Gaussian Scale Mixture Model Research Articles

Speech Enhancement Using Gaussian Scale Mixture Models.

This paper presents a novel probabilistic approach to speech enhancement. Instead of a deterministic logarithmic relationship, we assume a probabilistic relationship between the frequency coefficients and the log-spectra. The speech model in the log-spectral domain is a Gaussian mixture model (GMM). The frequency coefficients obey a zero-mean Gaussian whose covariance equals to the exponential of the log-spectra. This results in a Gaussian scale mixture model (GSMM) for the speech signal in the frequency domain, since the log-spectra can be regarded as scaling factors. The probabilistic relation between frequency coefficients and log-spectra allows these to be treated as two random variables, both to be estimated from the noisy signals. Expectation-maximization (EM) was used to train the GSMM and Bayesian inference was used to compute the posterior signal distribution. Because exact inference of this full probabilistic model is computationally intractable, we developed two approaches to enhance the efficiency: the Laplace method and a variational approximation. The proposed methods were applied to enhance speech corrupted by Gaussian noise and speech-shaped noise (SSN). For both approximations, signals reconstructed from the estimated frequency coefficients provided higher signal-to-noise ratio (SNR) and those reconstructed from the estimated log-spectra produced lower word recognition error rate because the log-spectra fit the inputs to the recognizer better. Our algorithms effectively reduced the SSN, which algorithms based on spectral analysis were not able to suppress.

Video Denoising Based on a Spatiotemporal Gaussian Scale Mixture Model

We propose a video denoising algorithm based on a spatiotemporal Gaussian scale mixture model in the wavelet transform domain. This model simultaneously captures the local correlations between the wavelet coefficients of natural video sequences across both space and time. Such correlations are further strengthened with a motion compensation process, for which a Fourier domain noise-robust cross correlation algorithm is proposed for motion estimation. Bayesian least square estimation is used to recover the original video signal from the noisy observation. Experimental results show that the performance of the proposed approach is competitive when compared with state-of-the-art video denoising algorithms based on both peak signal-to-noise-ratio and structural similarity evaluations.

Vonn distribution of relative phase for statistical image modeling in complex wavelet domain

With the assumptions of Gaussian as well as Gaussian scale mixture models for images in wavelet domain, marginal and joint distributions for phases of complex wavelet coefficients are studied in detail. From these hypotheses, we then derive a relative phase probability density function, which is called Vonn distribution, in complex wavelet domain. The maximum-likelihood method is proposed to estimate two Vonn distribution parameters. We demonstrate that the Vonn distribution fits well with behaviors of relative phases from various real images including texture images as well as standard images. The Vonn distribution is compared with other standard circular distributions including von Mises and wrapped Cauchy. The simulation results, in which images are decomposed by various complex wavelet transforms, show that the Vonn distribution is more accurate than other conventional distributions. Moreover, the Vonn model is applied to texture image retrieval application and improves retrieval accuracy.

A New Image Denoising Method Combining the Nonsubsampled Contourlet Transform and Adaptive Total Variation

该文提出了一种新的结合非下采样Contourlet变换(NSCT)和自适应全变差模型的图像去噪方法。首先通过NSCT对含噪图像进行分解，根据高斯比例混合(GSM)模型建立图像模型；然后利用贝叶斯估计进行图像去噪，重构后得到初次去噪图像；最后，结合自适应全变差模型对初次去噪图像进行重构滤波，得到最终的去噪图像。实验结果表明，该方法可以有效地消除图像中的Gibbs伪影及噪声，在去噪图像峰值信噪比(PSNR)和边缘保持性能上都优于已有的算法。

Wavelet-Based EM Algorithm for Multispectral-Image Restoration

In this paper, we present a technique for the restoration of multispectral images. The presented procedure is based on an expectation-maximization (EM) algorithm, which applies iteratively a deconvolution and a denoising step. The restoration is performed in a multispectral way instead of band-by-band. The deconvolution technique is a generalization of the EM-based grayscale-image restoration and allows for the reconstruction of spatial as well as spectral blurring. The denoising step is performed in wavelet domain. To account for interband correlations, a multispectral probability density model for the wavelet coefficients is chosen. Rather than using a multinormal model, we opted for a Gaussian scale mixture model, which is a heavy-tailed model. Also in this paper, the framework is extended to include an auxiliary image of the same scene to improve the restoration. Experiments on Landsat and AVIRIS multispectral remote-sensing images are conducted.

