Showing papers in "IEEE Transactions on Signal Processing in 1991"
TL;DR: The sampling of bandpass signals is discussed with respect to band position, noise considerations, and parameter sensitivity, and it is shown that the minimum sampling rate is pathological in that any imperfection in the implementation will cause aliasing.
Abstract: The sampling of bandpass signals is discussed with respect to band position, noise considerations, and parameter sensitivity. For first-order sampling, the acceptable and unacceptable sample rates are presented, with specific discussion of the practical rates which are nonminimum. It is shown that the minimum sampling rate is pathological in that any imperfection in the implementation will cause aliasing. In applying bandpass sampling to relocate signals to a base-band position, the signal-to-noise ratio is not preserved owing to the out-of-band noise being aliased. The degradation in signal-to-noise ratio is quantified in terms of the position of the bandpass signal. For the construction of a bandpass signal from second-order samples, the cost of implementing the interpolant (dynamic range and length) depends on Kohlenberg's sampling factor (1953) k, the relative delay between the uniform sampling streams. An elaboration on the disallowed discrete values of k shows that some allowed values are better than others for implementation. >
864 citations
TL;DR: It is shown that by introducing a specific weighting matrix, the multidimensional signal subspace method can achieve the same asymptotic properties as the ML method.
Abstract: Algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem. The methods considered are the deterministic maximum likelihood method (ML), ESPRIT, and a recently proposed multidimensional signal subspace method. These methods are formulated in a subspace-fitting-based framework, which provides insight into their algebraic and asymptotic relations. It is shown that by introducing a specific weighting matrix, the multidimensional signal subspace method can achieve the same asymptotic properties as the ML method. The asymptotic distribution of the estimation error is derived for a general subspace weighting, and the weighting that provides minimum variance estimates is identified. The resulting optimal technique is termed the weighted subspace fitting (WSF) method. Numerical examples indicate that the asymptotic variance of the WSF estimates coincides with the Cramer-Rao bound. The performance improvement compared to the other techniques is found to be most prominent for highly correlated signals. >
737 citations
TL;DR: The authors develop algorithms for the design of hierarchical tree structured color palettes incorporating performance criteria which reflect subjective evaluations of image quality, which produce higher-quality displayed images and require fewer computations than previously proposed methods.
Abstract: The authors develop algorithms for the design of hierarchical tree structured color palettes incorporating performance criteria which reflect subjective evaluations of image quality. Tree structured color palettes greatly reduce the computational requirements of the palette design and pixel mapping tasks, while allowing colors to be properly allocated to densely populated areas of the color space. The algorithms produce higher-quality displayed images and require fewer computations than previously proposed methods. Error diffusion techniques are commonly used for displaying images which have been quantized to very few levels. Problems related to the application of error diffusion techniques to the display of color images are discussed. A modified error diffusion technique is shown to be easily implemented using the tree structured color palettes developed earlier. >
543 citations
TL;DR: In this article, a multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed, based on the recently introduced weighted subspace fitting (WSF) criterion and includes schemes for detecting the number of sources and estimating the signal parameters.
Abstract: The problem of signal parameter estimation of narrowband emitter signals impinging on an array of sensors is addressed. A multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed. The method is based on the recently introduced weighted subspace fitting (WSF) criterion and includes schemes for both detecting the number of sources and estimating the signal parameters. A Gauss-Newton-type method is presented for solving the multidimensional WSF and maximum-likelihood optimization problems. The global and local properties of the search procedure are investigated through computer simulations. Most methods require knowledge of the number of coherent/noncoherent signals present. A scheme for consistently estimating this is proposed based on an asymptotic analysis of the WSF cost function. The performance of the detection scheme is also investigated through simulations. >
520 citations
TL;DR: The backpropagation algorithm that provides a popular method for the design of a multilayer neural network to include complex coefficients and complex signals so that it can be applied to general radar signal processing and communications problems is generalized.
