Practitioners successfully use hidden Markov chains (HMCs) in different problems for about sixty years. HMCs belong to the family of generative models and they are often compared to discriminative models, like conditional random fields (CRFs). Authors usually consider CRFs as quite different from HMCs, and CRFs are often presented as interesting alternative to HMCs. In some areas, like natural language processing (NLP), discriminative models have completely supplanted generative models. However, some recent results show that both families of models are not so different, and both of them can lead to identical processing power. In this paper we compare the simple linear-chain CRFs to the basic HMCs. We show that HMCs are identical to CRFs in that for each CRF we explicitly construct an HMC having the same posterior distribution. Therefore, HMCs and linear-chain CRFs are not different but just differently parametrized models.

Naive Bayes is a popular probabilistic model appreciated for its simplicity and interpretability. However, the usual form of the related classifier suffers from two major problems. First, as caring about the observations' law, it cannot consider complex features. Moreover, it considers the conditional independence of the observations given the hidden variable. This paper introduces the original Neural Naive Bayes, modeling the parameters of the classifier induced from the Naive Bayes with neural network functions. This allows to correct the first problem. We also introduce new Neural Pooled Markov Chain models, alleviating the independence condition. We empirically study the benefits of these models for Sentiment Analysis, dividing the error rate of the usual classifier by 4.5 on the IMDB dataset with the FastText embedding.

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When the state space dimension increases, the computational burden can become a major challenge for optimal Kalman filtering in Gaussian triplet Markov models (TMMs). In this paper, we introduce a new model order reduction technique applicable to linear time-homogeneous Gaussian TMMs. Taking advantage of the lower state dimension of the resulting approximate model, a low-complexity suboptimal Kalman filter is obtained. The proposed estimator provides complexity reduction without significant accuracy loss and is shown to outperform two classical methods in the case of Markovian process noise.

This paper presents recent results on conditionally Gaussian observed Markov switching models by incorporating fuzzy switches in the model, instead of hard ones. This kind of generalization is of interest for applications involving continuous switching regimes, such as tracking an object using cameras in intermittent sunlight and shadow conditions. The filter developed hereby is recursive, optimal, and exact, up to an approximation of integrals according to some fuzzy measures. Experiences on simulated and on real data-dealing with outdoor air temperature and power consumption of a building-confirm the accuracy and effectiveness of the proposed filter compared with the hard filter with “crisp” switches.

The object of this paper is to introduce a new estimation algorithm specifically designed for the latent high-order autoregressive models. It implements the concept of the filter-based maximum likelihood. Our approach is fully deterministic and is less computationally demanding than the traditional Monte Carlo Markov chain techniques. The simulation experiments and real-world data processing confirm the interest of our approach.

Hidden Markov fields have been extensively applied in the field of synthetic aperture radar (SAR) image processing, mainly for segmentation and change detection. In such models, the hidden process of interest X is assumed to be a Markov field that is to be searched from an observable process Y. The possibility of such estimation lies, however, on several assumptions that turn out to be unsuitable for many natural systems. These models have then been extended in many directions, leading to triplet Markov fields among other extensions. A link has then been established between these models and the theory of evidence, opening new possibilities of uncertainty modeling and information fusion. The aim of this letter is to further generalize the hidden evidential Markov field (EMF) to consider more general forms of noise with application to unsupervised segmentation of SAR images. For parameters estimation, we use iterative conditional estimation, whereas maximization is performed through iterative conditional mode. The performance of the proposed model is assessed against the original EMF on real SAR images.

Hidden Markov fields have been widely used in image processing thanks to their ability to characterize spatial information. In such models, the process of interest X is hidden and is to be estimated from an observable process Y . One common way to achieve the associated inference tasks is to define, on one hand, the prior distribution p(x); and on the other hand, the noise distribution p(y/x). While it is commonly established that the prior distribution is given by a Markov random field, the noise distribution is usually given through a set of Gaussian densities; one per each label. Hence, observed pixels belonging to the same class are assumed to be generated by the same Gaussian density. Such assumption turns out, however, to be too restrictive in some situations. For instance, due to light conditions, pixels belonging to a same label may present quite different visual aspects. In this letter, we overcome this drawback by considering an auxiliary field U in accordance with the triplet Markov field formalism. Experimental results on simulated and real images demonstrate the interest of the proposed model with respect to the common hidden Markov fields.

