Additive Gaussian Noise Research Articles

An extended Babai method for estimating linear model based integer parameters

Estimating the integer parameter vector in a linear model with additive Gaussian noise is considered. First, Babai’s nearest plane method is extended to a more general estimation method in order to give a better estimator, and its computational cost is analyzed. Then, lower and upper bounds on the success probability of the extended Babai estimator are derived. Based on this theory, a specific (K,L) extended Babai estimation method is proposed, where K and L are two parameters. Numerical results confirm the theoretical findings and show the advantages of the (K,L) extended Babai method over an existing one.

Distributed sparse normal means estimation with sublinear communication

Abstract We consider the problem of sparse normal means estimation in a distributed setting with communication constraints. We assume there are $M$ machines, each holding $d$-dimensional observations of a $K$-sparse vector $\boldsymbol \mu $ corrupted by additive Gaussian noise. The $M$ machines are connected in a star topology to a fusion center, whose goal is to estimate the vector $\boldsymbol \mu $ with a low communication budget. Previous works have shown that to achieve the centralized minimax rate for the $\ell _2$ risk, the total communication must be high—at least linear in the dimension $d$. This phenomenon occurs, however, at very weak signals. We show that at signal-to-noise ratios (SNRs) that are sufficiently high—but not enough for recovery by any individual machine—the support of $\boldsymbol \mu $ can be correctly recovered with significantly less communication. Specifically, we present two algorithms for distributed estimation of a sparse mean vector corrupted by either Gaussian or sub-Gaussian noise. We then prove that above certain SNR thresholds, with high probability, these algorithms recover the correct support with total communication that is sublinear in the dimension $d$. Furthermore, the communication decreases exponentially as a function of signal strength. If in addition $KM\ll \tfrac{d}{\log d}$, then with an additional round of sublinear communication, our algorithms achieve the centralized rate for the $\ell _2$ risk. Finally, we present simulations that illustrate the performance of our algorithms in different parameter regimes.

How separable median filters can get better results than full 2D versions

The well-known method of median filtering is used both in a wide range of application frameworks and as a standalone filter. Small-window median filters can highly reduce the power of salt and pepper or additive Gaussian noise and minimize edge blurring. Large-window filters are also used, for example to estimate the background of images. Currently, the window size should not be an issue as a constant time algorithm and several implementations, including GPU-based codes, have been proposed in recent years. Unfortunately, none of these constant time implementations manage to fully exploit the capabilities of modern GPUs, and thus the throughputs of large-window median filters remain far below the peak throughputs allowed by recent GPU models. This paper aims at showing that a separable approximation of a 2D median filtering is often stronger than its full 2D implementation. Statistical and theoretical analysis are conducted to show and explain this fact which had so far remained unobserved. It is confirmed by experimentations on a dataset composed of 10,000 images, corrupted by different levels of salt and pepper noise. Separable and full 2D median filter algorithms are compared with several metrics, notably PSNR and MSSIM. In addition, a GPU implementation of 2D separable median filters is also proposed. This implementation is able to output up to 125 billion pixels per second on a recent Volta V100, which significantly outperforms existing implementations like Nvidia’s NPP library or Green’s code, resulting in the fastest median filtering solution to date.

Blind estimation of noise level based on pixels values prediction

Noise parameters estimation is needed for many tasks of digital image processing. Many efficient algorithms of noise variance estimation were proposed during last two decades. However, most of those estimators are efficient only for a specific kind of noise for which they were designed. For example, methods of estimation of variance of white additive Gaussian noise (AWGN) fail in the case of additive colored Gaussian noise (ACGN) or for noises with other distributions. In this paper a new fully blind method of noise level estimation is proposed. For a given image, a distorted image with a removed part of pixels (around 10%) is generated. Then an inpainting (or impulse noise removal) method is used to recover missed pixels values. The difference between true and recovered values is used for a robust estimation of noise level. The algorithm is applied for different image scales to estimate noise spectrum. In the paper we propose a convolutional neural network PIXPNet for effective prediction of values of missing pixels. A comparative analysis shows that the proposed PIXPNet provides smallest error of recovered pixels values among all existing methods. A good efficiency of usage of the proposed approach in both AWGN and spatially correlated noise suppression is demonstrated.