Abstract: The backpropagation (BP) algorithm that provides a popular method for the design of a multilayer neural network to include complex coefficients and complex signals so that it can be applied to general radar signal processing and communications problems. It is shown that the network can classify complex signals. The generalization of the BP to deal with complex signals should make it possible to expand the line of applications of this powerful nonlinear signal processing algorithm. >
412 citations
TL;DR: The authors present a method to find the weighted median filter which is equivalent to a stack filter defined by a positive Boolean function, which allows expression of the cascade of WM filters as a single WM filter.
Abstract: The deterministic properties of weighted median (WM) filters are analyzed. Threshold decomposition and the stacking property together establish a unique relationship between integer and binary domain filtering. The authors present a method to find the weighted median filter which is equivalent to a stack filter defined by a positive Boolean function. Because the cascade of WM filters can always be expressed as a single stack filter this allows expression of the cascade of WM filters as a single WM filter. A direct application is the computation of the output distribution of a cascade of WM filters. The same method is used to find a nonrecursive expansion of a recursive WM filter. As applications of theoretical results, several interesting deterministic and statistical properties of WM filters are derived. >
363 citations
TL;DR: The adaptively restored images have better quality than the nonadaptively restored ones based on visual observations and on an objective criterion of merit which accounts for the noise masking property of the visual system.
Abstract: The development of the algorithm is based on a set theoretic approach to regularization. Deterministic and/or statistical information about the undistorted image and statistical information about the noise are directly incorporated into the iterative procedure. The restored image is the center of an ellipsoid bounding the intersection of two ellipsoids. The proposed algorithm, which has the constrained least squares algorithm as a special case, is extended into an adaptive iterative restoration algorithm. The spatial adaptivity is introduced to incorporate properties of the human visual system. Convergence of the proposed iterative algorithms is established. For the experimental results which are shown, the adaptively restored images have better quality than the nonadaptively restored ones based on visual observations and on an objective criterion of merit which accounts for the noise masking property of the visual system. >
342 citations
TL;DR: One result is an autocorrelation matching condition that overcomes the limitations of linear prediction and produces better fitting spectral envelopes for spectra that are representable by a relatively small discrete set of values, such as in voiced speech.
Abstract: A method for parametric modeling and spectral envelopes when only a discrete set of spectral points is given is introduced. This method, called discrete all-pole (DAP) modeling, uses a discrete version of the Itakura-Saito distortion measure as its error criterion. One result is an autocorrelation matching condition that overcomes the limitations of linear prediction and produces better fitting spectral envelopes for spectra that are representable by a relatively small discrete set of values, such as in voiced speech. An iterative algorithm for DAP modeling that is shown to converge to a unique global minimum is presented. Results of applying DAP modeling to real and synthetic speech are also presented. DAP modeling is extended to allow frequency-dependent weighting of the error measure, so that spectral accuracy can be enhanced in certain frequency regions. >
328 citations
TL;DR: The proposed technique focuses on the interferences only, resulting in superior cancellation performance, and achieves full effectiveness even for short observation times, when the number of samples used for processing is of the the order of theNumber of interferences.
Abstract: Eigenanalysis methods are applied to interference cancellation problems. While with common array processing methods the cancellation is effected by global optimization procedures that include the interferences and the background noise, the proposed technique focuses on the interferences only, resulting in superior cancellation performance. Furthermore, the method achieves full effectiveness even for short observation times, when the number of samples used for processing is of the the order of the number of interferences. Adaptive implementation is obtained with a simple, fast converging algorithm. >
325 citations
TL;DR: A solution is proposed to the long-standing problem of the numerical instability of fast recursive least squares transversal filter (FTF) algorithms with exponential weighting, an important class of algorithms for adaptive filtering.
