions of the fblms algorithm we also report a procedure for derivation of misadjustment equations of various versions of the fblms algorithm

a fast exact least mean square adaptive algorithm a general block formulation of the least mean square lms algorithm for adaptive filtering is presented this formulation has an exact equivalence with the original lms algorithm hence it retains its convergence properties while allowing a reduction in arithmetic complexity even for very small block lengths working with small block lengths is interesting from an implementation point of view large blocks result in large memory and large system delay and allows a significant reduction in the number of operations tradeoffs between a number of operations and a convergence rate are obtainable by applying certain approximations to a matrix involved in the algorithm hence the usual block lms appears as a special case which explains its convergence behavior according to the type of input signal correlated or uncorrelated

numerical evaluation of parabolic cylinder functions the numerical evaluation of the parabolic cylinder functions d sub p z in two cases is described case i is for the argument z xe sup i pi 4 with x real and the order p 1 2 iy with y real case ii is for z arbitrary but p an integer these cases are of special importance in the analysis of wave scattering from a parabolic cylinder expressions for d sub p z are presented which are numerically accurate and efficient

nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising part i theory we study the robust estimation of missing regions in images and video using adaptive sparse reconstructions our primary application is on missing regions of pixels containing textures edges and other image features that are not readily handled by prevalent estimation and recovery algorithms we assume that we are given a linear transform that is expected to provide sparse decompositions over missing regions such that a portion of the transform coefficients over missing regions are zero or close to zero we adaptively determine these small magnitude coefficients through thresholding establish sparsity constraints and estimate missing regions in images using information surrounding these regions unlike prevalent algorithms our approach does not necessitate any complex preconditioning segmentation or edge detection steps and it can be written as a sequence of denoising operations we show that the region types we can effectively estimate in a mean squared error sense are those for which the given transform provides a close approximation using sparse nonlinear approximants we show the nature of the constructed estimators and how these estimators relate to the utilized transform and its sparsity over regions of interest the developed estimation framework is general and can readily be applied to other nonstationary signals with a suitable choice of linear transforms part i discusses fundamental issues and part ii is devoted to adaptive algorithms with extensive simulation examples that demonstrate the power of the proposed techniques

steady state solution of the deficient length constrained fblms algorithm in almost all analyses of the frequency domain block least mean square fblms algorithm the length of the adaptive filter is assumed to be equal to that of the unknown system impulse response however in many practical situations where the length of the system impulse response is extremely long the adaptive filter usually works in an under modeling situation the analysis results for the sufficient length fblms algorithm are not applicable to the deficient length case in this correspondence the steady state solution of the deficient length constrained fblms algorithm is analyzed simulations illustrate the accuracy of the theoretical results

the use of the modified escalator algorithm to improve the performance of transform domain lms adaptive filters this paper describes a new algorithm that improves the convergence performance of the transform domain least mean square trlms algorithm the algorithm exploits the sparse structure of the correlation matrix of the transformed input process to derive a data dependent gram schmidt orthogonalization type transform of the process we show its faster convergence compared with the time domain least mean square lms algorithm and the dct or the dwt based trlms algorithm the gram schmidt orthogonalization is realized using a modified adaptive escalator algorithm the modification significantly reduces the computational complexity of the adaptive escalator algorithm and determines the computational complexity of the proposed algorithm

scaling properties of the number of random sequential adsorption iterations needed to generate saturated random packing the properties of the number of iterations in random sequential adsorption protocol needed to generate finite saturated random packing of spherically symmetric shapes were studied numerical results obtained for one two and three dimensional packings were supported by analytical calculations valid for any dimension d it has been shown that the number of iterations needed to generate finite saturated packing is subject to pareto distribution with exponent 1 1 d and the median of this distribution scales with packing size according to the power law characterized by exponent d obtained results can be used in designing effective random sequential adsorption simulations

