Detection threshold for non-parametric estimation

A new threshold is presented for better estimating a signal by sparse transform and soft thresholding. This threshold derives from a non-parametric statistical approach dedicated to the detection of a signal with unknown distribution and unknown probability of presence in independent and additive white Gaussian noise. This threshold is called the detection threshold and is particularly appropriate for selecting the few observations, provided by the sparse transform, whose amplitudes are sufficiently large to consider that they contain information about the signal. An upper bound for the risk of the soft thresholding estimation is computed when the detection threshold is used. For a wide class of signals, it is shown that, when the number of observations is large, this upper bound is from about twice to four times smaller than the standard upper bounds given for the universal and the minimax thresholds. Many real-world signals belong to this class, as illustrated by several experimental results.     

3-D maximum a posteriori estimation for single photon emission computed tomography on massively-parallel computers

A fully three-dimensional (3-D) implementation of the maximum a posteriori (MAP) method for single photon emission computed tomography (SPECT) is demonstrated. The 3-D reconstruction exhibits a major increase in resolution when compared to the generation of the series of separate 2-D slice reconstructions. As has been noted, the iterative EM algorithm for 2-D reconstruction is highly computational; the 3-D algorithm is far worse. To accommodate the computational complexity, previous work in the 2-D arena is extended, and an implementation on the class of massively parallel processors of the 3-D algorithm is demonstrated. Using a 16000- (4000-) processor MasPar/DECmpp-Sx machine, the algorithm is demonstrated to execute at 2.5 (7.8) s/EM-iteration for the entire 64x64x64 cube of 96 planar measurements obtained from the Siemens Orbiter rotating camera operating in the high-resolution mode.     

Approximate maximum likelihood hyperparameter estimation for Gibbspriors

The parameters of the prior, the hyperparameters, play an important role in Bayesian image estimation. Of particular importance for the case of Gibbs priors is the global hyperparameter, beta, which multiplies the Hamiltonian. Here we consider maximum likelihood (ML) estimation of beta from incomplete data, i.e., problems in which the image, which is drawn from a Gibbs prior, is observed indirectly through some degradation or blurring process. Important applications include image restoration and image reconstruction from projections. Exact ML estimation of beta from incomplete data is intractable for most image processing. Here we present an approximate ML estimator that is computed simultaneously with a maximum a posteriori (MAP) image estimate. The algorithm is based on a mean field approximation technique through which multidimensional Gibbs distributions are approximated by a separable function equal to a product of one-dimensional (1-D) densities. We show how this approach can be used to simplify the ML estimation problem. We also show how the Gibbs-Bogoliubov-Feynman (GBF) bound can be used to optimize the approximation for a restricted class of problems. We present the results of a Monte Carlo study that examines the bias and variance of this estimator when applied to image restoration.     

New perspectives for maximum likelihood time-delay estimation

This paper introduces a new realization for maximum likelihood time-delay estimation (TDE) that illuminates the relationships between maximum likelihood TDE and other methods. We obtain the result by deriving the likelihood function using a fundamental method that appears to be new to the field of array processing. This method is a natural complement to the generalized Karhunen-Loeve expansion     

Analytic threshold calculation of frequency estimation for OFDM communication

In this paper, we introduce an improved expression for the normalized variance of a frequency offset estimator, which successfully estimates the actual behavior of the normalized variance of the frequency offset estimator below and above the threshold. Therefore, an orthogonal frequency division multiplexing designer does not need any more to simulate the whole system in order to obtain the actual, normalized variance of the frequency offset estimator for the lower range of signal to noise ratio. We also present the source for the threshold phenomenon and the “threshold region”.     

Single tone parameter estimation from discrete-time observations

Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed. The appropriate Cramér-Rao bounds and maximum-likelihood (MI.) estimation algorithms are derived. Some properties of the ML estimators are proved. The relationship of ML estimation to the discrete Fourier transform is exploited to obtain practical algorithms. The threshold effect of one algorithm is analyzed and compared to simulation results. Other simulation results verify other aspects of the analysis.     

