arXiv subjects

Cédric Richard

Publications and source records attributed to Cédric Richard.

At least 37 records · Page 2Linked to original sources

arXiv2020

Kalman Filtering and Expectation Maximization for Multitemporal Spectral Unmixing

The recent evolution of hyperspectral imaging technology and the proliferation of new emerging applications presses for the processing of multiple temporal hyperspectral images. In this work, we propose a novel spectral unmixing (SU) strategy using physically motivated parametric endmember representations to account for temporal spectral variability. By representing the multitemporal mixing process using a state-space formulation, we are able to exploit the Bayesian filtering machinery to estimate the endmember variability coefficients. Moreover, by assuming that the temporal variability of the abundances is small over short intervals, an efficient implementation of the expectation maximization (EM) algorithm is employed to estimate the abundances and the other model parameters. Simulation results indicate that the proposed strategy outperforms state-of-the-art multitemporal SU algorithms.

eess.IV↗

arXiv2020

Deep Generative Models for Library Augmentation in Multiple Endmember Spectral Mixture Analysis

Multiple Endmember Spectral Mixture Analysis (MESMA) is one of the leading approaches to perform spectral unmixing (SU) considering variability of the endmembers (EMs). It represents each EM in the image using libraries of spectral signatures acquired a priori. However, existing spectral libraries are often small and unable to properly capture the variability of each EM in practical scenes, which compromises the performance of MESMA. In this paper, we propose a library augmentation strategy to increase the diversity of existing spectral libraries, thus improving their ability to represent the materials in real images. First, we leverage the power of deep generative models to learn the statistical distribution of the EMs based on the spectral signatures available in the existing libraries. Afterwards, new samples can be drawn from the learned EM distributions and used to augment the spectral libraries, improving the overall quality of the SU process. Experimental results using synthetic and real data attest the superior performance of the proposed method even under library mismatch conditions.

cs.CV↗

arXiv2020

Online Graph-Based Change Point Detection in Multiband Image Sequences

The automatic detection of changes or anomalies between multispectral and hyperspectral images collected at different time instants is an active and challenging research topic. To effectively perform change-point detection in multitemporal images, it is important to devise techniques that are computationally efficient for processing large datasets, and that do not require knowledge about the nature of the changes. In this paper, we introduce a novel online framework for detecting changes in multitemporal remote sensing images. Acting on neighboring spectra as adjacent vertices in a graph, this algorithm focuses on anomalies concurrently activating groups of vertices corresponding to compact, well-connected and spectrally homogeneous image regions. It fully benefits from recent advances in graph signal processing to exploit the characteristics of the data that lie on irregular supports. Moreover, the graph is estimated directly from the images using superpixel decomposition algorithms. The learning algorithm is scalable in the sense that it is efficient and spatially distributed. Experiments illustrate the detection and localization performance of the method.

eess.SP↗

arXiv2020

Diffusion LMS with Communication Delays: Stability and Performance Analysis

We study the problem of distributed estimation over adaptive networks where communication delays exist between nodes. In particular, we investigate the diffusion Least-Mean- Square (LMS) strategy where delayed intermediate estimates (due to the communication channels) are employed during the combination step. One important question is: Do the delays affect the stability condition and performance? To answer this question, we conduct a detailed performance analysis in the mean and in the mean-square-error sense of the diffusion LMS with delayed estimates. Stability conditions, transient and steady-state mean-square-deviation (MSD) expressions are provided. One of the main findings is that diffusion LMS with delays can still converge under the same step-sizes condition of the diffusion LMS without delays. Finally, simulation results illustrate the theoretical findings.