Markov chains are very efficient models and have been extensively applied in a wide range of fields covering queuing theory, signal processing, performance evaluation, time series, and finance. For discrete finite first-order Markov chains, which are among the most used models of this family, the transition matrix can be seen as the model parameter, since it encompasses the set of probabilities governing the system state. Estimating such a matrix is, however, not an easy task due to possible opposing expert reports or variability of conditions under which the estimation process is carried out. In this paper, we propose an original approach to infer a consensus transition matrix, defined in accordance with the theory of evidence, from a family of data samples or transition matrices. To validate our method, experiments are conducted on nonstationary label images and daily rainfall data. The obtained results confirm the interest of the proposed evidential modeling with respect to the standard Bayesian one.

Hidden Markov models have been extended in many directions, leading to pairwise Markov models, triplet Markov models, or discriminative random fields, all of which have been successfully applied in many fields covering signal and image processing. The Dempster-Shafer theory of evidence has also shown its interest in a wide range of situations involving reasoning under uncertainty and/or information fusion. There are, however, only few works dealing with both of these modeling tools simultaneously. The aim of this paper, which falls under this category of works, is to propose a general evidential Markov model offering wide modeling and processing possibilities regarding information imprecision, sensor unreliability, and data fusion. The main interest of the proposed model relies in the possibility of achieving, easily, the Dempster-Shafer fusion without destroying the Markovianity.

Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data.

We present a novel implementation of Triplet Markov Fields (TMF) for the unsupervised region segmentation of challenging eye images, representative of the iris recognition context. Results confirm the interest of such models over the classical Hidden Markov Field (HMF) and traditional gradient-based approaches for iris and periocular detection. We show that the precision of the resulting normalization circles is largely improved through the use of such TMF model as well as the quality of the image segmentation, despite of various degradations. These results are promising for further integration of TMF approaches in iris verification systems.

We consider triplet Markov Gaussian linear systems (X,R,Y), whereXis hidden continuous random sequence,Ris hidden discrete Markov chain,Yis observed continuous random sequence, and (X,Y) is Gaussian conditionally onR. In the classical “Conditionally Gaussian Linear State-Space Model” (CGLSSM), optimal filter is not workable with a reasonable complexity. The aim of the paper is to propose a new model, quite close to the CGLSSM, belonging to the general and recently proposed family of models, called “Conditionally Markov Switching Hidden Linear Models” (CMSHLMs), in which the computation of optimal filter with complexity linear in the number of observations is feasible. The new model and related filtering are immediately applicable in all situations where the classical CGLSSM is used via approximated filtering.

Hidden Markov models are very robust and have been widely used in a wide range of application fields; however, they can prove some limitations for data restoration under some complex situations. These latter include cases when the data to be recovered are nonstationary. The recent triplet Markov models have overcome such difficulty thanks to their rich formalism, that allows considering more complex data structures while keeping the computational complexity of the different algorithms linear to the data size. In this letter, we propose a new triplet Markov chain that allows the unsupervised restoration of random discrete data hidden with switching noise distributions. We also provide genuine parameters estimation and MPM restoration algorithms. The new model is validated through experiments conducted on synthetic data and on real images, whose results show its interest with respect to the standard hidden Markov chain.

The Independent Component Analysis (ICA) model is extended to the case where the components are not necessarily independent: depending on the value a hidden latent process at the same time, the unknown components of the linear mixture are assumed either mutually independent or dependent. We propose for this model a separation method which combines: (i) a classical ICA separation performed using the set of samples whose components are conditionally independent, and (ii) a method for estimation of the latent process. The latter task is performed by Iterative Conditional Estimation (ICE). It is an estimation technique in the case of incomplete data, which is particularly appealing because it requires only weak conditions. Finally, simulations validate our method and show that the separation quality is improved for sources generated according to our model.

This paper deals with SAR data segmentation in an unsupervised way. The model we propose is a combination of the nonstationary triplet Markov field recently introduced and the Fisher distributions. The first one allows modeling the different stationarities present in a given image. The second one has the advantage that is well adapted to this kind of data. We present an original technique based on Iterative Conditional Estimation method, to estimate the parameters of the model we propose. Application examples on simulated data and real SAR images are presented as well.

Recent developments in statistical theory and associated computational techniques have opened new avenues for image modeling as well as for image segmentation techniques. Thus, a host of models have been proposed and the ones which have probably received considerable attention are the hidden Markov fields (HMF) models. This is due to their simplicity of handling and their potential for providing improved image quality. Although these models provide satisfying results in the stationary case, they can fail in the nonstationary one. In this paper, we tackle the problem of modeling a nonstationary hidden random field and its effect on the unsupervised statistical image segmentation. We propose an original approach, based on the recent triplet Markov field (TMF) model, which enables one to deal with nonstationary class fields. Moreover, the noise can be correlated and possibly non-Gaussian. An original parameter estimation method which uses the Pearson system to find the natures of the noise margins, which can vary with the class, is also proposed and used to perform unsupervised segmentation of such images. Experiments indicate that the new model and related processing algorithm can improve the results obtained with the classical ones.

