MAP Estimation of Piecewise Constant Digital Signals

This research presents a development of the affine projection algorithm (APA) in voice communication applications. A method of controlling the parameters of the APA is devised to improve the performance in cancelling various types of ambient noise that could possibly corrupt speech signals in voice communication systems. Indicators are used to identify the type of noise accompanying the target signal. Then the corrupted signal is processed in a noise a cancellation setup in such a way that three parameters of algorithm are changed according to the nature of the noise. The spreading of elements in the covariance matrix of the noise is used as an indicator for the type of noise so that the projection order, step-size and filter length are changed at the same time. This way the performance of the canceller is improved rendering lower estimation error with a moderate computational power. The method was tested under various types of noise and showed better convergence performance than the original APA as well as other commonly used algorithms in noise cancellation systems. The MSE of the proposed VPAPA method drops to -65 dB in steady state compared to -20 dB using NLMS and just below -30 dB using standard APA with projection order of 8, while the powerful RLS reaches around -60dB under the same environment. The method can be useful for clearer voice communication in variable environmental noise.

A critical challenge in image restoration is the presence of various types of noise. Meanwhile, noise detection is a crucial step in mixed noise removal. This paper tackles the challenge of restoring images corrupted by a mixture of additive Gaussian and multiplicative Gamma noise. In the proposed method, we integrate the noise detection process into a variational model using a dual formulation of a maximum a posteriori (MAP) estimator. The variational model consists of a novel adaptive fidelity term and a plugin-and-play regularization term. The fidelity term contains an adaptive weight that can automatically detect the noise types, levels, and pollution ways for each pixel. There is flexibility in choosing a plugin-and-play regularization term. For example, we can use a model-based regularizer or a deep learning-based regularizer. In addition, we present a splitting algorithm to minimize the proposed cost functional. This splitting technique enables us to transfer a mixed noise removing problem to several subproblems, including noise removal and detection. The noise detection process can be iteratively estimated by the proposed algorithm itself. Therefore, in the numerical experiments, the proposed model outperforms the existing Rudin-Osher-Fatemi (ROF), Aubert-Aujol (AA), BM3D, and deep learning-based single type denoiser. Experimental results show that the proposed model can remove noise more efficiently and better preserve details in images. Compared to the existing best-performing single type denoiser, on average, the improvements of PSNR values range from 0.33 dB to 0.81 dB under noise mixture ratios α = 0.4, 0.6.

The contribution of type and levels of community noises to the perception of loudness, noisiness, and annoyance is being explored in ongoing research projects. Particular attention has been given to the relationship between scaling method and the conclusions it is possible to draw from the data, especially with regard to observers' abilities to differentiate noises according to the above attributes. Procedures for calibrating and possibly standardizing the perceptual scales have been attempted with preliminary success. Various types of noises have been investigated: aircraft noise under different flying conditions, traffic noise, and a number of other community noises. Besides specific scaling problems, the investigations have addressed the specific problems of observers' abilities to differentiate among noises that are combined in a complex setting as well as their ability to integrate various noises into a unitary perception of loudness and annoyance. Since the experimental setups reflect real‐life situations, the answers to these latter questions are relevant to understanding the responses of the individual who is exposed to combinations of noises in his or her community.The contribution of type and levels of community noises to the perception of loudness, noisiness, and annoyance is being explored in ongoing research projects. Particular attention has been given to the relationship between scaling method and the conclusions it is possible to draw from the data, especially with regard to observers' abilities to differentiate noises according to the above attributes. Procedures for calibrating and possibly standardizing the perceptual scales have been attempted with preliminary success. Various types of noises have been investigated: aircraft noise under different flying conditions, traffic noise, and a number of other community noises. Besides specific scaling problems, the investigations have addressed the specific problems of observers' abilities to differentiate among noises that are combined in a complex setting as well as their ability to integrate various noises into a unitary perception of loudness and annoyance. Since the experimental setups reflect real‐life situ...

Nowadays, voice interaction is increasingly applied to smart home appliances. There are various types of noises in our real lives, which requires speech enhancement technology to deal with multiple noisy speech scenarios and to process them in real-time. Traditional technologies of speech noise reduction require estimating the noise power spectrum first, then estimating the spectrogram gain value of noise reduction, such as minima controlled recursive averaging (MCRA), which can only deal with stationary environmental noises but cannot estimate noises with serious fluctuations of the power spectrum within quite limited durations. A highly complicated deep-learning model can estimate the power spectrum of various types of noise, but it cannot meet the requirement of real-time processing due to the large number of parameters of these general models. In this paper, we proposed a method combining deep-learning technologies with traditional signal processing techniques to estimate the power spectrum of various types of noises by designing a new model with fewer parameters, tiny deep convolutional recurrent network (TDCRN), and computing the speech gain value with the power spectrum. The result of our experiment indicates that, compared with the traditional technology and complicated deep-learning model, the proposed method, with only 0.29M parameters, increases the PESQ by more than 0.6, the STOI by more than 0.2 and the wake-up rate by more than 6%.