SAR Image Denoising Based on Lifting Directionlet Domain Gaussian Scale Mixtures Model

In this paper,a new speckle suppression method for SAR image is proposed.By combining Directionlet transform with a version of the hidden Markov model—Gaussian scale mixtures(GSM),the marginal distributions of neighbor coefficients in the lifting Directionlet domain are modeled.For removing the speckle noise,the Bayes least square estimation is adopted to evaluate each coefficient.Being regarded as a novel multiscale geometrical analysis tool,Directionlet transform retains the separable filtering,computation simplicity and filter design from the standard two-dimensional wavelet transform,which can capture anisotropic geometrical structures efficiently by multi-direction selection.The introduction of lifting scheme reduces computation amount greatly.Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables:A Gaussian vector and a hidden positive scalar multiplier.Under this model,the marginal of neighbor coefficients are well described and the strong correlation among the amplitudes of neighbor coefficients is also presented adequately.Experiments using plentiful real SAR images indicate that the proposed method outperforms the spatial filters and other methods based on wavelets in terms of speckle reduction as well as image detail preservation.

Security Analysis on Add-SS Watermarking with GSM

Watermarking security has emerged as the domain of extensive research in recent years. Attack to the security of watermarking is to estimate the secret keys used in watermarking communications. The security level of watermarking system can be evaluated by Cramer-Rao bound (CRB) for secret keys estimation. As a widely used method, the security issue of add spread spectrum (Add-SS) based watermarking has drawn great attention. The previous works on watermarking security were mainly based on the assumption that host signal was Gaussian distributed and ignored the impacts of non-Gaussian characteristics of nature images. With incorporation of the Gaussian scale mixture (GSM) model for host signals, this paper presents a theoretical analysis on the security of Add-SS watermarking system. By giving the CRB and MCRB (modified Cramer-Rao bound) for the estimation of secret carriers under KMA (known message attack) and WOA (watermarked only attack), this paper also reveals the factors that may influent the Add-SS watermarking security such as the times of observation, the length of secret carriers, the embedding energy, and the distribution of embedded messages. The results obtained in this paper will be helpful for designing the new secure and robust watermarking system.

Perceptual organization in the tilt illusion.

The tilt illusion is a paradigmatic example of contextual influences on perception. We analyze it in terms of a neural population model for the perceptual organization of visual orientation. In turn, this is based on a well-found treatment of natural scene statistics, known as the Gaussian Scale Mixture model. This model is closely related to divisive gain control in neural processing and has been extensively applied in the image processing and statistical learning communities; however, its implications for contextual effects in biological vision have not been studied. In our model, oriented neural units associated with surround tilt stimuli participate in divisively normalizing the activities of the units representing a center stimulus, thereby changing their tuning curves. We show that through standard population decoding, these changes lead to the forms of repulsion and attraction observed in the tilt illusion. The issues in our model readily generalize to other visual attributes and contextual phenomena, and should lead to more rigorous treatments of contextual effects based on natural scene statistics.