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

the generalized multidelay adaptive filter structure and convergence analysis frequency domain adaptive filters have long been recognized as an attractive alternative to time domain algorithms when dealing with systems with large impulse response and or correlated input new frequency domain lms adaptive schemes have been proposed these algorithms essentially retain the attractive features of frequency domain implementations while requiring a processing delay considerably smaller than the length of the impulse response the authors show that these algorithms can be seen as particular implementations of a more general scheme the generalized multidelay filter gmdf within this general class of algorithms we focus on implementations based on the weighted overlap and add reconstruction algorithms these variants overlooked in previous contributions provide an independent control of the overall processing delay and of the rate of update of the filter coefficients allowing a trade off between the computational complexity and the rate of convergence we present a comprehensive analysis of the performance of this new scheme and to provide insight into the influence of impulse response segmentation on the behavior of the adaptive algorithm exact analytical expressions for the steady state mean square error are first derived necessary and sufficient conditions for the convergence of the algorithm to the optimal solution within finite variance are then obtained and are translated into bounds for the stepsize parameter simulations are presented to support our analysis and to demonstrate the practical usefulness of the gmdf algorithm in applications where large impulse response has to be processed

wavelet domain approximation and compression of piecewise smooth images the wavelet transform provides a sparse representation for smooth images enabling efficient approximation and compression using techniques such as zerotrees unfortunately this sparsity does not extend to piecewise smooth images where edge discontinuities separating smooth regions persist along smooth contours this lack of sparsity hampers the efficiency of wavelet based approximation and compression on the class of images containing smooth c sup 2 regions separated by edges along smooth c sup 2 contours for example the asymptotic rate distortion r d performance of zerotree based wavelet coding is limited to d r spl lsim 1 r well below the optimal rate of 1 r sup 2 in this paper we develop a geometric modeling framework for wavelets that addresses this shortcoming the framework can be interpreted either as 1 an extension to the zerotree model for wavelet coefficients that explicitly accounts for edge structure at fine scales or as 2 a new atomic representation that synthesizes images using a sparse combination of wavelets and wedgeprints anisotropic atoms that are adapted to edge singularities our approach enables a new type of quadtree pruning for piecewise smooth images using zerotrees in uniformly smooth regions and wedgeprints in regions containing geometry using this framework we develop a prototype image coder that has near optimal asymptotic r d performance d r spl lsim logr sup 2 r sup 2 for piecewise smooth c sup 2 c sup 2 images in addition we extend the algorithm to compress natural images exploring the practical problems that arise and attaining promising results in terms of mean square error and visual quality

image restoration using space variant gaussian scale mixtures in overcomplete pyramids in recent years bayes least squares gaussian scale mixtures bls gsm has emerged as one of the most powerful methods for image restoration its strength relies on providing a simple and yet very effective local statistical description of oriented pyramid coefficient neighborhoods via a gsm vector this can be viewed as a fine adaptation of the model to the signal variance at each scale orientation and spatial location here we present an enhancement of the model by introducing a coarser adaptation level where a larger neighborhood is used to estimate the local signal covariance within every subband we formulate our model as a bls estimator using space variant gsm the model can be also applied to image deconvolution by first performing a global blur compensation and then doing local adaptive denoising we demonstrate through simulations that the proposed method besides being model based and noniterative it is also robust and efficient its performance measured visually and in l2 norm terms is significantly higher than the original bls gsm method both for denoising and deconvolution

on the steady state performance of frequency domain lms algorithms the use of the fast fourier transform fft in the implementation of the least mean square lms algorithm in the frequency manuscript received may 24 1990 revised may 4 1992 a feuer is with the department of electrical engineering technionisrael institute of technology haifa 32000 israel r cristi is with the department of electrical and computer engineering naval postgraduate school monterey ca 93943 ieee log number 9203376 1053 587x 93 03 00 1993 ieee 420 ieee transactions on signal processing vol 41 no i january 1993 domain results in several types of algorithms two of which can be classified as constrained and unconstrained in this correspondence we point out that in general especially with correlated data the unconstrained algorithm may have a significant performance advantage in steady state if block mean square error is the criterion furthermore we point out here that in the constrained algorithms the choice of different step sizes in different frequency bins as is commonly done will very likely result in a deterioration of steady state performance this does not happen in the unconstrained algorithm

the performance of hybrid adaptive beamforming algorithm for jammers suppression adaptive array processing is of growing importance in the fields of communications radar and sonar where the designer almost invariably faces the problem of interference suppression in general under some situations the conventional frost s 1972 beamforming algorithm may have some problems associated with performance degradation in multiple jammers environment it causes the convergence time to be essentially dependent on the jammer powers ratio a new hybrid adaptive beamforming algorithm is derived in the transformed domain for multiple jammers suppression here three popular orthonormal transformations i e discrete hartley discrete cosine and discrete fourier transforms are considered overall performance improvement in terms of convergence rate and the computational requirement is investigated from the simulation results we observed that the new presented beamforming algorithm is more robust than the conventional frost s beamforming algorithm in terms of jammers suppression and the convergence rate