Abstract: A solution is proposed to the long-standing problem of the numerical instability of fast recursive least squares transversal filter (FTF) algorithms with exponential weighting, an important class of algorithms for adaptive filtering. A framework for the analysis of the error propagation in FTF algorithms is first developed; within this framework, it is shown that the computationally most efficient 7N form is exponentially unstable. However, by introducing redundancy into this algorithm, feedback of numerical errors becomes possible; a judicious choice of the feedback gains then leads to a numerically stable FTF algorithm with a complexity of 8N multiplications and additions per time recursion. The results are presented for the complex multichannel joint-process filtering problem. >
320 citations
TL;DR: Two direction finding algorithms are presented for nonGaussian signals, which are based on the fourth-order cumulants of the data received by the array, which seem to confirm the insensitivity of these algorithms to the (Gaussian) noise parameters.
Abstract: Two direction finding algorithms are presented for nonGaussian signals, which are based on the fourth-order cumulants of the data received by the array. The first algorithm is similar to MUSIC, while the second is asymptotically minimum variance in a certain sense. The first algorithm requires singular value decomposition of the cumulant matrix, while the second is based on nonlinear minimization of a certain cost function. The performance of the minimum variance algorithm can be assessed by analytical means, at least for the case of discrete probability distributions of the source signals and spatially uncorrelated Gaussian noise. The numerical experiments performed seem to confirm the insensitivity of these algorithms to the (Gaussian) noise parameters. >
TL;DR: The results indicate that the colored noise Kalman filters provide a significant gain in signal-to- noise ratio (SNR), a visible improvement in the sound spectrogram, and an audible improvement in output speech quality, none of which are available with white-noise-assumption Kalman and Wiener filters.
Abstract: Scalar and vector Kalman filters are implemented for filtering speech contaminated by additive white noise or colored noise, and an iterative signal and parameter estimator which can be used for both noise types is presented. Particular emphasis is placed on the removal of colored noise, such as helicopter noise, by using state-of-the-art colored-noise-assumption Kalman filters. The results indicate that the colored noise Kalman filters provide a significant gain in signal-to-noise ratio (SNR), a visible improvement in the sound spectrogram, and an audible improvement in output speech quality, none of which are available with white-noise-assumption Kalman and Wiener filters. When the filter is used as a prefilter for linear predictive coding, the coded output speech quality and intelligibility are enhanced in comparison to direct coding of the noisy speech. >
TL;DR: A speaker adaptation procedure which is easily integrated into the segmental k-means training procedure for obtaining adaptive estimates of the CDHMM parameters is presented and shows that much better performance is achieved when two or more training tokens are used for speaker adaptation.
Abstract: For a speech-recognition system based on continuous-density hidden Markov models (CDHMM), speaker adaptation of the parameters of CDHMM is formulated as a Bayesian learning procedure. A speaker adaptation procedure which is easily integrated into the segmental k-means training procedure for obtaining adaptive estimates of the CDHMM parameters is presented. Some results for adapting both the mean and the diagonal covariance matrix of the Gaussian state observation densities of a CDHMM are reported. The results from tests on a 39-word English alpha-digit vocabulary in isolated word mode indicate that the speaker adaptation procedure achieves the same level of performance as that of a speaker-independent system, when one training token from each word is used to perform speaker adaptation. It shows that much better performance is achieved when two or more training tokens are used for speaker adaptation. When compared with the speaker-dependent system, it is found that the performance of speaker adaptation is always equal to or better than that of speaker-dependent training using the same amount of training data. >
TL;DR: A novel lattice-based adaptive infinite impulse response (IIR) notch filter is developed which features independent tuning of the notch frequency and attenuation bandwidth, and the estimation of extremal frequencies is less prone to overflow instability than previously reported structures.