The hidden Markov field (HMF) model has been used in many model-based solutions for image segmentation, and generally gives satisfying results. However, when the class image is non stationary, the unsupervised segmentation results provided by HMF can be poor. In this paper, we propose a new model based on triplet Markov fields (TMF) and the Pearson system which enables one to deal with non stationary hidden fields and correlated, possibly non Gaussian noise. Moreover, the nature of marginal distributions of the noise can vary with the class. We specify a new general parameter estimation method and apply it to unsupervised Bayesian image segmentation

This paper presents a contextual algorithm for the computation of Baum's forward and backward probabilities, which are intensively used in the framework of hidden Markov chain (HMC) models. The method differs from the original algorithm since it only takes into account a neighborhood of limited length and not all the chain for computations. Comparative experiments with respect to the neighborhood size have been conducted on both Markovian (simulations) and not Markovian (images) data, by mean of supervised and unsupervised classifications

This paper shows how to obtain a binary change map from similarity measures of the local statistics of images before and after a disaster. The decision process is achieved by the use of a zz-SVM in which a stochastic kernel has been defined. Stochastic kernel includes two similarity measures, based on the local statistics, to detect changes from the images: 1) A distance between maginal probability density functions (pdfs) and 2) the mutual information between the two observations. Distance between marginal pdfs is evaluated by using a series expansion of the Kullbak-Leibler distance. It is achieved by estimating cumulants up to order 4 from a sliding window of fixed size. Mutual information is estimated through a parametric model that is issued from the copulas theory. It is based on rank statistics and yields an analytic expression, that depends on the parameter of the copula only, to be evaluated to obtain the mutual information. Preliminary results are shown on a pair of Radarsat images acquire before and after a lava flow. A ground truth allows to show the accuracy of the stochastic kernels and the SVM decision.

Parametric estimation of non-Gaussian multidimensional probability density function (pdf) is a difficult problem that is required by many applications in signal and image processing. A lot of effort has been devoted to methods from multivariate analysis such as principal or independent component analysis (PCA and ICA). In this work, we introduce an alternative solution based on a very general class of multivariate models called 'copulas'. Useful copulas models for image classification are used in the frame of multidimensional mixture estimation arising in the segmentation of multicomponent images, when using a vectorial hidden Markov chain (HMC).

The hidden Markov field (HMF) model has been used in many model-based solutions to image analysis problems, including that of image segmentation, and generally gives satisfying results. However, when the class image is non stationary, the unsupervised segmentation results provided by HMF can be poor. In this paper, we tackle the problem of modeling a non stationary hidden random field and its effect on the unsupervised statistical image segmentation. We propose an original approach, based on the recent triplet Markov field (TMF) model, to segment non stationary images. Experiments indicate that the new algorithm performs better than the classical one.

The estimation of an unobservable process, x, from an observed process, y, is often performed in the framework of hidden Markov models (HMM). In the linear Gaussian case, the classical recursive solution is given by the Kalman filter. On the other hand, particle filters are Monte Carlo based methods which provide approximate solutions in more complex situations. We consider pairwise Markov models (PMM) by assuming that the pair (x, y) is Markovian. We show that this model is strictly more general than the HMM, and yet still enables particle filtering.

An important problem in signal processing consists in recursively estimating an unobservable process x={x/sub n/}/sub n/spl isin/IN/ from an observed process y={y/sub n/}/sub n/spl isin/IN/. This is done classically in the framework of hidden Markov models (HMM). In the linear Gaussian case, the classical recursive solution is given by the well-known Kalman filter. We consider pairwise Gaussian models by assuming that the pair (x, y) is Markovian and Gaussian. We show that this model is strictly more general than the HMM, and yet still enables Kalman-like filtering.

This work extents the hidden Markov chain (HMC) model for the unsupervised segmentation of multicomponent images. Although the vectorial extension of the model is almost straightforward, we are faced to the problem of estimating a mixture of nonGaussian multidimensional densities. In this work, we adopt an independent component analysis (ICA) approach that allows the mutual dependance between the layers to be taken into account in the segmentation process. Classification results on a four bands SPOT-IV image illustrates the method. Also, a comparison is performed when only mutual independence or correlation between the components is assumed.

