Fast Recursive Algorithm Research Articles

Image thresholding based on θ-division of 2-D histogram and maximum Shannon entropy

In view of the obvious wrong segmentation in commonly used region division of 2-D histogram and the non- universality of oblique segmentation method for image thresholding proposed recently, in this paper a much more widely suitable thresholding method is proposed based on the θ-division of 2-D histogram and the maximum Shannon entropy criterion. Firstly, the θ-division method of 2-D histogram is given. The region is divided by four parallel oblique lines and a line, where the angle between its normal line and gray level axis is θ degrees. Image thresholding is performed according to pixel's weighted average value of gray level and neighbour average gray level. The oblique segmentation method can be regarded as a special case of the proposed method at θ=45°. Then the formulae and its fast recursive algorithm of the method are deduced. Finally the segmented results and the running time at different values of θ are listed, which show that the segmented images achieve more accurate borders at smaller values of θ and the anti-noise is better at larger values of θ. The value of θ can be selected according to the real image characteristics and the requirements of segmented results. Compared with the algorithm of conventional 2-D maximum Shannon entropy method, the proposed method not only achieves more accurate segmentation results and more robust anti-noise, but also reduces the running time and memory space significantly.

Bi-iterative least squares algorithms for blind channel identification and equalization with second-order statistics

We present an adaptive algorithm for blind identification and equalization of single-input multiple-output (SIMO) FIR channels with second-order statistics. We first reformulate the blind channel identification problem into a low-rank matrix approximation solution based on the QR decomposition of the received data matrix. Then, a fast recursive algorithm is developed based on the bi-iterative least squares (Bi-LS) subspace tracking method. The new algorithm requires only a computational complexity of O(md2) at each iteration, or even as low as O(md) if only equalization is necessary, where m is the dimension of the received data vector (or the row rank of channel matrix) and d is the dimension of the signal subspace (or the column rank of channel matrix). To overcome the shortcoming of the back substitution, an inverse QR iteration algorithm for subspace tracking and channel equalization is also developed. The inverse QR iteration algorithm is well suited for the parallel implementation in the systolic array. Simulation results are presented to illustrate the effectiveness of the proposed algorithms for the channel identification and equalization.

Consistency of a recursive estimate of mixing distributions

Mixture models have received considerable attention recently and Newton [Sankhyā Ser. A 64 (2002) 306–322] proposed a fast recursive algorithm for estimating a mixing distribution. We prove almost sure consistency of this recursive estimate in the weak topology under mild conditions on the family of densities being mixed. This recursive estimate depends on the data ordering and a permutation-invariant modification is proposed, which is an average of the original over permutations of the data sequence. A Rao–Blackwell argument is used to prove consistency in probability of this alternative estimate. Several simulations are presented, comparing the finite-sample performance of the recursive estimate and a Monte Carlo approximation to the permutation-invariant alternative along with that of the nonparametric maximum likelihood estimate and a nonparametric Bayes estimate.

On Fast Recursive Algorithms for V-BLAST with Optimal Ordered SIC Detection

A fast recursive algorithm for the vertical Bell Laboratories layered space-time (V-BLAST) with the optimal ordered successive interference cancellation (SIC) detection has been proposed by Benesty-Huang-Chen and two improved algorithms have been also recently introduced by Szczecinski-Massicotte and Zhu-Lei-Chin independently. In this letter, our first contribution is to incorporate the existing improvements into the original fast recursive algorithm to provide the fastest known algorithm for the optimal ordered SIC detection of V-BLAST. Subsequently, we propose two new algorithms that result from one further improvement for the fast recursive algorithm. Compared with the fastest known algorithm built from the existing improvements, one new proposed algorithm has a speedup of 1.3 times in both the number of multiplications and the number of additions, and the other new proposed algorithm requires less intermediate variables and saves memories.

The fast recursive row-Householder subspace tracking algorithm

We introduce a new sequential algorithm for tracking the principal subspace and, optionally, the r dominant eigenvalues and associated eigenvectors of an exponentially updated covariance matrix of dimension N × N , where N > r . The method is based on an updated orthonormal-square (QS) decomposition using the row-Householder reduction. This new subspace tracker reaches a dominant complexity of only 3 Nr multiplications per time update for tracking the principal subspace, which is the lower bound in dominant complexity for an algorithm of this kind. The new method is completely reflection based. An updating of inverse matrices is not used.