Abstract: A novel lattice-based adaptive infinite impulse response (IIR) notch filter is developed which features independent tuning of the notch frequency and attenuation bandwidth. The internal structure is based on planar rotators, ensuring reliable numerical behaviour and high processing rates in CORDIC environments. A simple update law allows a simpler implementation than previously proposed designs. Rather than minimizing an output error cost function, the algorithm is designed to achieve a stable associated differential equation, resulting in a globally convergent unbiased frequency estimator in the single sinusoid case, independent of the notch filter bandwidth. Using a second-order structure in the multiple sinusoid case, unbiased estimation of one of the input frequencies is achieved by thinning the notch bandwidth. The tracking behavior is superior to conventional output error designs, and the estimation of extremal frequencies is less prone to overflow instability than previously reported structures. >
TL;DR: The asymptotic distribution of the estimation error for the total least squares (TLS) version of ESPRIT is derived, and the application to a uniform linear array is treated in some detail, and a generalization of ESPrIT to include row weighting is discussed.
Abstract: The asymptotic distribution of the estimation error for the total least squares (TLS) version of ESPRIT is derived. The application to a uniform linear array is treated in some detail, and a generalization of ESPRIT to include row weighting is discussed. The Cramer-Rao bound (CRB) for the ESPRIT problem formulation is derived and found to coincide with the asymptotic variance of the TLS ESPRIT estimates through numerical examples. A comparison of this method to least squares ESPRIT, MUSIC, and Root-MUSIC as well as to the CRB for a calibrated array is also presented. TLS ESPRIT is found to be competitive with the other methods, and the performance is close to the calibrated CRB for many cases of practical interest. For highly correlated signals, however, the performance deviates significantly from the calibrated CRB. Simulations are included to illustrate the applicability of the theoretical results to a finite number of data. >
TL;DR: The constrained total least squares method is a natural extension of TLS to the case when the noise components of the coefficients are algebraically related, and some of its applications to superresolution harmonic analysis are presented.
Abstract: The constrained total least squares (CTLS) method is a natural extension of TLS to the case when the noise components of the coefficients are algebraically related. The CTLS technique is developed, and some of its applications to superresolution harmonic analysis are presented. The CTLS problem is reduced to an unconstrained minimization problem over a small set of variables. A perturbation analysis of the CTLS solution is derived, and from it the root mean-square error (RMSE) of the CTLS solution, which is valid for small noise levels, is obtained in closed form. The complex version of the Newton method is derived and applied to determine the CTLS solution. It is also shown that the CTLS problem is equivalent to a constrained parameter maximum-likelihood problem. The CTLS technique is applied to estimate the frequencies of sinusoids in white noise and the angle of arrival of narrowband wavefronts at a linear uniform array. In both cases the CTLS method shows superior or similar accuracy to other advanced techniques. >
TL;DR: The algorithms are evaluated with respect to improving automatic recognition of speech in the presence of additive noise and shown to outperform other enhancement methods in this application.
Abstract: The basis of an improved form of iterative speech enhancement for single-channel inputs is sequential maximum a posteriori estimation of the speech waveform and its all-pole parameters, followed by imposition of constraints upon the sequence of speech spectra. The approaches impose intraframe and interframe constraints on the input speech signal. Properties of the line spectral pair representation of speech allow for an efficient and direct procedure for application of many of the constraint requirements. Substantial improvement over the unconstrained method is observed in a variety of domains. Informed listener quality evaluation tests and objective speech quality measures demonstrate the technique's effectiveness for additive white Gaussian noise. A consistent terminating point of the iterative technique is shown. The current systems result in substantially improved speech quality and linear predictive coding (LPC) parameter estimation with only a minor increase in computational requirements. The algorithms are evaluated with respect to improving automatic recognition of speech in the presence of additive noise and shown to outperform other enhancement methods in this application. >
TL;DR: The singular value decomposition (SVD) is explored as the common structure in the three basic algorithms: direct matrix pencil algorithm, pro-ESPRIT, and TLS, and several SVD-based steps inherent in the algorithms are equivalent to the first-order approximation.