Vertebrae segmentation in reduced radiation CT imaging for augmented reality applications.

There is growing evidence for the use of augmented reality (AR) navigation in spinal surgery to increase surgical accuracy and improve clinical outcomes. Recent research has employed AR techniques to create accurate auto-segmentations, the basis of patient registration, using reduced radiation dose intraoperative computed tomography images. In this study, we aimed to determine if spinal surgery AR applications can employ reduced radiation dose preoperative computed tomography (pCT) images. We methodically decreased the imaging dose, with the addition of Gaussian noise, that was introduced into pCT images to determine the image quality threshold that was required for auto-segmentation. The Gaussian distribution's standard deviation determined noise level, such that a scalar multiplier (L: [0.00, 0.45], with steps of 0.03) simulated lower doses as L increased. We then enhanced the images with denoising algorithms to evaluate the effect on the segmentation. The pCT radiation dose was decreased to below the current lowest clinical threshold and the resulting images produced segmentations that were appropriate for input into AR applications. This held true at simulated dose L = 0.06 (estimated 144 mAs) but not at L = 0.09 (estimated 136 mAs). The application of denoising algorithms to the images resulted in increased artifacts and decreased bone density. The pCT image quality that is required for AR auto-segmentation is lower than that which is currently employed in spinal surgery. We recommend a reduced radiation dose protocol of approximately 140 mAs. This has the potential to reduce the radiation experienced by patients in comparison to procedures without AR support. Future research is required to identify the specific, clinically relevant radiation dose thresholds required for surgical navigation.

NSTBNet: Toward a nonsubsampled shearlet transform for broad convolutional neural network image denoising

Deep convolutional neural networks (CNNs) have achieved huge success in the image denoising fields. However, there still have three drawbacks to be overcome: firstly, it is a big cost to train a deeper CNN model for better denoising performance, secondly, most models often lack the flexibility to remove spatially variant additive Gaussian noise (AWGN), finally, it is difficult to achieve a good trade-off between denoising performance and details preservation. In this paper, we propose a novel network integrated with nonsubsampled shearlet transform (NSST) and a broad convolutional neural network, namely NSTBNet. The proposed NSTBNet has the following desirable properties: (1) a single model has the ability to deal with different noise levels and spatially variant AWGN; (2) the model combines the two networks make it wider to improve denoising performance without increasing too much computational cost; (3) the NSST and inverse NSST are employed to acquire more texture and to avoid gridding effect. Extensive simulation experiments on AWGN and realistic noise show that NSTBNet has state-of-the-art denoising performance, making it a high application value.

Error Analysis for Repeatability Enhancement of a Dual-Rotation Mueller Matrix Ellipsometer

Since the Mueller matrix ellipsometer has been used as a highly accurate tool for thin film measurement, the error analysis and repeatability enhancement of such a tool are of great importance. The existence of the Poisson–Gaussian mixed noise and the random bias of the trigger signal in the optical measurement system may reduce the repeatability and accuracy of a measurement. Utilizing the probabilistic analysis, the random errors in the Mueller matrix measurements are quantified. A quantitative analysis on the instrument matrix has been carried out to assess the individual effects for different error sources. We proposed a general optimal instrument matrix which is capable of minimizing the estimation variance for both Gaussian additive noise and Poisson shot noise. Besides, a peak-matching algorithm is proposed to compress the repeatability errors due to the bias of the trigger signal and the limited sampling frequency. The effectiveness of the proposed methods is shown using both virtual simulations and experiments carried out on our self-developed instrument, which potentially paves a way to reduce the requirements on motor performance, acquisition card resolution, and trigger accuracy, which are critical to cost reduction.

Distinguishing Between Natural and GAN-Generated Face Images by Combining Global and Local Features

With the development of face image synthesis and generation technology based on generative adversarial networks (GANs), it has become a research hotspot to determine whether a given face image is natural or generated. However, the generalization capability of the existing algorithms is still to be improved. Therefore, this paper proposes a general algorithm. To do so, firstly, the learning on important local areas, containing many face key-points, is strengthened by combining the global and local features. Secondly, metric learning based on the ArcFace loss is applied to extract common and discriminative features. Finally, the extracted features are fed into the classification module to detect GAN-generated faces. The experiments are conducted on two publicly available natural datasets (CelebA and FFHQ) and seven GAN-generated datasets. Experimental results demonstrate that the proposed algorithm achieves a better generalization performance with an average detection accuracy over 0.99 than the state-of-the-art algorithms. Moreover, the proposed algorithm is robust against additional attacks, such as Gaussian blur, and Gaussian noise addition.