Low‐complexity robust adaptive generalized sidelobe canceller detector for DS/CDMA systems

AbstractA novel low computational complexity robust adaptive blind multiuser detector, based on the minimum output energy (MOE) detector with multiple constraints and a quadratic inequality (QI) constraint is developed in this paper. Quadratic constraint has been a widespread approach to improve robustness against mismatch errors, uncertainties in estimating the data covariance matrix, and random perturbations in detector parameters. A diagonal loading technique is compulsory to achieve the quadratic constraint where the diagonal loading level is adjusted to satisfy the constrained value. Integrating the quadratic constraint into recursive algorithms seems to be a moot point since there is no closed‐form solution for the diagonal loading term. In this paper, the MOE detector of DS/CDMA system is implemented using a fast recursive steepest descent adaptive algorithm anchored in the generalized sidelobe canceller (GSC) structure with multiple constraints and a QI constraint on the adaptive portion of the GSC structure. The Lagrange multiplier method is exploited to solve the QI constraint. An optimal variable loading technique, which is capable of providing robustness against uncertainties and mismatch errors with low computational complexity is adopted. Simulations for several mismatch and random perturbations scenarios are conducted in a rich multipath environment with near–far effect to explore the robustness of the proposed detector. Copyright © 2008 John Wiley & Sons, Ltd.

Modified fast recursive algorithm for efficient MMSE-SIC detection of the V-BLAST system

Detection of transmitted symbols in a V-BLAST system using the minimum mean squared error criterion with successive interference cancellation (MMSE-SIC) can provide satisfactory bit error rate performance at the cost of moderate computational complexity. The fast recursive algorithm (FRA), developed by Benesty et al., is one of the well-known implementation algorithms for the MMSE-SIC detector. We modify the FRA to compute an ordered set of nulling vectors from the estimated channel information. Our modified FRA can be used with the transformation based successive interference cancellation procedure to process a V-BLAST frame that contains the preamble and payload. To our knowledge, such implementation of the MMSE-SIC detector requires the lowest complexity to process a frame of preamble and payload.

Waiting times for M/M systems under state-dependent processor sharing

We consider a system where the arrivals form a Poisson process and the required service times of the requests are exponentially distributed. The requests are served according to the state-dependent (Cohen's generalized) processor sharing discipline, where each request in the system receives a service capacity which depends on the actual number of requests in the system. For this system we derive systems of ordinary differential equations for the LST and for the moments of the conditional waiting time of a request with given required service time as well as a stable and fast recursive algorithm for the LST of the second moment of the conditional waiting time, which in particular yields the second moment of the unconditional waiting time. Moreover, asymptotically tight upper bounds for the moments of the conditional waiting time are given. The presented numerical results for the first two moments of the sojourn times in M/M/m?PS systems show that the proposed algorithms work well.

Stochastic Approximation and Newton’s Estimate of a Mixing Distribution

Many statistical problems involve mixture models and the need for computationally efficient methods to estimate the mixing distribution has increased dramatically in recent years. Newton [Sankhya Ser. A 64 (2002) 306--322] proposed a fast recursive algorithm for estimating the mixing distribution, which we study as a special case of stochastic approximation (SA). We begin with a review of SA, some recent statistical applications, and the theory necessary for analysis of a SA algorithm, which includes Lyapunov functions and ODE stability theory. Then standard SA results are used to prove consistency of Newton's estimate in the case of a finite mixture. We also propose a modification of Newton's algorithm that allows for estimation of an additional unknown parameter in the model, and prove its consistency.

A fast model identification method for networked control system

Most control strategies for networked control system (NCS) assume that system model is known as ‘a priori’, which are however impractical in many industrial applications. To obtain a suitable model for networked control, this paper concentrates on model identification under the networked control environment. A networked identification scheme is proposed here, and nondeterministic factors such as network-induced delay, data packet out-of-order, and data packet loss between the sensor and identifier as well as the identifier and the actuator are considered. A discard-packet strategy is first developed to deal with network nondeterministic factors from the sensor to the identifier, and a cubic spline interpolation is used to compensate lost data. Actuator buffers are then introduced for actuator nodes to handle network nondeterministic factors between the identifier and the actuator. Finally, a fast recursive algorithm is used both to select the model structure and to estimate the unknown system parameters. Experiments on ARMA model identification and NARMAX model identification are performed respectively under different network loads. Simulation results show that the proposed networked identification scheme can effectively overcome the impact of various network-induced nondeterministic factors and significantly improve model identification performance.

