Noise power estimation is a key issue in modern wireless communication systems. It allows resource allocation by detecting white spectral spaces effectively, and gives control over the communication process by adjusting transmission power. Thus far, the proposed estimation methods in the literature are based on spectral averaging, eigenvalues of sample covariance matrix, information theory, and statistical signal analysis. Each method is characterized by certain stability, accuracy and complexity. However, the existing literature does not provide an appropriate comparison. In this paper, we evaluate the performance of the existing estimation techniques intensively in terms of stability and accuracy, followed by detailed complexity analysis. The basis for comparison is signal-to-noise ratio (SNR) estimation in simulated industrial, scientific and medical (ISM) band transmission. The source of used background distortions is complex noise measurement, recorded by USRP-2932 in an industrial production area. Based on the examined solutions, we also analyze the influence of noise samples separation techniques on the estimation process. As a response to the defects in the used methods, we propose a novel noise samples separation algorithm based on the adaptation of rank order filtering (ROF). In addition to simple implementation, the proposed method has a very good 0.5 dB root-mean-squared error (RMSE) and smaller than 0.1 dB resolution, thus achieving a performance that is comparable with the methods exploiting information theory concepts.
Modern researchers have proposed a number of approaches for estimating noise power, based on various properties. Most often referred to in the literature are maximum likelihood (ML) and minimum variance unbiased (MVU) estimators @cite_14 @cite_2 @cite_0 @cite_7 @cite_21 . Both ML and MVU estimators are based on the principle of power spectrum averaging. However, the range of proposed solutions is much wider and includes, for instance, information theoretic methods as Akaike Information Criteria @cite_16 @cite_8 and correlation-based methods e.g., covariance based estimator @cite_18 @cite_24 . More specialized solutions, for example based on statistical relations, can also be found as in minimum mean squared error (MMSE) estimator @cite_17 . All of these methods, although dedicated for similar applications, differ significantly in terms of accuracy, stability and complexity.
@cite_18 @cite_14 @cite_7 @cite_8 @cite_21 @cite_0 @cite_24 @cite_2 @cite_16 @cite_17
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In this paper, a new object-based method to estimate noise in magnitude MR images is proposed. The main advantage of this object-based method is its robustness to background artefacts such as ghosting. The proposed method is based on the adaptation of the Median Absolute Deviation (MAD) estimator in the wavelet domain for Rician noise. The MAD is a robust and efficient estimator initially proposed to estimate Gaussian noise. In this work, the adaptation of MAD operator for Rician noise is performed by using only the wavelet coefficients corresponding to the object and by correcting the estimation with an iterative scheme based on the SNR of the image. During the evaluation, a comparison of the proposed method with several state-of-the-art methods is performed. A quantitative validation on synthetic phantom with and without artefacts is presented. A new validation framework is proposed to perform quantitative validation on real data. The impact of the accuracy of noise estimation on the performance of a denoising filter is also studied. The results obtained on synthetic images show the accuracy and the robustness of the proposed method. Within the validation on real data, the proposed method obtained very competitive results compared to the methods under study. This paper proposes a minimum mean-square error (MMSE) filtering technique to estimate the noise power that takes into account the variation of the noise statistics across the orthogonal frequency division multiplexing (OFDM) sub-carrier index as well as across OFDM symbols. The proposed method provides many local estimates that allow tracking of the variation of the noise statistics in frequency and time. The MMSE filter coefficients are obtained from the mean-squared-error (MSE) expression, which can be calculated using the noise statistics. Evaluation of the performance with computer simulations shows that the proposed method tracks the local statistics of the noise more efficiently than conventional methods. In continuation to a recent work on the statistical-mechanical analysis of minimum mean square error (MMSE) estimation in Gaussian noise via its relation to the mutual information (the I-MMSE relation), here we propose a simple and more direct relationship between optimum estimation and certain information measures (e.g., the information density and the Fisher information), which can be viewed as partition functions and hence are amenable to analysis using statistical-mechanical techniques. The proposed approach has several advantages, most notably, its applicability to general sources and channels, as opposed to the I-MMSE relation and its variants which hold only for certain classes of channels (e.g., additive white Gaussian noise channels). We then demonstrate the derivation of the conditional mean estimator and the MMSE in a few examples. Two of these examples turn out to be generalizable to a fairly wide class of sources and channels. For this class, the proposed approach is shown to yield an approximate conditional mean estimator and an MMSE formula that has the flavor of a single-letter expression. We also show how our approach can easily be generalized to situations of mismatched estimation. In this paper, we present an optimally-modi#ed log-spectral amplitude (OM-LSA) speech estimator and a minima controlled recursive averaging (MCRA) noise estimation approach for robust speech enhancement. The spectral gain function, which minimizes the mean-square error of the log-spectra, is obtained as a weighted geometric mean of the hypothetical gains associated with the speech presence uncertainty. The noise estimate is given by averaging past spectral power values, using a smoothing parameter that is adjusted bythe speech presence probabilityin subbands. We introduce two distinct speech presence probabilityfunctions, one for estimating the speech and one for controlling the adaptation of the noise spectrum. The former is based on the time–frequencydistribution of the a priori signal-to-noise ratio. The latter is determined bythe ratio between the local energyof the noisysignal and its minimum within a speci6ed time window. Objective and subjective evaluation under various environmental conditions con6rm the superiorityof the OM-LSA and MCRA estimators. Excellent noise suppression is achieved, while retaining weak speech components and avoiding the musical residual noise phenomena. ? 2001 Elsevier Science B.V. All rights reserved.