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The article discusses a newly developed simple and usable noise model, which consists of a Poissonian part for the modeling of photon sensing and a Gaussian part for the remaining disturbances in the output. The model presents the pointwise standard-deviation of noise as a function of the pixel-raw-data output and is widely used in digital imaging sensors.

Local polynomial approximation (LPA) technique was used for estimating the absolute phase reconstruction from noisy wrapped phase data. Findings revealed a reasonable compromise between the noise smoothing and preservation of details in phase image due to window size adaptation.

A new method is described for spatially adaptive estimation and the local likelihood is used for nonparametric modeling of estimated signals. The new algorithm has performed well for image denoising and it is compared with the intersection of confidence interval (ICI) technique that has used a selection of an adaptive neighborhood for estimation.

Direction-of-arrival (DOA) estimation in a phased-array system is considered for a non-Gaussian noise environment. In this paper, a robust M-estimation scheme based on Huber's loss function with an adaptive threshold is proposed. The method is evaluated using experimental data from the University of California, Los Angeles, 60-GHz antennaarray system. It is shown that the proposed method enables a decreased sensitivity of the DOA estimates with respect to noise components having heavy-tailed distributions. Index Terms--Adaptive threshold, non-Gaussian noise, robust direction-of-arrival (DOA) estimation, 60-GHz antenna array.

A new image denoising strategy based on enhanced sparse representation in transform domain achieved an excellent denoising performance in both peak signal-to-noise ratio and subjective visual quality.

The shape-adaptive discrete cosine transform (SA-DCT) transform is found to be extremely useful for the denoising and deblocking of grayscale and color images, hence providing clean reconstructed edges without any unpleasant ringing artifacts due to the adaptive support provided by the structural constraints.

A novel nonparametric regression method for deblurring noisy images is proposed. The regularized inverse and Wiener inverse filters serve as deblurring operator used jointly with the local polynomial approximation-design directional kernel filters.

Modern standard high-resolution array signal processing techniques are based on simultaneous sampling of the whole multiple-sensor array. A switch antenna array system is a promising substitute for the multiple-channel array due to its lower cost and a simpler front-end circuitry. A system composed of a single transmitter, M receiving antennas, and a single receiving channel is explained.

A windowed local polynomial approximation (LPA) of time-varying directions of arrival is used to develop an LPA-beamformer for localization of rapidly moving sources. Closed-form expressions are obtained for the bias and variance of the LPA-beamformer in the moving source case and the problem of the optimal window choice is discussed. Index Terms--Array processing, beamforming, moving sources.

A unique strategy for solving a problem of bandwidth selection for filtering a signal with additive noise is shown. The linear local polynomial approximation is employed to demonstrate the efficiency of the technique, while a development to nonlinear observations and robust M-estimates is possible. The algorithm is simple to implement and needs the computation of the estimates and their standard deviations for a set of bandwidth values.

Minimax Huber's robust statistics is an alternative to the maximum likelihood approach in the estimation of the distribution of random errors. A new periodogram is developed based on the nonlinear estimates of the amplitude C. The M-periodogram is robust in the estimation of the distribution of errors with unknown but heavy-tailed distributions. A key point of the robust M-periodogram is the choice of the nonquadratic residual function F.

A new form of the Fourier transform and the local polynomial periodogram is developed as an estimator of the instantaneous frequency (IF) of a harmonic complex-valued signal, using the local polynomial approximation of the time-varying phase. An examination of the variance and bias of the estimate for the short- and long-time asymptotic behavior of the IF estimates shows that the orders for the optimal asymptotic mean squared error of the estimates of omega(super k-1)(t) are 0(N-(super 2k+1)) and 0(N-2(m-k+1)/2m+3), respectively, for a polynomial omega(t) of the degree m-1 and arbitrary smooth omega(t) with a bounded mth derivative.

An adaptive estimator for calculating instantaneous frequency (IF) of a harmonic complex-valued signal with additive noise was created using the Wigner distribution. This estimation tool uses an algorithm with a time-varying and data-driven window length that was observed to generate IF calculations based on the formula for the variance of the estimate. Simulation testing also showed that this adaptive estimator has good accuracy and is capable of enhancing time-frequency representation of signal with a nonlinear IF.

A study was conducted to analyze the problem of estimating the instantaneous frequency (IF). The asymptotic minimax lower bound was determined for the mean squared error of estimation while the local polynomial periodogram was represented as a nonparametric estimator of the IF. Results indicated that the optimal choice of the window size in the local polynomial periodogram estimator of the IF and its derivatives correlated with mean squared errors that were different from the minimax lower bounds.