Differential Entropy of the Conditional Expectation Under Additive Gaussian Noise

The conditional mean is a fundamental and important quantity whose applications include the theories of estimation and rate-distortion. It is also notoriously difficult to work with. This paper establishes novel bounds on the differential entropy of the conditional mean in the case of finite-variance input signals and additive Gaussian noise. The main result is a new lower bound in terms of the differential entropies of the input signal and the noisy observation. The main results are also extended to the vector Gaussian channel and to the natural exponential family. Various other properties such as upper bounds, asymptotics, Taylor series expansion, and connection to Fisher Information are obtained. Two applications of the lower bound in the remote-source coding and CEO problem are discussed.

A Comparison Between Various Human Detectors and CNN-Based Feature Extractors for Human Activity Recognition via Aerial Captured Video Sequences

Human detection and activity recognition (HDAR) in videos plays an important role in various real-life applications. Recently, object detection methods such as “you only look once” (YOLO), faster region based convolutional neural network (R-CNN), and EfficientDet have been used to detect humans in videos for subsequent decision-making applications. This paper aims to address the problem of human detection in aerial captured video sequences using a moving camera attached to an aerial platform with dynamical events such as varied altitudes, illumination changes, camera jitter, and variations in viewpoints, object sizes and colors. Unlike traditional datasets that have frames captured by a static ground camera with medium or large regions of humans in these frames, the UCF-ARG aerial dataset is more challenging because it contains videos with large distances between the humans in the frames and the camera. The performance of human detection methods that have been described in the literature are often degraded when input video frames are distorted by noise, blur, illumination changes, and the like. To address these limitations, the object detection methods used in this study were trained on the COCO dataset and evaluated on the publicly available UCF-ARG dataset. The comparison between these detectors was done in terms of detection accuracy. The performance evaluation considers five human actions (digging, waving, throwing, walking, and running). Experimental results demonstrated that EfficientDetD7 was able to outperform other detectors with 92.9% average accuracy in detecting all activities and various conditions including blurring, addition of Gaussian noise, lightening, and darkening. Additionally, deep pre-trained convolutional neural networks (CNNs) such as ResNet and EfficientNet were used to transfer learning from the ImageNet dataset to the UCF-ARG dataset and to extract highly informative features from the detected and cropped human patches. The extracted spatial features were utilized by Long Short-Term Memory (LSTM) to consider temporal relations between features for human activity recognition (HAR). Experimental results found that the EfficientNetB7-LSTM was able to outperform existing HAR methods in terms of average accuracy (80%), average precision (83%), average recall (80%), average F1 score (80%), average false negative rate (FNR) (20%), average false positive rate (FPR) (4.8%), and average Area Under Curve (AUC) (94%). The outcome is a robust HAR system which combines EfficientDetD7, and EfficientNetB7 with LSTM for human detection and activity classification, respectively.

Hyperspectral Image Denoising via Low-Rank Representation and CNN Denoiser

Hyperspectral images (HSIs) are widely used in various tasks such as earth observation and target detection. However, during the imaging process, HSIs are often corrupted by various noises. In this article, we firstly investigate the advantages of traditional physical restoration models and the denoising convolutional neural networks (CNN) for HSIs denoising tasks. The sparse based low-rank representation can explore the global correlations in both the spatial and spectral domains, and the CNN-based denoiser can represent the deep prior which cannot be designed by traditional restoration models. Then, we propose a HSI denoising model with low-rank representation and CNN denoiser prior in the flexible and extensible plug-and-play framework by combining the advantages of the two methods. The proposed model is user-friendly, requiring no retraining. Simulated data experiments show that, compared with competitive methods, the proposed one achieves better denoising results for both additive Gaussian noise and Poissonian noise in various quantitative evaluation indicators. Real data experiments show that the proposed model yields the best performance.