magnitude squared conherence function estimation an adaptive approach this paper concerns an adaptive approach for estimating the magnitude squared coherence msc function via widrow s least mean square lms algorithm analytical expressions for the bias and variance of the estimate so obtained are derived for the case when the input signals are stationary some computer simulation results are also included for both stationary and nonstationary signals

convergence analysis of adaptive filtering algorithms with singular data covariance matrix the paper provides a rigorous analysis of the behavior of adaptive filtering algorithms when the covariance matrix of the filter input is singular the analysis is done in the context of adaptive plant identification the considered algorithms are lms rls sign sa and signed regressor sra algorithms both the signal and weight behavior of the algorithms are considered the signal behavior is evaluated in terms of the moments of the excess output error of the filter the weight behavior is evaluated in terms of the moments of the filter weight misalignment vector it is found that the rls and sra diverge when the input covariance matrix is singular the steady state signal behavior of the lms and sa can be made arbitrarily fine by using sufficiently small step sizes of the algorithms indeed the long term average of the mean square excess error of the lms is proportional to the algorithm step size the long term average of the mean absolute excess error of the sa is proportional to the square root of the algorithm step size on the other hand the steady state weight behavior of both the lms and sa have biases that depend on the weight initialization the analytical results of the paper are supported by simulations

3 d kalman filter for image motion estimation this paper presents a new three dimensional 3 d markov model for motion vector fields the three dimensions consist of the two space dimensions plus a scale dimension we use a compound signal model to handle motion discontinuity in this 3 d markov random field mrf for motion estimation we use an extended kalman filter as a pel recursive estimator since a single observation can be sensitive to local image characteristics especially when the model is not accurate we employ windowed multiple observations at each pixel to increase accuracy these multiple observations employ different weighting values for each observation since the uncertainty in each observation is different finally we compare this 3 d model with earlier proposed one dimensional 1 d coarse to fine scale and two dimensional 2d spatial compound models in terms of motion estimation performance on a synthetic and a real image sequence

filter bank frame expansions with erasures we study frames for robust transmission over the internet in our previous work we used quantized finite dimensional frames to achieve resilience to packet losses here we allow the input to be a sequence in l sub 2 z and focus on a filter bank implementation of the system we present results in parallel r sup n or c sup n versus l sub 2 z and show that uniform tight frames as well as newly introduced strongly uniform tight frames provide the best performance

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

a new algorithm to compute the discrete cosine transform a new algorithm is introduced for the 2m point discrete cosine transform this algorithm reduces the number of multiplications to about half of those required by the existing efficient algorithms and it makes the system simpler

self orthogonalizing adaptive equalization in the discrete frequency domain a self orthogonalizing discrete adaptive equalizer for synchronous data transmission is presented based on the overlapsave filtering technique self orthogonalization in the discrete frequency domain is adaptively performed by premultiplying by a diagonal matrix the mse gradient estimates before projecting by means of rosen s gradient projection method the diagonal of the matrix is the inverse of the power spectrum of the received sequence taken at equally spaced frequencies and estimates are obtained by using bartlett s procedure of periodograms averaging for spectrum estimation projection is accomplished by means of an off line derived projection matrix confidence of gradient estimates is improved by means of a block correlated estimation technique using available dft s of blocks of data this equalizer is compared to time domain self orthogonalizing algorithms as regards speed of convergence and ease of implementation during the short startup phase convergence is competitive with that of godard s algorithm which is the fastest algorithm known and in the decision directed mode fast convolution performed by blocks results in a considerable reduction of the number of multiplications with respect to the time domain algorithms a computationally simpler unconstrained startup algorithm is also examined obtained by removing the projection while retaining gradient block estimates in the dfd

unconstrained frequency domain adaptive filter an unconstrained frequency domain least mean squares uflms algorithm is presented the algorithm is based on the overlap save technique used in frequency domain filtering the proposed algorithm converges to the wiener solution without the time domain constraint on the impulse response as proposed by ferrara for a large number of taps geq32 the uflms algorithm offers a significant reduction in computation another advantage is its fast convergence for highly correlated input signals the performance of the algorithm is illustrated by a simulation

