Improvement In Mean Square Error Research Articles

Reconstruction of long horizontal-path images under anisoplanatic conditions using multiframe blind deconvolution

All optical systems that operate in or through the atmosphere suffer from turbulence induced image blur. Both military and civilian surveillance, gun sighting, and target identification systems are interested in terrestrial imaging over very long horizontal paths, but atmospheric turbulence can blur the resulting images beyond usefulness. This work explores the mean square error (MSE) performance of a multiframe blind deconvolution (MFBD) technique applied under anisoplanatic conditions for both Gaussian and Poisson noise model assumptions. The technique is evaluated for use in reconstructing images of scenes corrupted by turbulence in long horizontal-path imaging scenarios. Performance is evaluated via the reconstruction of a common object from three sets of simulated turbulence degraded imagery representing low, moderate, and severe turbulence conditions. Each set consisted of 1000 simulated turbulence degraded images. The MSE performance of the estimator is evaluated as a function of the number of images, and the number of Zernike polynomial terms used to characterize the point spread function. A Gaussian noise model-based MFBD algorithm reconstructs objects that showed as much as 40% improvement in MSE with as few as 14 frames and 30 Zernike coefficients used in the reconstruction, despite the presence of anisoplanatism in the data. An MFBD algorithm based on the Poisson noise model required a minimum of 50 frames to achieve significant improvement over the average MSE for the data set. Reconstructed objects show as much as 38% improvement in MSE using 175 frames and 30 Zernike coefficients in the reconstruction.

Smoothing across time in repeated cross‐sectional data

Repeated cross-sectional samples are common in national surveys of health like the National Health Interview Survey (NHIS). Because population health outcomes generally evolve slowly, pooling data across years can improve the precision of current-year annual estimates of disease prevalence and other health outcomes. Pooling over time is particularly valuable in health disparities research, where outcomes for small groups are often of interest and pooling data across groups would bias disparity estimates. State-space modeling and Kalman filtering are appealing choices for smoothing data across time. However, filtering can be problematic when few time points are available, as is common with annual cross-sectional data. Problems arise because filtering relies on estimated variance components, which can be biased and imprecise when estimated with small samples, especially when estimated in tandem with linear trends. We conduct a simulation study showing that even when trends and variance components are estimated poorly, smoothing with these estimates can improve the mean squared error (MSE) of estimated health states for multiple racial/ethnic groups when the variance components are estimated with the pooled sample. We consider frequentist estimators with no trends, one common trend across groups, and separate trends for every group, as well as shrinkage estimators of trends through a Bayesian model. We show that the Bayesian model offers the greatest improvement in MSE, and that Bayesian Information Criterion (BIC)-based model averaging of the frequentist estimators with different trend assumptions performs nearly as well. We present empirical examples using the NHIS data.

Mass fraction spatiotemporal geostatistics and its application to map atmospheric polycyclic aromatic hydrocarbons after 9/11

This work proposes a space/time estimation method for atmospheric PM2.5 components by modelling the mass fraction at a selection of space/time locations where the component is measured and applying the model to the extensive PM2.5 monitoring network. The method we developed utilizes the nonlinear Bayesian maximum entropy framework to perform the geostatistical estimation. We implemented this approach using data from nine carcinogenic, particle-bound polycyclic aromatic hydrocarbons (PAHs) measured from archived PM2.5 samples collected at four locations around the World Trade Center (WTC) from September 22, 2001 to March 27, 2002. The mass fraction model developed at these four sites was used to estimate PAH concentrations at additional PM2.5 monitors. Even with limited PAH data, a spatial validation showed the application of the mass fraction model reduced the mean squared error (MSE) by 7–22%, while in the temporal validation there was an exponential improvement in MSE positively associated with the number of days of PAH data removed. Our results include space/time maps of atmospheric PAH concentrations in the New York area after 9/11.

Improved Mean-Square Error Estimate for the LMS Transversal Equalizer With Narrowband Interference

When the least-mean-square (LMS) algorithm is used to adapt an adaptive transversal equalizer that is subject to strong narrowband interference, a so-called non-Wiener or nonlinear effect takes place. This results in the mean-square error (MSE) performance of the adaptive equalizer being better than that of the fixed Wiener filter of equivalent structure. Reuter and Zeidler proposed a transfer-function-based approach to provide an estimate of the MSE performance of the equalizer in such an environment. We have recently shown that the mean of the LMS weights in this adaptive equalizer problem shifts away from the Wiener filter solution. As a result, we propose an MSE model for the LMS equalizer that is an improvement over the existing Reuter-Zeidler model. The new model uses the same transfer-function-based approach but incorporates the shift in the mean of the weights. Numerical simulations are provided to illustrate the improvement.

Optimal Sequential Energy Allocation for Inverse Problems

This paper investigates the advantages of adaptive waveform amplitude design for estimating parameters of an unknown channel/medium under average energy constraints. We present a statistical framework for sequential design (e.g., design of waveforms in adaptive sensing) of experiments that improves parameter estimation (e.g., unknown channel parameters) performance in terms of reduction in mean-squared error (MSE). We treat an N time step design problem for a linear Gaussian model where the shape of the N input design vectors (one per time step) remains constant and their amplitudes are chosen as a function of past measurements to minimize MSE. For N=2, we derive the optimal energy allocation at the second step as a function of the first measurement. Our adaptive two-step strategy yields an MSE improvement of at least 1.65 dB relative to the optimal nonadaptive strategy, but is not implementable since it requires knowledge of the noise amplitude. We then present an implementable design for the two-step strategy which asymptotically achieves optimal performance. Motivated by the optimal two-step strategy, we propose a suboptimal adaptive N-step energy allocation strategy that can achieve an MSE improvement of more than 5 dB for N=50. We demonstrate our general approach in the context of MIMO channel estimation and inverse scattering problems