Expected likelihood support for deterministic maximum likelihood DOA estimation

In this paper, a solution quality assessment method referred to as the “expected likelihood” (EL) approach, previously introduced for the stochastic (unconditional) Gaussian model, is extended over the deterministic (conditional) Gaussian model. This model is applied for arbitrary temporally correlated (narrowband) waveforms, emitted by point sources impinging upon an antenna array. Performance of direction of arrival (DOA) estimation is then examined.     

Exact maximum likelihood time delay estimation for shortobservation intervals

An exact solution is presented to the problem of maximum likelihood time delay estimation for a Gaussian source signal observed at two different locations in the presence of additive, spatially uncorrelated Gaussian white noise. The solution is valid for arbitrarily small observation intervals; that is, the assumption T≫τ _c, |d| made in the derivation of the conventional asymptotic maximum likelihood (AML) time delay estimator (where τ _c is the correlation time of the various random processes involved and d is the differential time delay) is relaxed. The resulting exact maximum likelihood (EML) instrumentation is shown to consist of a finite-time delay-and-sum beamformer, followed by a quadratic postprocessor based on the eigenvalues and eigenfunctions of a one-dimensional integral equation with nonconstant weight. The solution of this integral equation is obtained for the case of stationary signals with rational power spectral densities. Finally, the performance of the EML and AML estimators is compared by means of computer simulations     

Iterative maximum entropy power spectrum estimation for multirate systems

In multirate systems, observations are generally insufficient to determine the power spectrum of the input signal. In this paper, we reformulate the problem using a novel matrix notation and the discrete entropy function. Then we present an iterative maximum entropy power spectrum estimation algorithm for the solution of this problem. Contrary to the existing solutions, the new algorithm is computationally efficient since it is based on fast Fourier transform (FFT) and simple matrix calculations. Furthermore, simulation results show that the new algorithm converges to the maximum entropy solution and can be successfully used in multirate statistical data estimation.     

Vector-extrapolated fast maximum likelihood estimation algorithms for emission tomography

A new class of fast maximum-likelihood estimation (MLE) algorithms for emission computed tomography (ECT) is developed. In these cyclic iterative algorithms, vector extrapolation techniques are integrated with the iterations in gradient-based MLE algorithms, with the objective of accelerating the convergence of the base iterations. This results in a substantial reduction in the effective number of base iterations required for obtaining an emission density estimate of specified quality. The mathematical theory behind the minimal polynomial and reduced rank vector extrapolation techniques, in the context of emission tomography, is presented. These extrapolation techniques are implemented in a positron emission tomography system. The new algorithms are evaluated using computer experiments, with measurements taken from simulated phantoms. It is shown that, with minimal additional computations, the proposed approach results in substantial improvement in reconstruction.     

A recursive maximum likelihood algorithm for ARMA spectral estimation

A spectral estimation technique is presented for autoregressive moving-average (ARMA) processes. The technique is based on a parameter estimation technique known as the rec ursive maximum likelihood (RML) method. The recursive spectral estimation algorithm is presented and its asymptotic properties are discussed. Simulation results are presented to illustrate the performance of the estimator for various types of data.     

Fast algorithms for single frequency estimation

In this paper, some new estimators of the frequency of a single complex sinusoid are presented. The rotate-add-decimate (RAD) method of Crozier is first refined to more closely approach the Cramer-Rao Bound (CRB). An additional modification yields an unbiased estimator (ERAD) that essentially achieves the CRB above a signal-to-noise ratio (SNR) threshold comparable to that of RAD. In addition, this estimator is proven to achieve the CRB for high SNR. The ERAD method requires approximately 2N complex multiply-adds and log/sub 2/N arctangents. A modified ERAD (MERAD) is proposed that matches the SNR threshold and computational complexity of the RAD method (approximately 3N complex multiply-adds and log/sub 2/N arctangents) but achieves the CRB for high SNR.     

