International audienceDue to the enormous quantity of radar images acquired by satellites and through shuttle missions, there is an evident need for efficient automatic analysis tools. This paper describes unsupervised classification of radar images in the framework of hidden Markov models and generalized mixture estimation. Hidden Markov chain models, applied to a Hilbert-Peano scan of the image, constitute a fast and robust alternative to hidden Markov random field models for spatial regularization of image analysis problems, even though the latter provide a finer and more intuitive modeling of spatial relationships. We here compare the two approaches and show that they can be combined in a way that conserves their respective advantages. We also describe how the distribution families and parameters of classes with constant or textured radar reflectivity can be determined through generalized mixture estimation. Sample results obtained on real and simulated radar images are presente
We introduce the notion of a generalized mixture and propose some methods for estimating it, along with applications to unsupervised statistical image segmentation. A distribution mixture is said to be "generalized" when the exact nature of the components is not known, but each belongs to a finite known set of families of distributions. For instance, we can consider a mixture of three distributions, each being exponential or Gaussian. The problem of estimating such a mixture contains thus a new difficulty: we have to label each of three components (there are eight possibilities). We show that the classical mixture estimation algorithms-expectation-maximization (EM), stochastic EM (SEM), and iterative conditional estimation (ICE)-can be adapted to such situations once as we dispose of a method of recognition of each component separately. That is, when we know that a sample proceeds from one family of the set considered, we have a decision rule for what family it belongs to. Considering the Pearson system, which is a set of eight families, the decision rule above is defined by the use of "skewness" and "kurtosis". The different algorithms so obtained are then applied to the problem of unsupervised Bayesian image segmentation, We propose the adaptive versions of SEM, EM, and ICE in the case of "blind", i.e., "pixel by pixel", segmentation. "Global" segmentation methods require modeling by hidden random Markov fields, and we propose adaptations of two traditional parameter estimation algorithms: Gibbsian EM (GEM) and ICE allowing the estimation of generalized mixtures corresponding to Pearson's system. The efficiency of different methods is compared via numerical studies, and the results of unsupervised segmentation of three real radar images by different methods are presented.
International audienceIn many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such inference problems. However, in the presence of a high-dimensional and/or multimodal posterior distribution, it is widely documented that standard Monte-Carlo techniques could lead to poor performance. In this paper, the study is focused on a Sequential Monte- Carlo (SMC) sampler framework, a more robust and efficient Monte Carlo algorithm. Although this approach presents many advantages over traditional Monte-Carlo methods, the potential of this emergent technique is however largely underexploited in signal processing. In this work, we aim at proposing some novel strategies that will improve the efficiency and facilitate practical implementation of the SMC sampler specifically for signal processing applications. Firstly, we propose an automatic and adaptive strategy that selects the sequence of distributions within the SMC sampler that minimizes the asymptotic variance of the estimator of the posterior normalization constant. This is critical for performing model selection in modelling applications in Bayesian signal processing. The second original contribution we present improves the global efficiency of the SMC sampler by introducing a novel correction mechanism that allows the use of the particles generated through all the iterations of the algorithm (instead of only particles from the last iteration). This is a significant contribution as it removes the need to discard a large portion of the samples obtained, as is standard in standard SMC methods. This will improve estimation performance in practical settings where computational budget is important to consider
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