A delayless adaptive IFIR filterbank structure for wideband and narrowband active noise control

Active noise control (ANC) applications involve adaptive filters with hundreds of taps. These filters are associated with high computational burden depending on the number of taps in the filter and may suffer from slow convergence if the reference signal spectrum has a large dynamic range. Subband and filterbank techniques have been proposed to address these problems. It is known that linear systems can be modeled exactly using a set of filter bank basis functions. Filter bank adaptive filter (FBAF) is one such model in adaptive filterbank techniques. The FBAF model is a parallel bank of filters with each bank (channel) comprising of cascade of a set of short length filter called interpolator followed by adaptive sparse filter also called the model filter. The interpolator-sparse model filter cascade in each channel is identical to the classical interpolated finite impulse response (IFIR) filter. Hence, the structure is called IFIR filterbank structure. The filterbank basis functions are orthonormal, which introduces delay in the signal path, thereby, degrading the performance of the adaptive filter. In this paper, we propose a delayless adaptive IFIR filterbank structure for wideband and narrowband active noise control. The proposed delayless adaptive filter has improved mean square error (MSE) convergence rate and shows marginally better noise cancellation in the wideband and narrowband ANC domain when compared with the conventional fullband adaptive structure. The computational complexity of the proposed structure is compared with the fullband structure.

Array interpolation and DOA MSE reduction

Interpolation or mapping of data from a given real array to data from a virtual array of more suitable geometry is well known in array signal processing. This operation allows arrays of any geometry to be used with fast direction-of-arrival (DOA) estimators designed for linear arrays. In an earlier companion paper , a first-order condition for zero DOA bias under such mapping was derived and was also used to construct a design algorithm for the mapping matrix that minimized the DOA estimate bias. This bias-minimizing theory is now extended to minimize not only bias, but also to consider finite sample effects due to noise and reduce the DOA mean-square error (MSE). An analytical first-order expression for mapped DOA MSE is derived, and a design algorithm for the transformation matrix that minimizes this MSE is proposed. Generally, DOA MSE is not reduced by minimizing the size of the mapping errors but instead by rotating these errors and the associated noise subspace into optimal directions relative to a certain gradient of the DOA estimator criterion function. The analytical MSE expression and the design algorithm are supported by simulations that show not only conspicuous MSE improvements in relevant scenarios, but also a more robust preprocessing for low signal-to-noise ratios (SNRs) as compared with the pure bias-minimizing design developed in the previous paper.

Bootstrap Bias Adjusted Estimators of Beta Distribution Parameters

The standard beta distribution is one of the few well-studied distributions with continuous support on (0, 1] . In this paper, we propose a bootstrap bias corrected estimator of the standard beta shape parameters to improve on the traditional Method of Moments Estimators (MME) and Maximum Likelihood Estimators (MLE). Through empirical studies we show that the MME's have smaller bias but very large Mean Squared Error (MSE) as compared to the MLE's, while the MLE's have larger bias but substantially lower MSE. The bootstrap bias corrected estimators give substantial improvement in bias and MSE over both the MME and MLE.

Improved Estimators of Variance Components with Smaller Probability of Negativity

SUMMARY A linear model with two variance components is considered, one variance component (say, σ 1 2 ≥ 0) corresponding to a random effect, and a second variance component (say, σ 2 > 0) corresponding to the experimental errors. A class of invariant quadratic estimators (IQEs) is characterized, having uniformly smaller mean-squared error (MSE), and uniformly smaller probability of negativity, compared with the analysis-of-variance (ANOVA) estimator of σ 1 2. It turns out that for balanced models, among IQEs of σ 1 2 with uniformly smaller MSE than its ANOVA estimator, there exists an IQE with the smallest probability of being negative, uniformly in the parameters. The results are applied to the balanced one-way classification model. Numerical computations show that the MSE improvement achievable through the use of the proposed estimators is quite significant. It is noted that, for the nonnegative estimation of σ 1 2, truncation of one of the proposed estimators at 0 provides a satisfactory solution. Extension of the results to the unbalanced case, and to the general mixed model with balanced data, is also indicated.

Optimal and sub-optimal post-detection timing estimators for PET

The authors derive linear and nonlinear approximations to the postdetection likelihood function for scintillator interaction time in nuclear particle detection systems. The likelihood function is the optimal statistic for performing detection and estimation of scintillator events and event times. The authors derive the likelihood function approximations from a statistical model for the postdetection waveform which is common in the optical communications literature and takes account of finite detector bandwidth, random gains, and thermal noise. They present preliminary simulation results for the associated approximate maximum likelihood timing estimators which indicate that significant MSE (mean square error) improvements can be achieved for low postdetection signal-to-noise ratio.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Vector Quantizer Design for Memoryless Gaussian, Gamma, and Laplacian Sources

Locally optimum vector quantizer (VQ) designs are presented for memoryless Gaussian, gamma, and Laplacian sources. For Gaussian sources, low (2-6) dimensional vector quantization provides relatively little improvement in mean-squared error (MSE) compared to the minimum mean-squared error (MMSE) scalar quantizer. For Laplacian or gamma sources, however, significant improvement in MSE is available with vector quantization. The Laplacian and gamma 6 bit, sixdimensional vector quantizers achieve, respectively, improvements of 2 and 4.5 dB over the corresponding scalar MMSE quantizer distortions.