eess.SP↗

arXiv2019

Online Distributed Learning over Graphs with Multitask Graph-Filter Models

In this work, we are interested in adaptive and distributed estimation of graph filters from streaming data. We formulate this problem as a consensus estimation problem over graphs, which can be addressed with diffusion LMS strategies. Most popular graph-shift operators such as those based on the graph Laplacian matrix, or the adjacency matrix, are not energy preserving. This may result in an ill-conditioned estimation problem, and reduce the convergence speed of the distributed algorithms. To address this issue and improve the transient performance, we introduce a preconditioned graph diffusion LMS algorithm. We also propose a computationally efficient version of this algorithm by approximating the Hessian matrix with local information. Performance analyses in the mean and mean-square sense are provided. Finally, we consider a more general problem where the filter coefficients to estimate may vary over the graph. To avoid a large estimation bias, we introduce an unsupervised clustering method for splitting the global estimation problem into local ones. Numerical results show the effectiveness of the proposed algorithms and validate the theoretical results.

eess.SP↗

arXiv2019

Distributed Change Detection in Streaming Graph Signals

Detecting abrupt changes in streaming graph signals is relevant in a variety of applications ranging from energy and water supplies, to environmental monitoring. In this paper, we address this problem when anomalies activate localized groups of nodes in a network. We introduce an online change-point detection algorithm, which is fully distributed across nodes to monitor large-scale dynamic networks. We analyze the detection statistics for controlling the probability of a global type 1 error. Finally we illustrate the detection and localization performance with simulated data.

eess.SP↗

arXiv2018

Tech Report: A Fast Multiscale Spatial Regularization for Sparse Hyperspectral Unmixing

Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can benefit from spatial regularization strategies. While existing spatial regularization methods improve the problem conditioning and promote piecewise smooth solutions, they lead to large nonsmooth optimization problems. Thus, efficiently introducing spatial context in the unmixing problem remains a challenge, and a necessity for many real world applications. In this paper, a novel multiscale spatial regularization approach for sparse unmixing is proposed. The method uses a signal-adaptive spatial multiscale decomposition based on superpixels to decompose the unmixing problem into two simpler problems, one in the approximation domain and another in the original domain. Simulation results using both synthetic and real data indicate that the proposed method can outperform state-of-the-art Total Variation-based algorithms with a computation time comparable to that of their unregularized counterparts.

cs.CV↗

arXiv2018

On reducing the communication cost of the diffusion LMS algorithm

The rise of digital and mobile communications has recently made the world more connected and networked, resulting in an unprecedented volume of data flowing between sources, data centers, or processes. While these data may be processed in a centralized manner, it is often more suitable to consider distributed strategies such as diffusion as they are scalable and can handle large amounts of data by distributing tasks over networked agents. Although it is relatively simple to implement diffusion strategies over a cluster, it appears to be challenging to deploy them in an ad-hoc network with limited energy budget for communication. In this paper, we introduce a diffusion LMS strategy that significantly reduces communication costs without compromising the performance. Then, we analyze the proposed algorithm in the mean and mean-square sense. Next, we conduct numerical experiments to confirm the theoretical findings. Finally, we perform large scale simulations to test the algorithm efficiency in a scenario where energy is limited.

stat.ML↗

arXiv2017

Diffusion LMS for Multitask Problems with Local Linear Equality Constraints

We consider distributed multitask learning problems over a network of agents where each agent is interested in estimating its own parameter vector, also called task, and where the tasks at neighboring agents are related according to a set of linear equality constraints. Each agent possesses its own convex cost function of its parameter vector and a set of linear equality constraints involving its own parameter vector and the parameter vectors of its neighboring agents. We propose an adaptive stochastic algorithm based on the projection gradient method and diffusion strategies in order to allow the network to optimize the individual costs subject to all constraints. Although the derivation is carried out for linear equality constraints, the technique can be applied to other forms of convex constraints. We conduct a detailed mean-square-error analysis of the proposed algorithm and derive closed-form expressions to predict its learning behavior. We provide simulations to illustrate the theoretical findings. Finally, the algorithm is employed for solving two problems in a distributed manner: a minimum-cost flow problem over a network and a space-time varying field reconstruction problem.

