SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling

Synthetic aperture radar (SAR) images are inherently affected by multiplicative speckle noise, which is due to the coherent nature of the scattering phenomenon. This paper proposes a novel Bayesian-based algorithm within the framework of wavelet analysis, which reduces speckle in SAR images while preserving the structural features and textural information of the scene. First, we show that the subband decompositions of logarithmically transformed SAR images are accurately modeled by alpha-stable distributions, a family of heavy-tailed densities. Consequently, we exploit this a priori information by designing a maximum a posteriori (MAP) estimator. We use the alpha-stable model to develop a blind speckle-suppression processor that performs a nonlinear operation on the data and we relate this nonlinearity to the degree of non-Gaussianity of the data. Finally, we compare our proposed method to current state-of-the-art soft thresholding techniques applied on real SAR imagery and we quantify the achieved performance improvement.     

Scalar quantisation of heavy-tailed signals

Efficient stochastic data processing presupposes proper modelling of the statistics of the data source. The authors address the issues that arise when the data to be processed exhibits statistical properties which depart significantly from those implied under the Gaussianity assumption. First, they present a study on the modelling of coefficient data obtained when applying the wavelet transform (WT) to images. They show that WT coefficients are heavy-tailed and can be modelled with alpha-stable distributions. Then, they introduce an alternative to the common mean-square error (MSE) quantiser for the efficient, scalar quantisation of heavy-tailed data by means of distortion minimisation. The proposed quantiser is based on a particular member of the family of alpha-stable distributions, namely the Cauchy distribution, and it employs a distortion measure based on the mean square root absolute value of the quantisation error. Results of the performance of this quantiser when applied to simulated as well as real data are also presented     

Maximum likelihood localization of sources in noise modeled as astable process

This paper introduces a new class of robust beamformers which perform optimally over a wide range of non-Gaussian additive noise environments. The maximum likelihood approach is used to estimate the bearing of multiple sources from a set of snapshots when the additive interference is impulsive in nature. The analysis is based on the assumption that the additive noise can be modeled as a complex symmetric α-stable (SαS) process. Transform-based approximations of the likelihood estimation are used for the general SαS class of distributions while the exact probability density function is used for the Cauchy case. It is shown that the Cauchy beamformer greatly outperforms the Gaussian beamformer in a wide variety of non-Gaussian noise environments, and performs comparably to the Gaussian beamformer when the additive noise is Gaussian. The Cramer-Rao bound for the estimation error variance is derived for the Cauchy case, and the robustness of the SαS beamformers in a wide range of impulsive interference environments is demonstrated via simulation experiments     

Surrounded by sound

The authors discuss immersive audio systems and the signal processing issues that pertain to the acquisition and subsequent rendering of 3D sound fields over loudspeakers. On the acquisition side, recent advances in statistical methods for achieving acoustical arrays in audio applications are reviewed. Classical array signal processing addresses two major aspects of spatial filtering, namely localization of a signal of interest, and adaptation of the spatial response of an array of sensors to achieve steering in a given direction. The achieved spatial focusing in the direction of interest makes array signal processing a necessary component in immersive sound acquisition systems. On the rendering side, 3D audio signal processing methods are described that allow rendering of virtual sources around the listener using only two loudspeakers. Finally, the authors discuss the commercial implications of audio DSP     

Rotation-invariant texture retrieval with Gaussianized steerable pyramids.

This paper presents a novel rotation-invariant image retrieval scheme based on a transformation of the texture information via a steerable pyramid. First, we fit the distribution of the subband coefficients using a joint alpha-stable sub-Gaussian model to capture their non-Gaussian behavior. Then, we apply a normalization process in order to Gaussianize the coefficients. As a result, the feature extraction step consists of estimating the covariances between the normalized pyramid coefficients. The similarity between two distinct texture images is measured by minimizing a rotation-invariant version of the Kullback-Leibler Divergence between their corresponding multivariate Gaussian distributions, where the minimization is performed over a set of rotation angles.     

