Simultaneous Denoising and Illumination Correction via Local Data-Fidelity and Nonlocal Regularization

Summary Local maximum likelihood estimation is a nonparametric counterpart of the widely used parametric maximum likelihood technique. It extends the scope of the parametric maximum likelihood method to a much wider class of parametric spaces. Associated with this nonparametric estimation scheme is the issue of bandwidth selection and bias and variance assessment. This paper provides a unified approach to selecting a bandwidth and constructing confidence intervals in local maximum likelihood estimation. The approach is then applied to least squares nonparametric regression and to nonparametric logistic regression. Our experiences in these two settings show that the general idea outlined here is powerful and encouraging.

On the consistency of the maximum likelihood estimator for the three parameter lognormal distribution

Robust image compressive sensing based on m-estimator and nonlocal low-rank regularization

Spectrum sensing is important for a cognitive radio (CR) system to protect primary users (PUs) from harmful interference. At present, most of the existing sensing schemes are proposed in Gaussian noise environments. Nevertheless, a CR system actually also suffers from non-Gaussian noise, such as man-made impulsive noise, ultrawideband interference and co-channel interference. In this article, to handle the degradation of detection performance in non-Gaussian impulsive noise environments, a robust spectrum sensing scheme named hyperbolic tangent-based energy detector (HT-ED) is proposed. The hyperbolic tangent function is applied to suppress the impulsive noise by the nonlinear behavior, but without restraining the normal noise by the linear behavior. This property enables the new method to achieve the good detection performance in both Gaussian and non-Gaussian noise environments. In addition, it is similar to an energy detector, the new detector does not need to know the characteristics of the PU's signal. The performance analysis of the proposed HT-ED scheme is also presented. The simulation results show the HT-ED is robust against impulsive noise, which is modeled as Laplace or α-stable noise. Moreover, the HT-ED provides a superior detection performance compared with the other existing relative methods in a wide range of non-Gaussian noise.

The purpose of this correspondence is to report on some nxasurements of output SNR (signal-to-noise ratio or S/N), characteristics for a square-law detector extracting signals from non-Gaussian noise, specifically, impulsive noise. Non-Garlssian noise arises in varioas communication media such as the atmosphere, wire lines, and under water. In experimental and theoretical investigations of the effects of non-Gaussian noise on various communications systems, a simple correlator is often considered because it is possible to obtain theoretical predictions of the (S/N), for signal and additive non-Gaussian noise at the correlator input if an appropriate noise model is available for calculating the required fourth-order moment. Middleton (1962), in his analysis of correlator performance in non-Gaussian background noise, employed the so-called Poisson impulse noise model. His theoretical predictions reveal that impulsive noise always degrades the (S/N), as compared with Gaussian noise backgrounds having the same spectral distribution for a given input SNR. However, his theoretical formulas are rather difficult to check experimentally in their full generality and assess the relative importance of various parameters. We compare a study restricted to the case of a square-law detector with Middleton's results.

Accurate channel-estimation algorithms are critical for enhancing the throughput of wireless communication systems, including millimetre wave (mmWave) multiple-input multiple-output (MIMO) systems, where precise channel knowledge enables reliable signal detection and beamforming. In practical wireless environments, impulsive non-Gaussian noise with unknown statistics often occurs due to electromagnetic interference and harsh propagation conditions, significantly degrading estimation accuracy and overall system performance. In this context, the maximum correntropy criterion (MCC) has emerged as an attractive solution for robust channel estimation that outperforms state-of-the-art algorithms. However, the MCC-based algorithm’s performance is sensitive to the tuning of hyperparameters, which is challenging in the presence of non-Gaussian noise, such as impulsive noise (IN). Furthermore, a recent genre of kernel width sampling methods makes MCC hyperparameter-free and allows for asymptotic convergence to the squared-error performance of MCC with the ideal kernel width. To ensure their practical applicability, convergence analysis is essential to theoretically guarantee stability and performance under various IN scenarios. This study presents convergence analysis of hyperparameter-free MCC-based channel estimation for mmWave MIMO systems considering various IN scenarios. To validate the theoretical analysis, simulations are conducted on practical mmWave MIMO system models. Simulation results closely match the analytical findings, which confirms the accuracy and effectiveness of the analysis we here present.

Local damage detection based on vibration data analysis in the presence of Gaussian and heavy-tailed impulsive noise

Robust adaptive sparse channel estimation problem has been attracted highly attention in the next-generation wireless communications systems. Re-weighted L1-norm penalized sign least mean square error (RL1-SLMS) algorithm is considered as one of attractive methods to estimate unknown sparse system as well as to mitigate impulsive noises. However, the convergence performance of RL1-SLMS is very ambiguous comparing with its preliminary version. This paper provides comprehensive convergence analysis for the RL1-SLMS algorithm under non-Gaussian impulsive noise environment. Numerical simulations are given to show the fast convergence and robustness with respect to system sparsity as well as non-Gaussian noise.