Gaussian invariant measures and stationary solutions of 2D primitive equations

<p style='text-indent:20px;'>We introduce a Gaussian measure formally preserved by the 2-dimensional Primitive Equations driven by additive Gaussian noise. Under such measure the stochastic equations under consideration are singular: we propose a solution theory based on the techniques developed by Gubinelli and Jara in [<xref ref-type="bibr" rid="b15">15</xref>] for a hyperviscous version of the equations.</p>

Probabilistic Simplex Component Analysis

This study presents PRISM, a probabilistic simplex component analysis approach to identifying the vertices of a data-circumscribing simplex from data. The problem has a rich variety of applications, the most notable being hyperspectral unmixing in remote sensing and non-negative matrix factorization in machine learning. PRISM uses a simple probabilistic model, namely, uniform simplex data distribution and additive Gaussian noise, and it carries out inference by maximum likelihood. The inference model is sound in the sense that the vertices are provably identifiable under some assumptions, and it suggests that PRISM can be effective in combating noise when the number of data points is large. PRISM has strong, but hidden, relationships with simplex volume minimization, a powerful geometric approach for the same problem. We study these fundamental aspects, and we also consider algorithmic schemes based on importance sampling and variational inference. In particular, the variational inference scheme is shown to resemble a matrix factorization problem with a special regularizer, which draws an interesting connection to the matrix factorization approach. Numerical results are provided to demonstrate the potential of PRISM.

Coded Modulation and Shaping for Multivalued Physical Unclonable Functions

In this paper, a coded modulation scheme employing signal shaping is proposed and designed for use in multi-valued physical unclonable functions (PUFs). In the literature, usually binary PUFs are considered, where less than one bit of entropy is extracted from each fundamental building block (PUF node). This randomness in the hardware may then used for the derivation of cryptographic keys. Meanwhile, PUFs over higher-order alphabets, so-called multi-valued PUFs (MVPUFs) have been presented. Typically, symbols from a higher-order alphabet are extracted by suited quantization. In contrast, in this paper we propose a coded modulation scheme which directly works on the analog values provided by the PUF nodes. We establish an interpretation as digital transmission with randomness at the transmitter, and thereon calculate the respective capacities of bit levels for the Gaussian distributed reference PUF readout in additive Gaussian noise. In addition, the metric for optimum soft-decision decoding is derived. Thereby, the coded modulation scheme can be designed for the present situation. A helper data scheme adapted to the given situation is proposed and analyzed. Moreover, on top of the multilevel coding scheme, we employ signal shaping for the first time in the context of PUFs. In particular, trellis shaping is applied. By this, the coded modulation scheme can be perfectly matched to the PUF statistics. This is reflected by the results of conducted numerical simulations. High coding rates can be used, i.e., a large entropy per PUF node can be extracted, with very high reliabilities.

An Asymptotically MSE-Optimal Estimator Based on Gaussian Mixture Models

This paper investigates a channel estimator based on Gaussian mixture models (GMMs) in the context of linear inverse problems with additive Gaussian noise. We fit a GMM to given channel samples to obtain an analytic probability density function (PDF) which approximates the true channel PDF. Then, a conditional mean estimator (CME) corresponding to this approximating PDF is computed in closed form and used as an approximation of the optimal CME based on the true channel PDF. This optimal CME cannot be calculated analytically because the true channel PDF is generally unknown. We present mild conditions which allow us to prove the convergence of the GMM-based CME to the optimal CME as the number of GMM components is increased. Additionally, we investigate the estimator's computational complexity and present simplifications based on common model-based insights. Further, we study the estimator's behavior in numerical experiments including multiple-input multiple-output (MIMO) and wideband systems.

Automatic Detection and Tracking of Random Frequency Signals Using Magnitude and Phase Information

This paper presents an approach to the problems of detection and frequency estimation of a frequency modulated narrow-band signal in additive complex Gaussian noise. The signal is assumed to have an unknown amplitude, initial phase and frequency trajectory over time, while a <i>priori</i> information regarding random frequency variability is taken to be available. The proposed approach operates in the frequency domain and uses the magnitude and phase of the discrete-time Fourier transforms computed over nonoverlapping signal segments. Robustness at low signal-to-noise ratios is achieved by suppressing the segment-related likelihoods for which the phase estimation error is large. The approach utilises unthresholded transform data and thus works in a track-before-detect manner, and the frequency trajectory is estimated by applying a search over the frequency-time bins. The results of a simulation study involving two signal types with different frequency variability are described.