cs.MA↗

arXiv2017

Distributed Deblurring of Large Images of Wide Field-Of-View

Image deblurring is an economic way to reduce certain degradations (blur and noise) in acquired images. Thus, it has become essential tool in high resolution imaging in many applications, e.g., astronomy, microscopy or computational photography. In applications such as astronomy and satellite imaging, the size of acquired images can be extremely large (up to gigapixels) covering wide field-of-view suffering from shift-variant blur. Most of the existing image deblurring techniques are designed and implemented to work efficiently on centralized computing system having multiple processors and a shared memory. Thus, the largest image that can be handle is limited by the size of the physical memory available on the system. In this paper, we propose a distributed nonblind image deblurring algorithm in which several connected processing nodes (with reasonable computational resources) process simultaneously different portions of a large image while maintaining certain coherency among them to finally obtain a single crisp image. Unlike the existing centralized techniques, image deblurring in distributed fashion raises several issues. To tackle these issues, we consider certain approximations that trade-offs between the quality of deblurred image and the computational resources required to achieve it. The experimental results show that our algorithm produces the similar quality of images as the existing centralized techniques while allowing distribution, and thus being cost effective for extremely large images.

math.OC↗

arXiv2017

Adaptation and learning over networks for nonlinear system modeling

In this chapter, we analyze nonlinear filtering problems in distributed environments, e.g., sensor networks or peer-to-peer protocols. In these scenarios, the agents in the environment receive measurements in a streaming fashion, and they are required to estimate a common (nonlinear) model by alternating local computations and communications with their neighbors. We focus on the important distinction between single-task problems, where the underlying model is common to all agents, and multitask problems, where each agent might converge to a different model due to, e.g., spatial dependencies or other factors. Currently, most of the literature on distributed learning in the nonlinear case has focused on the single-task case, which may be a strong limitation in real-world scenarios. After introducing the problem and reviewing the existing approaches, we describe a simple kernel-based algorithm tailored for the multitask case. We evaluate the proposal on a simulated benchmark task, and we conclude by detailing currently open problems and lines of research.

stat.ML↗

arXiv2017

Multitask diffusion adaptation over networks with common latent representations

Online learning with streaming data in a distributed and collaborative manner can be useful in a wide range of applications. This topic has been receiving considerable attention in recent years with emphasis on both single-task and multitask scenarios. In single-task adaptation, agents cooperate to track an objective of common interest, while in multitask adaptation agents track multiple objectives simultaneously. Regularization is one useful technique to promote and exploit similarity among tasks in the latter scenario. This work examines an alternative way to model relations among tasks by assuming that they all share a common latent feature representation. As a result, a new multitask learning formulation is presented and algorithms are developed for its solution in a distributed online manner. We present a unified framework to analyze the mean-square-error performance of the adaptive strategies, and conduct simulations to illustrate the theoretical findings and potential applications.

cs.MA↗

arXiv2016

Technical Report: Band selection for nonlinear unmixing of hyperspectral images as a maximal clique problem

Kernel-based nonlinear mixing models have been applied to unmix spectral information of hyperspectral images when the type of mixing occurring in the scene is too complex or unknown. Such methods, however, usually require the inversion of matrices of sizes equal to the number of spectral bands. Reducing the computational load of these methods remains a challenge in large scale applications. This paper proposes a centralized method for band selection (BS) in the reproducing kernel Hilbert space (RKHS). It is based upon the coherence criterion, which sets the largest value allowed for correlations between the basis kernel functions characterizing the unmixing model. We show that the proposed BS approach is equivalent to solving a maximum clique problem (MCP), that is, searching for the biggest complete subgraph in a graph. Furthermore, we devise a strategy for selecting the coherence threshold and the Gaussian kernel bandwidth using coherence bounds for linearly independent bases. Simulation results illustrate the efficiency of the proposed method.