Cyclostationary analysis has several applications in communications, e.g., spectral sensing, signal parameter estimation, and modulation classification. Most of them consider the additive white Gaussian noise (AWGN) channel model, although wireless communication systems may also be subject to non-Gaussian interference and impulsive noise. In this context, the communication channel can be better modeled by heavy-tailed distributions, such as the non-Gaussian alpha-stable one. Some applications of the cyclostationary approach based on the spatial sign cyclic correlation function (SSCCF), fractional lower-order cyclic autocorrelation function (FLOCAF), and cyclic correntropy function (CCF) demonstrate that these are promising solutions for the analysis of signals in the presence of impulsive non-Gaussian noise. However, the investigation of functions above applied to digital modulation recognition in impulsive environments, and the comparison among them are topics that did not adequately explore yet. This work demonstrates that SSCCF is a particular case of the FLOCAF. Besides, a detailed analysis of the use of the FLOCAF and CCF is presented to obtain cyclostationary descriptors for the recognition of digital modulations BPSK, QPSK, 8-QAM, 16-QAM, and 32-QAM. Automatic modulation classification (AMC) architectures, based on the functions mentioned above, are also proposed. Besides, another contribution showed is that both the FLOCAF and CCF allow the symbol rate parameter estimation. The performances of AMC architectures were evaluated in the scenario with modulated signals contaminated with additive non-Gaussian alpha-stable noise. The results demonstrate that both architectures can classify signals in different contamination scenarios. However, the architecture based on the CCF is more efficient than the FLOCAF-based one.

This article compares the modeling of nonstationary extreme events using parametric models with local parametric and semiparametric approaches also motivated by extreme value theory. Specifically, three estimators are compared based on (a) (local) semiparametric moment estimation, (b) (local) maximum likelihood estimation, and (c) spline‐based maximum likelihood estimation. Inference is performed in a sequential manner, highlighting the synergies between the different approaches to estimating extreme quantiles, including the T‐year level and right endpoint when finite. We present a novel heuristic to estimate nonstationary extreme value threshold with exceedances varying on a circular domain, and hypothesis‐testing procedures for identifying max‐domain of attraction in the nonstationary setting. Bootstrapping is used to estimate nonstationary confidence bounds throughout. We provide step‐by‐step guides for estimation, and explore the different inference strategies in application to directional modeling of hindcast storm peak significant wave heights recorded in the North Sea.

Uneven illumination is a recurrent problem in image processing. This is essentially due to image acquisition sensors’ malfunction or external interference. In this paper we propose a variational model for nonuniform illumination correction, that incorporates a penalty term that performs the intensity distribution transfer between two pre-defined sub-regions of the input scalar image, one uniformly illuminated and the other nonuniformly illuminated. This term representing the illumination correction is a Wasserstein distance. It corresponds to the optimal permutation minimizing the cost of rearranging the intensity distribution of the nonuniformly illuminated sub-region into the other, the uniformly illuminated. Simultaneously, this variational model also carries out a regularization of the image by means of a total variation penalty term, to reduce noise. The effectiveness of the model is illustrated for some images.

In many applications non-stationary Gaussian or stationary non Gaussian noises can be observed. In this paper we present a maximum a posteriori estimation jointly of spectral amplitude and phase (JMAP). It principally allows for arbitrary speech models (Gaussian, super-Gaussian, ...), while the noise DFT coefficients pdf is modeled as Gaussian mixture (GMM). Such a GMM covers both a non-Gaussian stationary noise process, but also a non-stationary process that changes between Gaussian noise modes of different variance with probability of the GMM weight. Accordingly, we provide results for these two types of noise, showing superiority over the Gaussian noise model JMAP estimator even in case of ideal noise power estimation.

Performance of 5G NR-polar QAM-OFDM in nonlinear distortion plus Non-Gaussian noise over Rayleigh fading channel

Vitesse de convergence presque sûre de l'estimateur à noyau du maximum de vraisemblance local

A robust method for detecting the communication signals impinging on an antenna with interference and non-Gaussian impulsive noise is introduced in this paper. Degradation of the conventional cyclic detector which based on max-output-SNR criterion in impulsive noise is shown both theoretically and experimentally. By fusing second-order cyclostationarity and fractional lower-order statistics, a type of cyclic fractional lower-order statistics is developed which is defined for exploiting cyclostationarity property. Then, a new robust type of detection algorithm is developed using the theory of optimal filtering based on max-output-SNR criterion and alpha-stable distribution, including the fractional lower-order cyclic matched filter, which is formulated for detecting the communication signals in the presence of interference and non-Gaussian alpha-stable distribution impulsive noise. It is shown that the new method is robust to Gaussian and non-Gaussian impulsive noises, and is immune to the interfering signals which occupy the same spectral band as that of the received signal. Simulation results show the robustness and effectiveness of the proposed algorithm.