A Markov chain model is applied for the segmentation of oil slicks acquired by SAR sensors. Actually, oil slicks have specific impact on ocean wave spectra. Initial wave spectra may be characterized by three kinds of waves, big, medium and small, which correspond physically to gravity and gravity-capillary waves. The increase of viscosity due to the presence of oil damps gravity-capillary waves. This induces a damping of the backscattering to the sensor, but also a dampening of the energy of the wave spectra. Thus, local segmentation of wave spectra may be achieved by the segmentation of a multiscale decomposition of the original SAR image. In this work, the unsupervised segmentation is achieved by using a vectorial extension of the Hidden Markov Chain (HMC) model. Parameters estimation is performed using the general Iterative Conditional Estimation (ICE) method. The problem of estimating multi-dimensional and non-Gaussian densities is solved by using a Principal Component Analysis (PCA). The algorithm has been applied on an ERS-PRI image. It yields interesting segmentation results with a very limited number of false alarms. Also, the multiscale segmentation proved to be an interesting alternative to classify marginal or degraded slicks.

We propose a model called a pairwise Markov chain (PMC), which generalizes the classical hidden Markov chain (HMC) model. The generalization, which allows one to model more complex situations, in particular implies that in PMC the hidden process is not necessarily a Markov process. However, PMC allows one to use the classical Bayesian restoration methods like maximum a posteriori (MAP), or maximal posterior mode (MPM). So, akin to HMC, PMC allows one to restore hidden stochastic processes, with numerous applications to signal and image processing, such as speech recognition, image segmentation, and symbol detection or classification, among others. Furthermore, we propose an original method of parameter estimation, which generalizes the classical iterative conditional estimation (ICE) valid for a classical hidden Markov chain model, and whose extension to possibly non-Gaussian and correlated noise is briefly treated. Some preliminary experiments validate the interest of the new model.

Due 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 presented.

In non-Rayleigh distributed radar images, the number of scatterers can be viewed as a Poisson distributed random variable, with the mean itself random. When this mean is Gamma distributed, then the image classically satisfies the K distribution. We add three new possible distributions for this mean: inverse Gamma, Beta of the first kind, and Beta of the second kind. We show that new intensity distributions so obtained can be estimated, with the interest of the extension validated on a real image.

This paper deals with the statistical segmentation of multisensor images. In a Bayesian context, the interest of using hidden Markov random fields, which allows one to take contextual information into account, has been well known for about 20 years. In other situations, the Bayesian framework is insufficient and one must make use of the theory of evidence. The aim of the authors' work is to propose evidential models that can take into account contextual information via Markovian fields. They define a general evidential Markovian model and show that it is usable in practice. Different simulation results presented show the interest of evidential Markovian field model-based segmentation algorithms. Furthermore, an original variant of generalized mixture estimation, making possible the unsupervised evidential fusion in a Markovian context, is described. It is applied to the unsupervised segmentation of real radar and SPOT images showing the relevance of the proposed models and corresponding segmentation methods in real situations.

This paper deals with unsupervised Bayesian classification of multidimensional data. We propose an extension of a previous method of generalized mixture estimation to the correlated sensors case. The method proposed is valid in the independent data case, as well as in the hidden Markov chain or field model case, with known applications in signal processing, particularly speech or image processing. The efficiency of the method proposed is shown via some simulations concerning hidden Markov fields, with application to unsupervised image segmentation.

The problem addressed in this paper is that of statistical segmentation of images using hidden Markov models. The problem is to introduce a prior evidential knowledge, defined by a mass function, or equivalently, by a belief function. We notice that the result of the Dempster-Shafer fusion of an evidential Markov field with a probability provided by the observations is not necessarily a Markov field. Thus using classical Bayesian segmentation as MPM or MAP is not tractable. In order to solve this problem, we show that the use of Markov trees, which is another way of modelling the spatial dependence of the class random process, leads to tractable segmentation methods. In fact, the Dempster-Shafer fusion does not destroy the Markovianity in the a posteriori distribution and thus the classical Bayesian segmentation methods like as MPM or MAP may used. Furthermore, some ways of the model parameter estimation are indicated.

This paper attacks the problem of generalized multisensor mixture estimation. A distribution mixture is said to be generalized when the exact nature of components is not known, but each of them belongs to a finite known set of families of distributions. Estimating such a mixture entails a supplementary difficulty: one must label, for each class and each sensor, the exact nature of the corresponding distribution. Such generalized mixtures have been studied assuming that the components lie in the Pearson system. We propose a more general procedure with applications to estimating generalized multisensor hidden Markov chains. Our proposed method is applied to the problem of unsupervised image segmentation. The method proposed allows one to: 1) identify the conditional distribution for each class and each sensor, 2) estimate the unknown parameters in this distribution, 3) estimate priors, and 4) estimate the "true" class image.