wavelet transform based adaptive filters analysis and new results in this paper the wavelet transform is used in an adaptive filtering structure the coefficients of the adaptive filter are updated by the help of the least mean square lms algorithm first the wavelet transform based adaptive filter wtaf is described and it is analyzed for its wiener optimal solution then the performance of the wtaf is studied by the help of learning curves for three different convergence factors 1 constant convergence factor 2 time varying convergence factor and 3 exponentially weighted convergence factor the exponentially weighted convergence factor is proposed to introduce scale based variation to the weight update equation it is shown for two different sets of data that the rate of convergence increases significantly for all three wtaf structures as compared to that of time domain lms the high convergence rates of the wtaf give us reason to expect that it will perform well in tracking rapid changes in a signal

a set of algorithms linking nlms and block rls algorithms this paper describes a set of block processing algorithms which contains as extremal cases the normalized least mean squares nlms and the block recursive least squares brls algorithms all these algorithms use small block lengths thus allowing easy implementation and small input output delay it is shown that these algorithms require a lower number of arithmetic operations than the classical least mean squares lms algorithm while converging much faster a precise evaluation of the arithmetic complexity is provided and the adaptive behavior of the algorithm is analyzed simulations illustrate that the tracking characteristics of the new algorithm are also improved compared to those of the nlms algorithm the conclusions of the theoretical analysis are checked by simulations illustrating that even in the case where noise is added to the reference signal the proposed algorithm allows altogether a faster convergence and a lower residual error than the nlms algorithm finally a sample by sample version of this algorithm is outlined which is the link between the nlms and recursive least squares rls algorithms

what s in a set of points straight line fitting the problem of fitting a straight line to a planar set of points is reconsidered a parameter space computational approach capable of fitting one or more lines to a set of points is presented the suggested algorithm handles errors in both coordinates of the data points even when the error variances vary between coordinates and among points and can be readily made robust to outliers the algorithm is quite general and allows line fitting according to several useful optimality criteria to be performed within a single computational framework it is observed that certain extensions of the hough transform can be turned to be equivalent to well known m estimators thus allowing computationally efficient approximate m estimation

spatio temporal adaptive 3 d kalman filter for video this paper presents three dimensional spatio temporal kalman filters for video as the extension of the two dimensional 2 d reduced update kalman filter rukf approach for images we start out with three dimensional 3 d rukf a shift invariant recursive estimator with efficiency advantages over the 3 d wiener filter then we turn to the motion compensated extension mc rukf which gives improved performance when coupled with a motion estimator since motion compensation sometimes fails causing severe fluctuations in temporal correlation we then present multimodel mc rukf to adapt to variation in temporal and spatial correlation by detecting the local image model out of a class and using it in mc rukf finally we introduce a novel multiscale model detection algorithm for use in high noise environments

a multistep size mss frequency domain adaptive filter a multistep size frequency domain adaptive filter capable of tracking both stationary and nonstationary signals is proposed this algorithm makes use of the simple structure of the least mean square error algorithm to update the filter coefficients and process the signal it then proceeds further by incorporating a set of three step sizes and a knowledge based strategy to select the best set of filter coefficients and the optimum step size iteratively the main advantage of the mss algorithm over the conventional lms algorithm is that better performance is achieved without the knowledge of the input signal characteristics such as signal power degree of nonstationarity signal to noise ratio and stability bounds experimentally the mss algorithm is tested under various signal environments the transient characteristics of the step sizes are found to be in agreement with previous theoretical studies of nonstationary characteristics of the lms algorithm in order to reduce the complexity the conventional frequency domain block lms structure is also modified so that the mss algorithm can be embedded more efficiently by exploiting the block structure

efficient multiframe wiener restoration of blurred and noisy image sequences computationally efficient multiframe wiener filtering algorithms that account for both intraframe spatial and interframe temporal correlations are proposed for restoring image sequences that are degraded by both blur and noise one is a general computationally efficient multiframe filter the cross correlated multiframe ccmf wiener filter which directly utilizes the power and cross power spectra of only n n matrices where n is the number of frames used in the restoration in certain special cases the ccmf lends itself to a closed form solution that does not involve any matrix inversion a special case is the motion compensated multiframe mcmf filter where each frame is assumed to be a globally shifted version of the previous frame in this case the interframe correlations can be implicitly accounted for using the estimated motion information thus the mcmf filter requires neither explicit estimation of cross correlations among the frames nor matrix inversion performance and robustness results are given