Abstract: Several algorithms for estimating generalized eigenvalues (GEs) of singular matrix pencils perturbed by noise are reviewed. The singular value decomposition (SVD) is explored as the common structure in the three basic algorithms: direct matrix pencil algorithm, pro-ESPRIT, and TLS-ESPRIT. It is shown that several SVD-based steps inherent in the algorithms are equivalent to the first-order approximation. In particular, the Pro-ESPRIT and its variant TLS-Pro-ESPRIT are shown to be equivalent, and the TLS-ESPRIT and its earlier version LS-ESPRIT are shown to be asymptotically equivalent to the first-order approximation. For the problem of estimating superimposed complex exponential signals, the state-space algorithm is shown to be also equivalent to the previous matrix pencil algorithms to the first-order approximation. The second-order perturbation and the threshold phenomenon are illustrated by simulation results based on a damped sinusoidal signal. An improved state-space algorithm is found to be the most robust to noise. >
TL;DR: The authors derive the Cramer-Rao lower bound (CRLB) for complex signals with constant amplitude and polynomial phase, measured in additive Gaussian white noise, which is found to be excellent in most cases.
Abstract: The authors derive the Cramer-Rao lower bound (CRLB) for complex signals with constant amplitude and polynomial phase, measured in additive Gaussian white noise. The exact bound requires numerical inversion of an ill-conditioned matrix, while its O(N/sup -1/) approximation is free of matrix inversion. The approximation is tested for several typical parameter values and is found to be excellent in most cases. The formulas derived are of practical value in several radar applications, such as electronic intelligence systems (ELINT) for special pulse-compression radars, and motion estimation from Doppler measurements. Consequently, it is of interest to analyze the best possible performance of potential estimators of the phase coefficients, as a function of signal parameters, the signal-to-noise ratio, the sampling rate, and the number of measurements. This analysis is carried out. >
TL;DR: An algorithm is proposed for the solution of the class of multidimensional detection problems concerning the detection of small, barely discernible, moving objects of unknown position and velocity in a sequence of digital images, modeled as GWN.
Abstract: An algorithm is proposed for the solution of the class of multidimensional detection problems concerning the detection of small, barely discernible, moving objects of unknown position and velocity in a sequence of digital images. A large number of candidate trajectories, organized into a tree structure, are hypothesized at each pixel in the sequence and tested sequentially for a shift in mean intensity. The practicality of the algorithm is facilitated by the use of multistage hypothesis testing (MHT) for simultaneous inference, as well as the existence of exact, closed-form expressions for MHT test performance in Gaussian white noise (GWN). These expressions predict the algorithm's computation and memory requirements, where it is shown theoretically that several orders of magnitude of processing are saved over a brute-force approach based on fixed sample-size tests. The algorithm is applied to real data by using a robust preprocessing procedure to eliminate background structure and transform the image sequence into a residual representation, modeled as GWN. Results are verified experimentally on a variety of video image sequences. >
TL;DR: An efficient, in-place algorithm for the batch processing of linear data arrays and the binomial filter, suitable as front-end filters for a bank of quadrature mirror filters and for pyramid coding of images.
Abstract: The authors present an efficient, in-place algorithm for the batch processing of linear data arrays. These algorithms are efficient, easily scaled, and have no multiply operations. They are suitable as front-end filters for a bank of quadrature mirror filters and for pyramid coding of images. In the latter application, the binomial filter was used as the low-pass filter in pyramid coding of images and compared with the Gaussian filter devised by P.J. Burt (Comput. Graph. Image Processing, vol.16, p.20-51, 1981). The binomial filter yielded a slightly larger signal-to-noise ratio in every case tested. More significantly, for an (L+1)*(L+1) image array processed in (N+1)*(N+1) subblocks, the fast Burt algorithm requires a total of 2(L+1)/sup 2/N adds and 2(L+1)/sup 2/ (N/2+1) multiplies. The binomial algorithm requires 2L/sup 2/N adds and zero multiplies. >
IBM1
TL;DR: Based on a new similarity model for the voice excitation process, a novel pitch determination procedure is derived that has infinite (super) resolution, better accuracy than the difference limen for F/sub 0/, robustness to noise, reliability, and modest computational complexity.
