Véronique Delouille

Robust Distributed Estimation Using the Embedded Subgraphs Algorithm

We propose a new iterative, distributed approach for linear minimum mean-square-error (LMMSE) estimation in graphical models with cycles. The embedded subgraphs algorithm (ESA) decomposes a loopy graphical model into a number of linked embedded subgraphs and applies the classical parallel block Jacobi iteration comprising local LMMSE estimation in each subgraph (involving inversion of a small matrix) followed by an information exchange between neighboring nodes and subgraphs. Our primary application is sensor networks, where the model encodes the correlation structure of the sensor measurements, which are assumed to be Gaussian. The resulting LMMSE estimation problem involves a large matrix inverse, which must be solved in-network with distributed computation and minimal intersensor communication. By invoking the theory of asynchronous iterations, we prove that ESA is robust to temporary communication faults such as failing links and sleeping nodes, and enjoys guaranteed convergence under relatively mild conditions. Simulation studies demonstrate that ESA compares favorably with other recently proposed algorithms for distributed estimation. Simulations also indicate that energy consumption for iterative estimation increases substantially as more links fail or nodes sleep. Thus, somewhat surprisingly, sensor network energy conservation strategies such as low-powered transmission and aggressive sleep schedules could actually prove counterproductive. Our results can be replicated using MATLAB code from www.dsp.rice.edu/software

Distributed wavelet transform for irregular sensor network grids

Wavelet-based distributed data processing holds much promise for sensor networks; however, irregular sensor node placement precludes the direct application of standard wavelet techniques. In this paper, we develop a new distributed wavelet transform based on lifting that takes into account irregular sampling and provides a piecewise-planar multiresolution representation of the sensed data. We develop the transform theory; outline how to implement it in a multi-hop, wireless sensor network; and illustrate with several simulations. The new transform performs on par with conventional wavelet methods in a head-to-head comparison on a regular grid of sensor nodes

Fast and robust segmentation of solar EUV images: algorithm and results for solar cycle 23

Context. The study of the variability of the solar corona and the monitoring of coronal holes, quiet sun and active regions are of great importance in astrophysics as well as for space weather and space climate applications. Aims. In a previous work, we presented the spatial possibilistic clustering algorithm (SPoCA). This is a multi-channel unsupervised spatially-constrained fuzzy clustering method that automatically segments solar extreme ultraviolet (EUV) images into regions of interest. The results we reported on SoHO-EIT images taken from February 1997 to May 2005 were consistent with previous knowledge in terms of both areas and intensity estimations. However, they presented some artifacts due to the method itself. Methods. Herein, we propose a new algorithm, based on SPoCA, that removes these artifacts. We focus on two points: the definition of an optimal clustering with respect to the regions of interest, and the accurate definition of the cluster edges. We moreover propose methodological extensions to this method, and we illustrate these extensions with the automatic tracking of active regions. Results. The much improved algorithm can decompose the whole set of EIT solar images over the 23rd solar cycle into regions that can clearly be identified as quiet sun, coronal hole and active region. The variations of the parameters resulting from the segmentation, i.e. the area, mean intensity, and relative contribution to the solar irradiance, are consistent with previous results and thus validate the decomposition. Furthermore, we find indications for a small variation of the mean intensity of each region in correlation with the solar cycle. Conclusions. The method is generic enough to allow the introduction of other channels or data. New applications are now expected, e.g. related to SDO-AIA data.

Second-generation wavelet denoising methods for irregularly spaced data in two dimensions

This paper discusses bivariate scattered data denoising. The proposed method uses second-generation wavelets constructed with the lifting scheme. Starting from a simple initial transform, we propose predictor operators based on a stabilized bivariate generalization of the Lagrange interpolating polynomial. These predictors are meant to provide a smooth reconstruction. Next, we include an update step which helps to reduce the correlation amongst the detail coefficients, and hence stabilizes the final estimator. We use a Bayesian thresholding algorithm to denoise the empirical coefficients, and we show the performance of the resulting estimator through a simulation study.

Virtual Super Resolution of Scale Invariant Textured Images Using Multifractal Stochastic Processes

We present a new method of magnification for textured images featuring scale invariance properties. This work is originally motivated by an application to astronomical images. One goal is to propose a method to quantitatively predict statistical and visual properties of images taken by a forthcoming higher resolution telescope from older images at lower resolution. This is done by performing a virtual super resolution using a family of scale invariant stochastic processes, namely compound Poisson cascades, and fractional integration. The procedure preserves the visual aspect as well as the statistical properties of the initial image. An augmentation of information is performed by locally adding random small scale details below the initial pixel size. This extrapolation procedure yields a potentially infinite number of magnified versions of an image. It allows for large magnification factors (virtually infinite) and is physically conservative: zooming out to the initial resolution yields the initial image back. The (virtually) super resolved images can be used to predict the quality of future observations as well as to develop and test compression or denoising techniques.