A Novel Fast Recursive MMSE-SIC Detection Algorithm for V-BLAST Systems

A novel fast recursive minimum mean square error successive interference cancellation (MMSE-SIC) algorithm with optimal detection order for vertical Bell Laboratories layered space-time (V-BLAST) systems is proposed. In this algorithm, the MMSE Alter matrices and the optimal detection order are successively computed from the previously obtained filter matrices according to simple recursive pseudoinverse formulas, so that the algorithmic complexity is reduced significantly, especially for the practical number of transmit/receive antennas.

Adaptive noise reduction using numerically stable fast recursive least squares algorithm

AbstractThis paper is concerned with adaptive noise reduction based on the fast recursive least squares (FRLS) algorithm. It is well known that the fast recursive least squares (FRLS) algorithm suffers from numerical instability when operating under the effects of finite precision arithmetic. Several numerical solutions of stabilization were proposed in the case of stationary signals. In this work a new version of a numerically stable FRLS algorithm (NS‐FRLS) is proposed. The stability characteristics of this new stabilized algorithm are analysed. The analysis is based on a linear model for the errors in the states of the adaptive filter. Experimental results confirm the merits of adaptive filtering with the NS‐FRLS algorithm over optimum filtering using the solution provided by Wiener–Hopf equations. Copyright © 2006 John Wiley & Sons, Ltd.

Fast Approximate Inverse Power Iteration Algorithm for Adaptive Total Least-Squares FIR Filtering

The presence of contaminating noises at both the input and the output of an finite-impulse-response (FIR) system constitutes a major impediment to unbiased parameter estimation. The total least-squares (TLS) method is known to be effective in achieving unbiased estimation. In this correspondence, we develop a fast recursive algorithm with a view to finding the TLS solution for adaptive FIR filtering. Given the fact that the TLS solution is obtainable via inverse power iteration, we introduce a novel but approximate inverse power iteration in combination with Galerkin method so that the TLS solution can be updated adaptively at a lower computational cost. We also take advantage of the regular form of the TLS solution to constrain the last element of the filter parameter vector to the negative one. We further reduce the computational complexity of the developed algorithm by making efficient computation of the fast gain vector defined in and using rank-one update of the augmented autocorrelation matrix. The developed algorithm saves seven M MAD's (number of multiplies, divides, and square roots) when compared with the recursive TLS algorithm in . Moreover, unlike the algorithms given in and , the developed algorithm does not deal with the solution to a one-variable quadratic equation and it avoids square root operation. Therefore, it has the simpler structure and may be more easily implemented. We then make a careful investigation into global convergence of the developed algorithm. Simulation results are provided that clearly illustrate appealing performance of the developed algorithm, including its good long-term numerical stability

Robust and Efficient Algorithm of Image Enhancement

A method for enhancing the local contrast of a noisy image using sliding discrete transforms is proposed. A minimum mean-square error estimator in the domain of a sliding transform for noise removal is derived. This estimator is based on a fast inverse sliding transform. Local contrast enhancement is performed by a nonlinear modification of denoised local spectrum coefficients. To provide image processing in real time, a fast recursive algorithm for computing the sliding transform is utilized. The algorithm is based on a recursive relationship between three subsequent local spectra. Computer simulation results using a real image are provided and discussed.

The fast normalized cross-correlation double-talk detector

In this paper, we present a method for handling double-talk. This approach uses a robust fast recursive least-squares algorithm (FRLS) and the normalized cross-correlation double-talk detector (NCC DTD). The NCC DTD is developed into a fast version, called FNCC, by reusing computational results from the FRLS algorithm. The major advantage of this detector is that it is much less dependent on the actual echo path attenuation than, e.g., the Geigel DTD. This makes it much more suitable for the acoustic application.