Abstract: Based on a new similarity model for the voice excitation process, a novel pitch determination procedure is derived. The unique features of the proposed algorithm are infinite (super) resolution, better accuracy than the difference limen for F/sub 0/, robustness to noise, reliability, and modest computational complexity. The algorithm is instrumental to speech processing applications which require pitch synchronous spectral analysis. The computational complexity of the proposed algorithm is well within the capacity of modern digital signal processing (DSP) technology and therefore can be implemented in real time. >
TL;DR: The bistatic SAR inversion is also utilized to formulate an inversion for multistatic measurements made along a physical linear array due to a single transmission to image a dynamic object.
Abstract: An inversion method is presented for bistatic synthetic aperture radar imaging. The method is based on a Fourier analysis (Doppler processing) of the bistatic synthesized array's data followed by a phase modulation analysis of the Doppler data. The approach incorporates the phase information of the wavefront curvature in the transmitted waves as well as the resultant echoed signals. The Doppler data are shown to provide samples of the reflectivity function's spatial Fourier transform within a band that depends upon the bistatic angles and ranges. Associated resolution, reconstruction, and sampling constraints for the imaging problem are discussed. The bistatic SAR inversion is also utilized to formulate an inversion for multistatic measurements made along a physical linear array due to a single transmission to image a dynamic object. >
TL;DR: Consideration is given to the analysis of the large-sample second-order properties of multiple signal classification (MUSIC) and subspace rotation (SUR) methods, such as ESPRIT, for sinusoidal frequency estimation.
Abstract: Consideration is given to the analysis of the large-sample second-order properties of multiple signal classification (MUSIC) and subspace rotation (SUR) methods, such as ESPRIT, for sinusoidal frequency estimation. Explicit expressions for the covariance elements of the estimation errors associated with either method are derived. These expressions of covariances are then used to analyze and compare the statistical performances of the MUSIC and SUR estimation (SURE) methods. Both MUSIC and SURE are based on the eigendecomposition of a sample data covariance matrix. The expressions for the estimation error variances derived are used to study the dependence of MUSIC and SURE performances on the dimension of the data covariance matrix used. >
TL;DR: The authors consider both the maximum a posteriori probability (MAP) estimate and the minimum mean-squared error (MMSE) estimate for image estimation and image restoration for images modeled as compound Gauss-Markov random fields.
Abstract: Algorithms for obtaining approximations to statistically optimal estimates for images modeled as compound Gauss-Markov random fields are discussed. The authors consider both the maximum a posteriori probability (MAP) estimate and the minimum mean-squared error (MMSE) estimate for image estimation and image restoration. Compound image models consist of several submodels having different characteristics along with an underlying structure model which govern transitions between these image submodels. Two different compound random field models are employed, the doubly stochastic Gaussian (DSG) random field and a compound Gauss-Markov (CGM) random field. The authors present MAP estimators for DSG and CGM random fields using simulated annealing. A fast-converging algorithm called deterministic relaxation, which, however, converges to only a locally optimal MAP estimate, is also presented as an alternative for reducing computational loading on sequential machines. For comparison purposes, the authors include results on the fixed-lag smoothing MMSE estimator for the DSG field and its suboptimal M-algorithm approximation. >
TL;DR: It is shown that specific 1-D slices of the fourth-order cumulant of the noisy signal for the direction of arrival (DOA) and retrieval of harmonics in noise (RHN) problems are identical to the autocorrelation of a related noiseless signal, so correlation-based high-resolution methods may be used with fourth- order cumulants as well.