The article investigates the influence of stochastic interference of various natures on the parametric stability of radio signals. It is established that each type of noise has a different effect on the metrological characteristics of the signal - amplitude, frequency, phase and waveform. In particular, the most significant effect on the signal parameters is exerted by brown noise and Gaussian noise, which are characterized by a complex structure of spectral density and high intensity in certain frequency ranges. While uniform, blue and violet noise have a minimal effect on the main metrological parameters, which opens up opportunities for their use as background or compensating components in data transmission systems. The practical value of the results obtained lies in the possibility of adapting digital signal processing algorithms to the conditions of the presence of various types of noise, which is especially important for telecommunication systems operating in difficult radio-electronic conditions. The application of approaches to the assessment and compensation of the impact of noise allows to increase the accuracy of measurements, reduce errors in the transmission of information, and also to improve the means of protecting signals from interference of natural and artificial origin.In the future, further research may be aimed at the development of adaptive filters and noise suppression algorithms taking into account the type of interference, as well as the use of machine learning methods for classifying signals by type of interference. In addition, it is advisable to study the combined effect of several types of noise simultaneously, as well as the influence of nonlinear properties of radio channels on the effectiveness of metrological control of signal parameters. In general, the results of the work contribute to the development of scientific approaches to modeling and analyzing signals in stochastic conditions, which is important for improving technologies in such areas as digital television, mobile communications, satellite communications, navigation systems and radar.

This paper investigates the influence of the signal to noise ratio (SNR) and the type of a noise on the performance of two adaptive novelty detection methods. The evaluated methods are Learning Entropy (LE) and Error and Learning Based Novelty Detection (ELBND). The methods are compared in empirical way in classification framework. A classification based only on the error of the adaptive model was used as a reference. The research in this field is important, because a noise is present in every measured data and can drastically influence the result of tasks like the novelty detection. Moreover, various types of noise can influence the novelty detection in different ways, therefore the optimal method of adaptive novelty detection can be hard to choose. This assumption is supported by experimental results in this study.

A Bayesian estimation approach for enhancing speech signals which have been degraded by statistically independent additive noise is motivated and developed. In particular, minimum mean square error (MMSE) and maximum a posteriori (MAP) signal estimators are developed using hidden Markov models (HMMs) for the clean signal and the noise process. It is shown that the MMSE estimator comprises a weighted sum of conditional mean estimators for the composite states of the noisy signal, where the weights equal the posterior probabilities of the composite states given the noisy signal. The estimation of several spectral functionals of the clean signal such as the sample spectrum and the complex exponential of the phase is also considered. A gain-adapted MAP estimator is developed using the expectation-maximization algorithm. The theoretical performance of the MMSE estimator is discussed, and convergence of the MAP estimator is proved. Both the MMSE and MAP estimators are tested in enhancing speech signals degraded by white Gaussian noise at input signal-to-noise ratios of from 5 to 20 dB. >

Electrocardiogram (ECG) signals are crucial for monitoring cardiac activity and diagnosing various cardiovascular conditions. However, these signals are often contaminated by different types of noise, such as baseline wander, muscle artifacts, and power line interference, which can obscure critical information and hinder accurate diagnosis. This study used a 1-Dimensional Convolutional Neural Network (1D CNN) architecture with seven convolutional layers for denoising ECG signals. The model utilizes a fully convolutional autoencoder approach, comprising an encoder that transforms noisy input signals into compact feature representations and a decoder that reconstructs the cleaned signals. The proposed architecture was tested using the MIT-BIH Noise Stress Test Database, which includes ECG recordings with simulated noise conditions. Performance evaluation metrics such as Mean Squared Error (MSE), Signal-to-Noise Ratio (SNR), and Mean Absolute Deviation (MAD) were used to assess the model's effectiveness. Results showed a low MSE of 0.034, a high SNR of 15.8 dB, and a MAD of 0.754, indicating significant noise reduction and high-quality signal reconstruction. These findings demonstrate that the 1D CNN architecture effectively reduces various types of noise in ECG signals, thereby enhancing signal quality and facilitating more accurate analysis and diagnosis. The model's ability to maintain the integrity of crucial ECG features while removing noise suggests its potential utility in clinical applications for improving cardiovascular disease diagnosis

Noise estimation and suppression is very important for improving the quality of speech signal. Noises exist in almost all places. In reality, more than one noise degrades the speech signal. It is hard to find and supress various types of noise that affect the speech quality. This paper proposed a method for noise estimation of mixed non-stationary noisy speech signal. This method uses Spectral properties of the noisy speech signal to detect the frequency regions of noise signal. Highest frequency of speech signal is calculated and it is considered as the threshold value for separating noise signal and clean speech signal. Using Spectral subtraction, Standard deviation of noise spectrum is subtracted with noisy spectrum to acquire enhanced speech signal. Performance of the method is evaluated using SNR and Spectrogram. The main focus of this paper is to propose an independent method which estimates the noise of any type and nature.