Image patch analysis of sunspots and active regions - I. Intrinsic dimension and correlation analysis

Context. The flare productivity of an active region is observed to be related to its spatial complexity. Mount Wilson or McIntosh sunspot classifications measure such complexity but in a categorical way, and may therefore not use all the information present in the observations. Moreover, such categorical schemes hinder a systematic study of an active region’s evolution for example. Aims . We propose fine-scale quantitative descriptors for an active region’s complexity and relate them to the Mount Wilson classification. We analyze the local correlation structure within continuum and magnetogram data, as well as the cross-correlation between continuum and magnetogram data. Methods . We compute the intrinsic dimension, partial correlation, and canonical correlation analysis (CCA) of image patches of continuum and magnetogram active region images taken from the SOHO-MDI instrument. We use masks of sunspots derived from continuum as well as larger masks of magnetic active regions derived from magnetogram to analyze separately the core part of an active region from its surrounding part. Results . We find relationships between the complexity of an active region as measured by its Mount Wilson classification and the intrinsic dimension of its image patches. Partial correlation patterns exhibit approximately a third-order Markov structure. CCA reveals different patterns of correlation between continuum and magnetogram within the sunspots and in the region surrounding the sunspots. Conclusions . Intrinsic dimension has the potential to distinguish simple from complex active regions. These results also pave the way for patch-based dictionary learning with a view toward automatic clustering of active regions.

Image patch analysis of sunspots and active regions - II. Clustering via matrix factorization

Context . Separating active regions that are quiet from potentially eruptive ones is a key issue in Space Weather applications. Traditional classification schemes such as Mount Wilson and McIntosh have been effective in relating an active region large scale magnetic configuration to its ability to produce eruptive events. However, their qualitative nature prevents systematic studies of an active region’s evolution for example. Aims . We introduce a new clustering of active regions that is based on the local geometry observed in Line of Sight magnetogram and continuum images. Methods . We use a reduced-dimension representation of an active region that is obtained by factoring the corresponding data matrix comprised of local image patches. Two factorizations can be compared via the definition of appropriate metrics on the resulting factors. The distances obtained from these metrics are then used to cluster the active regions. Results . We find that these metrics result in natural clusterings of active regions. The clusterings are related to large scale descriptors of an active region such as its size, its local magnetic field distribution, and its complexity as measured by the Mount Wilson classification scheme. We also find that including data focused on the neutral line of an active region can result in an increased correspondence between our clustering results and other active region descriptors such as the Mount Wilson classifications and the R -value. Conclusions . Matrix factorization of image patches is a promising new way of characterizing active regions. We provide some recommendations for which metrics, matrix factorization techniques, and regions of interest to use to study active regions.

Image patch analysis and clustering of sunspots: A dimensionality reduction approach

Sunspots, as seen in white light or continuum images, are associated with regions of high magnetic activity on the Sun, visible on magnetogram images. Their complexity is correlated with explosive solar activity and so classifying these active regions is useful for predicting future solar activity. Current classification of sunspot groups is visually based and suffers from bias. Supervised learning methods can reduce human bias but fail to optimally capitalize on the information present in sunspot images. This paper uses two image modalities (continuum and magnetogram) to characterize the spatial and modal interactions of sunspot and magnetic active region images and presents a new approach to cluster the images. Specifically, in the framework of image patch analysis, we estimate the number of intrinsic parameters required to describe the spatial and modal dependencies, the correlation between the two modalities and the corresponding spatial patterns, and examine the phenomena at different scales within the images. To do this, we use linear and nonlinear intrinsic dimension estimators, canonical correlation analysis, and multiresolution analysis of intrinsic dimension.

Estimation of nonlinear autoregressive models using design-adapted wavelets

We estimate nonlinear autoregressive models using a design-adapted wavelet estimator. We show two properties of the wavelet transform adapted to an autoregressive design. First, in an asymptotic setup, we derive the order of the threshold that removes all the noise with a probability tending to one asymptotically. Second, with this threshold, we estimate the detail coefficients by soft-thresholding the empirical detail coefficients. We show an upper bound on thel2-risk of these soft-thresholded detail coefficients. Finally, we illustrate the behavior of this design-adapted wavelet estimator on simulated and real data sets.

Segmentation of Extreme Ultraviolet Solar Images using a Multispectral Data Fusion Process

Accurate means of quantifying the respective contributions of different structures to the solar irradiance is now a key issue in Solar Physics, with implications to Sun-Earth relationships and space weather study. In this paper, we propose a three-step fusion scheme, that allows to aggregate (17.1 nm, 19.5 nm) data stemming from the solar EIT instrument onboard the SoHO mission, and that is flexible enough to allow the integration of other type of information. The method is based on both a spatially constrained possibilistic clustering algorithm and a context dependent fusion operator. It aggregates the complementary and redundant information coming from the input sources. The results obtained on a 9-year dataset are consistent with those found in the solar physics literature. Unlike previous algorithms used in solar physics, our method has the ability to add further heterogeneous sources and sensors (e.g. human knowledge, images in other bandpasses, ratio of images) to the process, in order to postpone the decision step (here the segmentation of structures of interest) until sufficient information is available.