Abstract: A frequently encountered problem in signal processing is that of estimating the frequencies and amplitudes of harmonics observed in additive colored Gaussian noise. In practice, the observed signals are contaminated with spatially and temporally colored noise of unknown power spectral density. A cumulant-based approach to these problems is proposed. The cumulants of complex processes are defined, and it is shown that specific 1-D slices of the fourth-order cumulant of the noisy signal for the direction of arrival (DOA) and retrieval of harmonics in noise (RHN) problems are identical to the autocorrelation of a related noiseless signal. Hence correlation-based high-resolution methods may be used with fourth-order cumulants as well. The effectiveness of the proposed methods is demonstrated through standard simulation examples. >
TL;DR: A spatially adaptive, multichannel least squares filter that utilizes local within- and between-channel image properties is proposed, and a geometric interpretation of the estimates of both filters is given.
Abstract: Multichannel restoration using both within- and between-channel deterministic information is considered. A multichannel image is a set of image planes that exhibit cross-plane similarity. Existing optimal restoration filters for single-plane images yield suboptimal results when applied to multichannel images, since between-channel information is not utilized. Multichannel least squares restoration filters are developed using the set theoretic and the constrained optimization approaches. A geometric interpretation of the estimates of both filters is given. Color images (three-channel imagery with red, green, and blue components) are considered. Constraints that capture the within- and between-channel properties of color images are developed. Issues associated with the computation of the two estimates are addressed. A spatially adaptive, multichannel least squares filter that utilizes local within- and between-channel image properties is proposed. Experiments using color images are described. >
TL;DR: A vector gradient approach is proposed to detect boundaries in multidimensional data with multiple attributes (a vector field) and used to extend a gradient edge detector to color images.
Abstract: A vector gradient approach is proposed to detect boundaries in multidimensional data with multiple attributes (a vector field). It is used to extend a gradient edge detector to color images. The statistical effects of noise on the distribution of the amplitudes and directions of the vector gradient are characterized. The noise behavior of the L/sub 2/ norm of the scalar gradients is also characterized for comparison. When the attribute components are highly correlated, as is often the case in color images, use of the vector gradient shows a small gain in signal-to-noise ratio over that of the L/sub 2/ norm of the scalar gradients. This small gain may or may not be significant, depending on other measures an edge detector uses to deal with noise. >
TL;DR: The two-dimensional Gabor filters possess strong optimality properties for this task, and local spatial frequency estimation approaches are suggested that use the responses as constraints in estimating the locally emergent texture frequencies.
Abstract: A model for texture analysis and segmentation using multiple oriented channel filters is analyzed in the general framework. Several different arguments are applied leading to the conclusion that the two-dimensional Gabor filters possess strong optimality properties for this task. Properties of the multiple-channel segmentation approach are analyzed. In particular, perturbations of textures from an ideal model are found to have important effects on the segmentation that can usually be ameliorated by simply preceding the segmentation process by a logarithmic operation and using a low-pass postfilter prior to making region assignments. The difficult problems of space-variant textures and multiple component textures are also considered. Local spatial frequency estimation approaches are suggested that use the responses as constraints in estimating the locally emergent texture frequencies. Complex texture aggregates containing multiple shared frequency components can be analyzed if the textures are distinct and few in number. >
TL;DR: The convergence of iterations is proved, and general regions for convergence are found, and the iterative method is shown to be applicable to other forms of nonuniform sampling, i.e. natural sampling and interpolated sampling.
Abstract: An iterative method to recover a bandlimited signal from its ideal nonuniform samples is proposed. The convergence of iterations is proved, and general regions for convergence are found. It is shown that the iterative method is also applicable to other forms of nonuniform sampling, i.e. natural sampling and interpolated sampling (such as sample-and-hold signal). Simulation results show that this method works effectively and fairly fast, and the errors after a few iterations are negligible if a particular sufficient condition is satisfied or the sampling rate is higher than the Nyquist rate. >