The strength and shape of the dose-response relationship between different types of noise and myocardial infarction (MI) remain unclear. Therefore, we aimed to summarize the evidence of the association between various types of noise and MI incidence and mortality through a dose-response meta-analysis. We performed a systematic search of the PubMed, Embase, and Web of Science databases up to December 19, 2021. The generalized least-squares method and restricted cubic splines were used to assess the potential linear and nonlinear dose-response relationships between noise exposure and the risk of MI events. Twenty observational studies with 34 reports met the eligibility criteria. In the linear models, the pooled relative risk and corresponding 95% confidence interval (CI) for MI incidence was 1.04 (95% CI: 1.02 - 1.05), and the MI mortality was 1.02 (95% CI: 1.02 - 1.03) for each 10dB(A) increase in noise exposure. In addition, we observed an approximately J-shaped dose-response relationship between noise and MI mortality (Pnonlinearity = 0.0037), whereas the threshold for the statistical impact of noise on MI mortality may be 42dB(A). Our findings support the notion that various types of noise exposure have a positive dose-response relationship with the risk of MI incidence and mortality.

Digital image quality is crucial for reliable analysis in applications such as medical imaging, satellite remote sensing, and video surveillance. However, traditional denoising methods struggle to balance noise removal with detail preservation and lack adaptability to various types of noise. We propose a novel three-module architecture for image denoising, comprising a generator, a dual-path-UNet-based denoiser, and a discriminator. The generator creates synthetic noise patterns to augment training data, while the dual-path-UNet denoiser uses multiple receptive field modules to preserve fine details and dense feature fusion to maintain global structural integrity. The discriminator provides adversarial feedback to enhance denoising performance. This dual-path adversarial training mechanism addresses the limitations of traditional methods by simultaneously capturing both local details and global structures. Experiments on the SIDD, DND, and PolyU datasets demonstrate superior performance. We compare our architecture with the latest state-of-the-art GAN variants through comprehensive qualitative and quantitative evaluations. These results confirm the effectiveness of noise removal with minimal loss of critical image details. The proposed architecture enhances image denoising capabilities in complex noise scenarios, providing a robust solution for applications that require high image fidelity. By enhancing adaptability to various types of noise while maintaining structural integrity, this method provides a versatile tool for image processing tasks that require preserving detail.

An ECG denoising technique based on AHIN block and gradient difference max loss

Low-rank matrix factorizations such as Principal Component Analysis (PCA), Singular Value Decomposition (SVD) and Non-negative Matrix Factorization (NMF) are a large class of methods for pursuing the low-rank approximation of a given data matrix. The conventional factorization models are based on the assumption that the data matrices are contaminated stochastically by some type of noise. Thus the point estimations of low-rank components can be obtained by Maximum Likelihood (ML) estimation or Maximum a posteriori (MAP). In the past decade, a variety of probabilistic models of low-rank matrix factorizations have emerged. The most significant difference between low-rank matrix factorizations and their corresponding probabilistic models is that the latter treat the low-rank components as random variables. This paper makes a survey of the probabilistic models of low-rank matrix factorizations. Firstly, we review some probability distributions commonly-used in probabilistic models of low-rank matrix factorizations and introduce the conjugate priors of some probability distributions to simplify the Bayesian inference. Then we provide two main inference methods for probabilistic low-rank matrix factorizations, i.e., Gibbs sampling and variational Bayesian inference. Next, we classify roughly the important probabilistic models of low-rank matrix factorizations into several categories and review them respectively. The categories are performed via different matrix factorizations formulations, which mainly include PCA, matrix factorizations, robust PCA, NMF and tensor factorizations. Finally, we discuss the research issues needed to be studied in the future.

Lévy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Lévy process admits exponential moments, then there exists a parametric family of measure changes called Esscher transformations. If the parameter is replaced with an independent random variable, the true value of which represents a ‘message’, then under the transformed measure the original Lévy process takes on the character of an ‘information process’. In this paper we develop a theory of such Lévy information processes. The underlying Lévy process, which we call the fiducial process, represents the ‘noise type’. Each such noise type is capable of carrying a message of a certain specification. A number of examples are worked out in detail, including information processes of the Brownian, Poisson, gamma, variance gamma, negative binomial, inverse Gaussian and normal inverse Gaussian type. Although in general there is no additive decomposition of information into signal and noise, one is led nevertheless for each noise type to a well-defined scheme for signal detection and enhancement relevant to a variety of practical situations.

After studying this chapter, you should be able to: Understand the various types of noise that appear in seismic images and volumes. Simulate some commonly used type of noise. Estimate noise parameters.