Extending the threshold and frequency range for phase-basedfrequency estimation

Standard phase-based frequency estimation has a threshold that is high, is frequency dependent, and does not decrease with increasing signal length. These problems are solved by processing the signal with a highly overlapped filter bank before applying phase-based frequency estimation. By exploiting decimation, a closed-form matrix inversion, and cascades of simple filter banks, the computational complexity is kept low     

Nonlinear maximum likelihood estimation of autoregressive timeseries

Describes an algorithm for finding the exact, nonlinear, maximum likelihood (ML) estimators for the parameters of an autoregressive time series. The authors demonstrate that the ML normal equations can be written as an interdependent set of cubic and quadratic equations in the AR polynomial coefficients. They present an algorithm that algebraically solves this set of nonlinear equations for low-order problems. For high-order problems, the authors describe iterative algorithms for obtaining a ML solution     

On maximum likelihood estimation for the two parameter Weibull distribution

This paper examines recent results presented on maximum likelihood estimation for the two parameter Weibull distribution. In particular, we seek to explain some recently reported values for estimator bias when the data for analysis contains both times to failure and censored times in operation; our discussion centres on the generation of sample data sets. We conclude that, under appropriate conditions, estimators are asymptotically unbiased, with relatively low bias in small to moderate samples. We then present the results of some further experiments which suggest that the previously reported values for estimator bias can be attributed to the method of generating sample data sets in simulation experiments.     

Two-stage maximum likelihood estimation for diversity combining indigital mobile radio

For space diversity, it is shown that it is related to maximal-ratio combining (MRC). Unlike MRC, it allows the receiver to collect diversity signals without gain adjustments or cophasing. Some worst-case bit error rate (BER) simulation results that show the influence of time delay spread, Doppler, shadow loss, and diversity for a seven-cell cluster using quadrature modulation are presented     

Symmetric adaptive maximum likelihood estimation for noisecancellation and signal separation

The symmetric adaptive maximum likelihood estimation (SAMLE) algorithm is proposed. It is shown to be a generalisation of the symmetric adaptive decorrelation (SAD) algorithm for noise cancellation and signal separation. Both the SAD and SAMLE algorithms are applied to the separation of a mixture of natural speech recorded in a realistic acoustic environment. A comparative simulation confirms that the SAMLE algorithm provides superior separation capabilities     

A model-based approach for estimation of two-dimensional maximum entropy power spectra

A stochastic model-based approach is presented for estimation of the two-dimensional maximum entropy power spectrum (MEPS) from given finite uniform array data. The method consists of fitting an appropriate two-dimensional noncausal Gaussian-Markov random field (GMRF) model to the given data using the maximum likelihood (ML) technique for parameter estimation. The nonlinear criterion function used for ML estimation is similar in structure to the function arising in the deterministic approach of Lang and McClellan. The model-based approach provides new insights into the two-dimensional MEPS estimation problem. For example, using the asymptotic normality of ML estimates, we derive simultaneous confidence bands for the estimated MEPS. It turns out that when the true correlations are generated by a noncausal GMRF model, the two-dimensional MEPS can be obtained by solving linear equations. This approach also suggests techniques for realizing two-dimensional GMRF models from the given correlation data. Several numerical examples are given to illustrate the usefulness of the approach.     

Cramer-Rao bounds and maximum likelihood estimation for randomamplitude phase-modulated signals

The problem of estimating the phase parameters of a phase-modulated signal in the presence of colored multiplicative noise (random amplitude modulation) and additive white noise (both Gaussian) is addressed. Closed-form expressions for the exact and large-sample Cramer-Rao Bounds (CRBs) are derived. It is shown that the CRB is significantly affected by the color of the modulating process when the signal-to-noise ratio (SNR) or the intrinsic SNR is small. Maximum likelihood type estimators that ignore the noise color and optimize a criterion with respect to only the phase parameters are proposed. These estimators are shown to be equivalent to the nonlinear least squares estimators, which consist of matching the squared observations with a constant amplitude phase-modulated signal when the mean of the multiplicative noise is forced to zero. Closed-form expressions are derived for the efficiency of these estimators and are verified via simulations     

Asymptotic results for maximum likelihood estimation with an arrayof sensors

In many cases, the maximum likelihood (ML) estimator is consistent and asymptotically normal with covariance equal to the inverse of the Fisher's information matrix. It does not follow, though, that the covariance of the ML estimator approaches the Cramer-Rao lower bound as the sample size increases. However, it is possible to draw such a conclusion for the adaptive array problem in which direction of arrival and signal magnitude are being estimated. Proofs of w-asymptotic efficiency, which comes with a convergence-of-moments condition, and strong consistency (almost-sure convergence) of the ML estimator are given. Strong consistency is also proved for a popular quasi-ML estimator