This paper addresses the problem of summarizing the posterior distributions that typically arise, in a Bayesian framework, when dealing with signal decomposition problems with unknown number of components. Such posterior distributions are defined over union of subspaces of differing dimensionality and can be sampled from using modern Monte Carlo techniques, for instance the increasingly popular RJ-MCMC method. No generic approach is available, however, to summarize the resulting variable-dimensional samples and extract from them component-specific parameters. We propose a novel approach to this problem, which consists in approximating the complex posterior of interest by a "simple"-but still variable-dimensional-parametric distribution. The distance between the two distributions is measured using the Kullback-Leibler divergence, and a Stochastic EM-type algorithm, driven by the RJ-MCMC sampler, is proposed to estimate the parameters. The proposed algorithm is illustrated on the fundamental signal processing example of joint detection and estimation of sinusoids in white Gaussian noise.

Here we address the problem of adaptive digital-transmission systems. New systems based on a nonuniform transmission (NUT) principle are proposed, utilizing a recently proposed algorithm for adaptive identification and reconstruction of AR processes subject to missing data. We propose a new adaptive sampling (nonuniform transmission) method combined with the adaptive reconstruction algorithm. A new NUT-ADPCM coding-decoding system is designed. The proposed system is demonstrated for audio-signal compression and compared to the ADPCM G.726 standard. The new system yields improvements in both signal-to-noise ratio and average bit rate.

The scalar shrinkage-thresholding operator is a key ingredient in variable selection algorithms arising in wavelet denoising, JPEG2000 image compression and predictive analysis of gene microarray data. In these applications, the decision to select a scalar variable is given as the solution to a scalar sparsity penalized quadratic optimization. In some other applications, one seeks to select multidimensional variables. In this work, we present a natural multidimensional extension of the scalar shrinkage thresholding operator. Similarly to the scalar case, the threshold is determined by the minimization of a convex quadratic form plus an Euclidean norm penalty, however, here the optimization is performed over a domain of dimensionN≥ 1. The solution to this convex optimization problem is called the multidimensional shrinkage threshold operator (MSTO). The MSTO reduces to the scalar case in the special case ofN=1. In the general case ofN>; 1 the optimal MSTO shrinkage can be found through a simple convex line search. We give an efficient algorithm for solving this line search and show that our method to evaluate the MSTO outperforms other state-of-the art optimization approaches. We present several illustrative applications of the MSTO in the context of Group LASSO penalized estimation.

In this paper, we present a kernel-based approach to the clustering of diffusion tensors and fiber tracts. We propose to use a Mercer kernel over the tensor space where both spatial and diffusion information are taken into account. This kernel highlights implicitly the connectivity along fiber tracts. Tensor segmentation is performed using kernel-PCA compounded with a landmark-Isomap embedding and k-means clustering. Based on a soft fiber representation, we extend the tensor kernel to deal with fiber tracts using the multi-instance kernel that reflects not only interactions between points along fiber tracts, but also the interactions between diffusion tensors. This unsupervised method is further extended by way of an atlas-based registration of diffusion-free images, followed by a classification of fibers based on nonlinear kernel Support Vector Machines (SVMs). Promising experimental results of tensor and fiber classification of the human skeletal muscle over a significant set of healthy and diseased subjects demonstrate the potential of our approach.

The Kullback information criterion (KIC) (Cavanaugh, J.E., Statistics and Probability Letters, vol.42, p.333-43, 1999) and the bias corrected version, KICc, (Seghouane, A.-K. et al., Proc. ICASSP, p.145-8, 2003) are two methods for statistical model selection of regression variables and autoregressive models. Both criteria may be viewed as estimators of the Kullback symmetric divergence between the true model and the fitted approximating model. The bias of KIC and KICc is studied in the underfitting case, where none of the candidate models includes the true model. Here, only normal linear regression models are considered, where an exact expression of the bias is obtained for KIC and KICc. The bias of KICc is often smaller, in most cases drastically smaller, than KIC. A simulation study, in which the true model is of infinite order polynomial expansion, shows that, in small and moderate sample size, KICc provides a better model selection than KIC. Furthermore KICc outperforms the two well-known criteria, AIC and MDL.

In a previous paper (Lahalle et al. (2000)) we introduced an adaptive ARMA estimation method for time series with missing samples. Due to the non-linearity of the optimization criterion in the case of missing observations, the proposed method has led to an LMS-like algorithm with a higher computational complexity than the standard LMS. As many applications require very low complexity algorithms, the purpose of the present paper is to introduce simplified versions of the LMS adapted to the non-uniform sampling context. Both waveform reconstruction performance and computational costs are evaluated as a function of probability density of the sampling process. Stationary and non-stationary contexts are considered.

The Kullback information criterion (KIC) is a recently developed tool for statistical model selection (Cavanaugh, J.E., Statistics and Probability Letters, vol.42, p.333-43, 1999). KIC serves as an asymptotically unbiased estimator of a variant of the Kullback symmetric divergence, known also as J-divergence. A bias correction of the Kullback symmetric information criterion is derived for linear models. The correction is of particular use when the sample size is small or when the number of fitted parameters is of a moderate to large fraction of the sample size. For linear regression models, the corrected method, called KICc, is an exactly unbiased estimator of a variant of the Kullback symmetric divergence between the true unknown model and the candidate fitted model. Furthermore, KICc is found to provide better model order choice than any other asymptotically efficient methods when applied to autoregressive time series models.

We introduce a robust method for detecting evolutionary trends of gene expression from a temporal sequence of microarray data. In this method we perform gene clustering via multi-objective optimization to reveal genes with interesting and statistically significant temporal patterns. We illustrate this gene filtering methodology in the context of exploring the time trajectories of mouse retinal genes acquired at different points over the lifetimes of a population of mice. For 6 time points sampled over 24 mouse subjects, our method can reliably reveal genes whose expression level increases or decreases monotonically, hits a peak or valley at birth, or exhibits other trends.

In this paper, a real-time CAR (Continuous AR) parameter estimation method from randomly sampled observations is presented. For this purpose, a new concept is introduced: the Pseudo Correlation Vector. This vector, which is equal to the Correlation Vector in the uniform sampling case, reflects the statistical dependencies between successive values of the CAR signal. As a matter of fact, being the limit of a series recursively related to the observations, its real-time estimation becomes especially easy. An inversion of its dependence on the CAR parameters leads then to an estimate of the latter. Theoretical and simulation results regarding the proposed estimator are given.