A unified Bayesian framework for MEG/EEG source imaging

The ill-posed nature of the MEG (or related EEG) source localization problem requires the incorporation of prior assumptions when choosing an appropriate solution out of an infinite set of candidates. Bayesian approaches are useful in this capacity because they allow these assumptions to be explicitly quantified using postulated prior distributions. However, the means by which these priors are chosen, as well as the estimation and inference procedures that are subsequently adopted to affect localization, have led to a daunting array of algorithms with seemingly very different properties and assumptions. From the vantage point of a simple Gaussian scale mixture model with flexible covariance components, this paper analyzes and extends several broad categories of Bayesian inference directly applicable to source localization including empirical Bayesian approaches, standard MAP estimation, and multiple variational Bayesian (VB) approximations. Theoretical properties related to convergence, global and local minima, and localization bias are analyzed and fast algorithms are derived that improve upon existing methods. This perspective leads to explicit connections between many established algorithms and suggests natural extensions for handling unknown dipole orientations, extended source configurations, correlated sources, temporal smoothness, and computational expediency. Specific imaging methods elucidated under this paradigm include the weighted minimum ℓ2-norm, FOCUSS, minimum current estimation, VESTAL, sLORETA, restricted maximum likelihood, covariance component estimation, beamforming, variational Bayes, the Laplace approximation, and automatic relevance determination, as well as many others. Perhaps surprisingly, all of these methods can be formulated as particular cases of covariance component estimation using different concave regularization terms and optimization rules, making general theoretical analyses and algorithmic extensions/improvements particularly relevant.

Denoising of multicomponent images using wavelet least-squares estimators

In this paper, we study denoising of multicomponent images. The presented procedures are spatial wavelet-based denoising techniques, based on Bayesian least-squares optimization procedures, using prior models for the wavelet coefficients that account for the correlations between the spectral bands. We analyze three mixture priors: Gaussian scale mixture models, Bernoulli-Gaussian mixture models and Laplacian mixture models. These three prior models are studied within the same framework of least-squares optimization. The presented procedures are compared to Gaussian prior model and single-band denoising procedures. We analyze the suppression of non-correlated as well as correlated white Gaussian noise on multispectral and hyperspectral remote sensing data and Rician distributed noise on multiple images of within-modality magnetic resonance data. It is shown that a superior denoising performance is obtained when (a) the interband covariances are fully accounted for and (b) prior models are used that better approximate the marginal distributions of the wavelet coefficients.

Wavelet Denoising of Multicomponent Images Using Gaussian Scale Mixture Models and a Noise-Free Image as Priors

In this paper, a Bayesian wavelet-based denoising procedure for multicomponent images is proposed. A denoising procedure is constructed that (1) fully accounts for the multicomponent image covariances, (2) makes use of Gaussian scale mixtures as prior models that approximate the marginal distributions of the wavelet coefficients well, and (3) makes use of a noise-free image as extra prior information. It is shown that such prior information is available with specific multicomponent image data of, e.g., remote sensing and biomedical imaging. Experiments are conducted in these two domains, in both simulated and real noisy conditions.

Optimality of KLT for High-Rate Transform Coding of Gaussian Vector-Scale Mixtures: Application to Reconstruction, Estimation, and Classification

The Karhunen-Loeacuteve transform (KLT) is known to be optimal for high-rate transform coding of Gaussian vectors for both fixed-rate and variable-rate encoding. The KLT is also known to be suboptimal for some non-Gaussian models. This paper proves high-rate optimality of the KLT for variable-rate encoding of a broad class of non-Gaussian vectors: Gaussian vector-scale mixtures (GVSM), which extend the Gaussian scale mixture (GSM) model of natural signals. A key concavity property of the scalar GSM (same as the scalar GVSM) is derived to complete the proof. Optimality holds under a broad class of quadratic criteria, which include mean-squared error (MSE) as well as generalized f-divergence loss in estimation and binary classification systems. Finally, the theory is illustrated using two applications: signal estimation in multiplicative noise and joint optimization of classification/reconstruction systems

Topographic Product Models Applied to Natural Scene Statistics

We present an energy-based model that uses a product of generalized Student-t distributions to capture the statistical structure in data sets. This model is inspired by and particularly applicable to "natural" data sets such as images. We begin by providing the mathematical framework, where we discuss complete and overcomplete models and provide algorithms for training these models from data. Using patches of natural scenes, we demonstrate that our approach represents a viable alternative to independent component analysis as an interpretive model of biological visual systems. Although the two approaches are similar in flavor, there are also important differences, particularly when the representations are overcomplete. By constraining the interactions within our model, we are also able to study the topographic organization of Gabor-like receptive fields that our model learns. Finally, we discuss the relation of our new approach to previous work--in particular, gaussian scale mixture models and variants of independent components analysis.