cs.CV↗

arXiv2016

Multitask diffusion adaptation over asynchronous networks

The multitask diffusion LMS is an efficient strategy to simultaneously infer, in a collaborative manner, multiple parameter vectors. Existing works on multitask problems assume that all agents respond to data synchronously. In several applications, agents may not be able to act synchronously because networks can be subject to several sources of uncertainties such as changing topology, random link failures, or agents turning on and off for energy conservation. In this work, we describe a model for the solution of multitask problems over asynchronous networks and carry out a detailed mean and mean-square error analysis. Results show that sufficiently small step-sizes can still ensure both stability and performance. Simulations and illustrative examples are provided to verify the theoretical findings. The framework is applied to a particular application involving spectral sensing.

eess.SY↗

arXiv2016

Proximal Multitask Learning over Networks with Sparsity-inducing Coregularization

In this work, we consider multitask learning problems where clusters of nodes are interested in estimating their own parameter vector. Cooperation among clusters is beneficial when the optimal models of adjacent clusters have a good number of similar entries. We propose a fully distributed algorithm for solving this problem. The approach relies on minimizing a global mean-square error criterion regularized by non-differentiable terms to promote cooperation among neighboring clusters. A general diffusion forward-backward splitting strategy is introduced. Then, it is specialized to the case of sparsity promoting regularizers. A closed-form expression for the proximal operator of a weighted sum of $\ell_1$-norms is derived to achieve higher efficiency. We also provide conditions on the step-sizes that ensure convergence of the algorithm in the mean and mean-square error sense. Simulations are conducted to illustrate the effectiveness of the strategy.

eess.SY↗

arXiv2015

Stochastic Behavior of the Nonnegative Least Mean Fourth Algorithm for Stationary Gaussian Inputs and Slow Learning

Some system identification problems impose nonnegativity constraints on the parameters to estimate due to inherent physical characteristics of the unknown system. The nonnegative least-mean-square (NNLMS) algorithm and its variants allow to address this problem in an online manner. A nonnegative least mean fourth (NNLMF) algorithm has been recently proposed to improve the performance of these algorithms in cases where the measurement noise is not Gaussian. This paper provides a first theoretical analysis of the stochastic behavior of the NNLMF algorithm for stationary Gaussian inputs and slow learning. Simulation results illustrate the accuracy of the proposed analysis.

math.NA↗

arXiv2015

Distributed image reconstruction for very large arrays in radio astronomy

Current and future radio interferometric arrays such as LOFAR and SKA are characterized by a paradox. Their large number of receptors (up to millions) allow theoretically unprecedented high imaging resolution. In the same time, the ultra massive amounts of samples makes the data transfer and computational loads (correlation and calibration) order of magnitudes too high to allow any currently existing image reconstruction algorithm to achieve, or even approach, the theoretical resolution. We investigate here decentralized and distributed image reconstruction strategies which select, transfer and process only a fraction of the total data. The loss in MSE incurred by the proposed approach is evaluated theoretically and numerically on simple test cases.

astro-ph.IM↗

arXiv2015

Nonparametric Detection of Nonlinearly Mixed Pixels and Endmember Estimation in Hyperspectral Images

Mixing phenomena in hyperspectral images depend on a variety of factors such as the resolution of observation devices, the properties of materials, and how these materials interact with incident light in the scene. Different parametric and nonparametric models have been considered to address hyperspectral unmixing problems. The simplest one is the linear mixing model. Nevertheless, it has been recognized that mixing phenomena can also be nonlinear. The corresponding nonlinear analysis techniques are necessarily more challenging and complex than those employed for linear unmixing. Within this context, it makes sense to detect the nonlinearly mixed pixels in an image prior to its analysis, and then employ the simplest possible unmixing technique to analyze each pixel. In this paper, we propose a technique for detecting nonlinearly mixed pixels. The detection approach is based on the comparison of the reconstruction errors using both a Gaussian process regression model and a linear regression model. The two errors are combined into a detection statistics for which a probability density function can be reasonably approximated. We also propose an iterative endmember extraction algorithm to be employed in combination with the detection algorithm. The proposed Detect-then-Unmix strategy, which consists of extracting endmembers, detecting nonlinearly mixed pixels and unmixing, is tested with synthetic and real images.

cs.CV↗