A fast nonlinear model identification method

The identification of nonlinear dynamic systems using linear-in-the-parameters models is studied. A fast recursive algorithm (FRA) is proposed to select both the model structure and to estimate the model parameters. Unlike orthogonal least squares (OLS) method, FRA solves the least-squares problem recursively over the model order without requiring matrix decomposition. The computational complexity of both algorithms is analyzed, along with their numerical stability. The new method is shown to require much less computational effort and is also numerically more stable than OLS.

Generalized smoothing splines and the optimal discretization of the Wiener filter

We introduce an extended class of cardinal L/sup */L-splines, where L is a pseudo-differential operator satisfying some admissibility conditions. We show that the L/sup */L-spline signal interpolation problem is well posed and that its solution is the unique minimizer of the spline energy functional /spl par/Ls/spl par//sub L2//sup 2/, subject to the interpolation constraint. Next, we consider the corresponding regularized least squares estimation problem, which is more appropriate for dealing with noisy data. The criterion to be minimized is the sum of a quadratic data term, which forces the solution to be close to the input samples, and a "smoothness" term that privileges solutions with small spline energies. Here, too, we find that the optimal solution, among all possible functions, is a cardinal L/sup */L-spline. We show that this smoothing spline estimator has a stable representation in a B-spline-like basis and that its coefficients can be computed by digital filtering of the input signal. We describe an efficient recursive filtering algorithm that is applicable whenever the transfer function of L is rational (which corresponds to the case of exponential splines). We justify these algorithms statistically by establishing an equivalence between L/sup */L smoothing splines and the minimum mean square error (MMSE) estimation of a stationary signal corrupted by white Gaussian noise. In this model-based formulation, the optimum operator L is the whitening filter of the process, and the regularization parameter is proportional to the noise variance. Thus, the proposed formalism yields the optimal discretization of the classical Wiener filter, together with a fast recursive algorithm. It extends the standard Wiener solution by providing the optimal interpolation space. We also present a Bayesian interpretation of the algorithm.

A fast recursive total least squares algorithm for adaptive IIR filtering

This work develops a new fast recursive total least squares (N-RTLS) algorithm to recursively compute the total least squares (TLS) solution for adaptive infinite-impulse-response (IIR) filtering. The new algorithm is based on the minimization of the constraint Rayleigh quotient in which the first entry of the parameter vector is fixed to the negative one. The highly computational efficiency of the proposed algorithm depends on the efficient computation of the gain vector and the adaptation of the Rayleigh quotient. Using the shift structure of the input data vectors, a fast algorithm for computing the gain vector is established, which is referred to as the fast gain vector (FGV) algorithm. The computational load of the FGV algorithm is smaller than that of the fast Kalman algorithm. Moreover, the new algorithm is numerically stable since it does not use the well-known matrix inversion lemma. The computational complexity of the new algorithm per iteration is also O(L). The global convergence of the new algorithm is studied. The performances of the relevant algorithms are compared via simulations.

Fast recursive algorithm for broadband APFs using complex cepstrums

Integrated-optical All-Pass Filters are of interest for their potential compactness and economy of production. For broadband applications, the number of APFs involved can be as large as 50. To find optima for all the large number of parameters involved, we need a fast and efficient algorithm based on recursive equations. APF design algorithms based on complex cepstrum are proposed in digital signal processing. In this paper, we enhance these algorithms to efficiently fit the differential phase profile required for in-line broadband Polarization Mode Dispersion and Polarization Dependent Loss compensation.

Extension of the schur-cohn stability test for 2-d ar quarter-plane model

The Schur-Cohn test plays an essential role in checking the stability of one-dimensional (1D) random processes such as autoregressive (AR) models, via the so-called reflection coefficients, partial correlations, or Schur-Szego coefficients. In the context of two-dimensional (2D) random field modeling, one of the authors recently proposed a 2D AR quarter-plane model representation using 2D reflection coefficients estimated by a fast recursive adaptive algorithm. Based on such 2D reflection coefficients, we can therefore derive two necessary stability conditions for a 2D AR quarter-plane model. One of these conditions can be considered as an extension of the Schur-Cohn stability criterion based on the 2D reflection coefficients.