Hidden messages in heavy-tails: DCT-domain watermark detection using alpha-stable models

This paper addresses issues that arise in copyright protection systems of digital images, which employ blind watermark verification structures in the discrete cosine transform (DCT) domain. First, we observe that statistical distributions with heavy algebraic tails, such as the alpha-stable family, are in many cases more accurate modeling tools for the DCT coefficients of JPEG-analyzed images than families with exponential tails such as the generalized Gaussian. Motivated by our modeling results, we then design a new processor for blind watermark detection using the Cauchy member of the alpha-stable family. The Cauchy distribution is chosen because it is the only non-Gaussian symmetric alpha-stable distribution that exists in closed form and also because it leads to the design of a nearly optimum detector with robust detection performance. We analyze the performance of the new detector in terms of the associated probabilities of detection and false alarm and we compare it to the performance of the generalized Gaussian detector by performing experiments with various test images.     

A Spectral Conversion Approach to Single-Channel Speech Enhancement

In this paper, a novel method for single-channel speech enhancement is proposed, which is based on a spectral conversion feature denoising approach. Spectral conversion has been applied previously in the context of voice conversion, and has been shown to successfully transform spectral features with particular statistical properties into spectral features that best fit (with the constraint of a piecewise linear transformation) different target statistics. This spectral transformation is applied as an initialization step to two well-known single channel enhancement methods, namely the iterative Wiener filter (IWF) and a particular iterative implementation of the Kalman filter. In both cases, spectral conversion is shown here to provide a significant improvement as opposed to initializations using the spectral features directly from the noisy speech. In essence, the proposed approach allows for applying these two algorithms in a user-centric manner, when "clean" speech training data are available from a particular speaker. The extra step of spectral conversion is shown to offer significant advantages regarding output signal-to-noise ratio (SNR) improvement over the conventional initializations, which can reach 2 dB for the IWF and 6 dB for the Kalman filtering algorithm, for low input SNRs and for white and colored noise, respectively     

Alpha-stable modeling of noise and robust time-delay estimation inthe presence of impulsive noise

A new representation of audio noise signals is proposed, based on symmetric α-stable (SαS) distributions in order to better model the outliers that exist in real signals. This representation addresses a shortcoming of the Gaussian model, namely, the fact that it is not well suited for describing signals with impulsive behavior. The α-stable and Gaussian methods are used to model measured noise signals. It is demonstrated that the α-stable distribution, which has heavier tails than the Gaussian distribution, gives a much better approximation to real-world audio signals. The significance of these results is shown by considering the time delay estimation (TDE) problem for source localization in teleimmersion applications. In order to achieve robust sound source localization, a novel time delay estimation approach is proposed. It is based on fractional lower order statistics (FLOS), which mitigate the effects of heavy-tailed noise. An improvement in TDE performance is demonstrated using FLOS that is up to a factor of four better than what can be achieved with second-order statistics     

Novel Bayesian multiscale method for speckle removal in medical ultrasound images

A novel speckle suppression method for medical ultrasound images is presented. First, the logarithmic transform of the original image is analyzed into the multiscale wavelet domain. We show that the subband decompositions of ultrasound images have significantly non-Gaussian statistics that are best described by families of heavy-tailed distributions such as the alpha-stable. Then, we design a Bayesian estimator that exploits these statistics. We use the alpha-stable model to develop a blind noise-removal processor that performs a nonlinear operation on the data. Finally, we compare our technique with current state-of-the-art soft and hard thresholding methods applied on actual ultrasound medical images and we quantify the achieved performance improvement.     

Trend forecasting based on Singular Spectrum Analysis of traffic workload in a large-scale wireless LAN

Network traffic load in an IEEE802.11 infrastructure arises from the superposition of traffic accessed by wireless clients associated with access points (APs). An accurate load characterization can be beneficial in modeling network traffic and addressing a variety of problems including coverage planning, resource reservation and network monitoring for anomaly detection. This study focuses on the statistical analysis of the traffic load measured in a campus-wide IEEE802.11 infrastructure at each AP.Using the Singular Spectrum Analysis approach, we found that the time-series of traffic load at a given AP has a small intrinsic dimension. In particular, these time-series can be accurately modeled using a small number of leading (principal) components. This proved to be critical for understanding the main features of the components forming the network traffic.Statistical analysis of leading components has demonstrated that even a few first components form the main part of the information. The residual components capture the small irregular variations, which do not fit in the basic part of the network traffic and can be interpreted as a stochastic noise. Based on these properties, we also studied contributions of the various components to the overall structure of the traffic load of an AP and its variation over time.Finally, we designed and evaluated the performance of a traffic predictor for the trend component, obtained by projecting the original time-series on the set of leading components.