This paper addresses the estimation of fuzzy Gaussian distribution mixture with applications to unsupervised statistical fuzzy image segmentation. In a general way, the fuzzy approach enriches the current statistical models by adding a fuzzy class, which has several interpretations in signal processing. One such interpretation in image segmentation is the simultaneous appearance of several thematic classes on the same site. We introduce a new procedure for estimating of fuzzy mixtures, which is an adaptation of the iterative conditional estimation (ICE) algorithm to the fuzzy framework, We first describe the blind estimation, i.e., without taking into account any spatial information, valid in any context of independent noisy observations. Then we introduce, in a manner analogous to classical hard segmentation, the spatial information by two different approaches: contextual segmentation and adaptive blind segmentation. In the first case, the spatial information is taken into account at the segmentation step level, and in the second case it is taken into account at the parameter estimation step level. The results obtained with the iterative conditional estimation algorithm are compared to those obtained with expectation-maximization (EM) and the stochastic EM algorithms, on both parameter estimation and unsupervised segmentation levels, via simulations. The methods proposed appear as complementary to the fuzzy C-means algorithms.

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.

This work addresses the problem of unsupervised multisensor image segmentation. We propose the use of a recent method which estimates parameters of generalized multisensor hidden Markov chains. A hidden Markov chain is said to be "generalized" when the exact nature of the noise components is not known; we assume however, that each of them belongs to a finite known set of families of distributions. The observed process is a mixture of distributions and the problem of estimating such a "generalized" mixture contains a supplementary difficulty: one has to label, for each state and each sensor, the exact nature of the corresponding distribution. The general ICE-TEST method recently proposed allows one to solve such problems.

This paper deals with the problem of unsupervised Bayesian segmentation of images modeled by Markov random fields (MRF). If the model parameters are known then we have various methods to solve the segmentation problem (simulated annealing, ICM, etc...). However, when they are not known, the problem becomes more difficult. One has to estimate the hidden label field parameters from the available image only. Our approach consists of a recent iterative method of estimation, called iterative conditional estimation (ICE), applied to a monogrid Markovian image segmentation model. The method has been tested on synthetic and real satellite images.

The aim of our paper is to present a new unsupervised Bayesian image segmentation method using a recent model by hidden fuzzy Markov fields. The main problem of parameter estimation is solved using a recent general method of estimation regarding hidden data, called iterative conditional estimation (ICE). This has been successfully applied in classical hidden Markov fields based segmentations. The first part of our work involves estimating the parameters defining the Markovian distribution of the fuzzy picture without noise. We then combine this algorithm with the ICE method in order to estimate all the parameters of the noisy picture.

Statistical unsupervised image segmentation using fuzzy random fields is treated. A fuzzy model containing a hard component, which describes pure pixels, and a fuzzy component which describes mixed pixels, is introduced. A procedure for simulating, a fuzzy field based on a Gibbs sampler step followed by a second step involving white or correlated Gaussian noises is given. Then the different steps of unsupervised image segmentation are studied. Four different blind segmentation methods are performed: the conditional expectation, two variants of the maximum likelihood, and the least squares approach. The parameters required are estimated by the stochastic estimation maximization (SEM) algorithm, a stochastic variant of the expectation maximization (EM) algorithm. These fuzzy segmentation methods are compared with a classical hard segmentation method, without taking the fuzzy class into account. The study shows that the fuzzy SEM algorithm provides reliables estimators. Furthermore, fuzzy segmentation always improves upon the hard segmentation results.>

The work addresses Bayesian unsupervised satellite image segmentation, using contextual methods. It is shown, via a simulation study, that the spatial or spectral context contribution is sensitive to image parameters such as homogeneity, means, variances, and spatial or spectral correlations of the noise. From this one may choose the best context contribution according to the estimated values of the above parameters. The parameter estimation is done by SEM, a densities mixture estimator which is a stochastic variant of the EM (expectation-maximization) algorithm. Another simulation study shows good robustness of the SEM algorithm with respect to different image parameters. Thus, modification of the behavior of the contextual methods, when the SEM-based unsupervised approaches are considered, is limited, and the conclusions of the supervised simulation study stay valid. An adaptive unsupervised method using more relevant contextual features is proposed. Different SEM-based unsupervised contextual segmentation methods, applied to two real SPOT images, give consistently better results than a classical histogram-based method.>

Deals with unsupervised Bayesian segmentation of images. The authors introduce a new algorithm based on a recent general method of estimation in the case of incomplete data (iterative conditional estimation). The efficiency of the method is compared with a recent algorithm based on the stochastic gradient by L. Younes (1989). Results of numerous simulations are given and an application to a real radar image is also derived.>