Simulation of the influence of negative internal factors on performance indicators of the synchronization system of a coherent demodulator of satellite telecommunications in permanent and transient modes of carrier frequency estimation

The subject of study in the article is the system of phase synchronization of radio technical devices of communication technology. The purpose of the article is theoretical research in the direction of development, analysis and improvement of known and synthesis of new phase synchronization schemes, which are characterized by high interference resistance, accuracy and speed of operation with a simple design. The problem to be solved is to investigate the possibilities of closed and combined synchronization systems in terms of operation in conditions of internal noise and disturbances against the background of external additive Gaussian noise and Doppler frequency shift. The article presents a model that allows you to investigate the influence of negative internal factors on the performance indicators of the synchronization system of the coherent demodulator of satellite telecommunications in stable and transient modes of carrier frequency estimation. With its help, the article analyzes closed-type synchronization systems when operating under the influence of negative internal factors and shows its inconsistency in minimizing the dispersion of the phase error and increasing the dynamics during tracking of the carrier frequency. The process of synthesis of open communication in the combined synchronization system has been clarified and analytical dependencies have been proposed, which allow to clarify the methodology of synthesis of open communication for the combined synchronization system, taking into account the influence of internal negative factors. It was established that under the influence of negative internal factors for the combined synchronization system, by selecting the parameters of the proportionalintegrating filter, it is possible to achieve an expansion of the noise bandwidth of the input signal and thereby ensure the necessary dynamics of the system and achieve the preservation of the optimal value of the dispersion of the phase error in it.

An Approach for Power Quantification Based on Stockwell Transform and CPC Power Theory

This article presents a power calculation method for non-sinusoidal signals with non-stationary characteristics based on currents’ physical components (CPC) power theory and the discrete Stockwell transform (DST). The DST independently localizes the real and imaginary components of the spectrum at any given time interval, being suitable for analyzing non-stationary waveforms. The proposed method allows for an instantaneous tracking of the power components defined in CPC power theory based on a time–frequency analysis provided by the DST. Thus, the proposed method is able to identify alterations in the harmonic content, and consequently track variations on the powers, in all time instants. The proposed method is validated using non-stationary signals, including a scenario with frequency deviation, presenting rather promising results when compared to the Fourier-based approach. Additionally, the proposed method is also assessed in noisy environments by inserting an additive Gaussian noise, based on real oscillographic records, presenting a good performance, which attests its suitability for power quality (PQ) analysis and power calculation.

Evaluation of Noise Distributions for Additive and Multiplicative Smart Meter Data Obfuscation

In this paper, we compare and analyze light-weight approaches for instantaneous smart meter (SM) data obfuscation from a group of consumers. In the literature, the common approach is to use additive Gaussian noise based SM data obfuscation. In order to investigate the effects of different approaches, we consider Gaussian, Rayleigh, generalized Gaussian and chi-square distributions to achieve either additive or multiplicative data obfuscation. For each type of obfuscation approach, we calculate the required parameters to achieve obfuscation such that 50&#x0025; of the obfuscated data fall outside an interval equalling twice the mean of the instantaneous SM measurements. We also calculate the minimum number of SMs required to estimate the mean of the actual SM measurements, such that the estimate varies within only 0.5&#x0025; of the actual mean with a 99.5&#x0025; probability. Simulation results are used to verify the calculations, and it is shown that multiplicative Rayleigh and generalized Gaussian noise require the least number of SMs, which is 90&#x0025; less than the traditional approach of additive Gaussian noise-based SM data obfuscation.

Estimating Quantum and Private Capacities of Gaussian Channels via Degradable Extensions.

We present upper bounds on the quantum and private capacity of single-mode, phase-insensitive bosonic Gaussian channels based on degradable extensions. Our findings are state of the art in the following parameter regions: low temperature and high transmissivity for the thermal attenuator, low temperature for additive Gaussian noise, high temperature and intermediate amplification for the thermal amplifier.