Approximate Sparse Multinomial Logistic Regression for Classification.

We propose a new learning rule for sparse multinomial logistic regression (SMLR). The new rule is the generalization of the one proposed in the pioneering work by Krishnapuram et al. In our proposed method, the parameters of SMLR are iteratively estimated from log-posterior by using some approximations. The proposed update rule provides a faster convergence compared to the state-of the-art methods used for SMLR parameter estimation. The estimated parameters are tested on the pixel-based classification of hyperspectral images. The experimental results on real hyperspectral images show that the classification accuracy of proposed method is also better than those of the state-of-the-art methods.

Unsupervised amplitude and texture classification of SAR images with multinomial latent model.

In this paper, we combine amplitude and texture statistics of the synthetic aperture radar images for the purpose of model-based classification. In a finite mixture model, we bring together the Nakagami densities to model the class amplitudes and a 2-D auto-regressive texture model with t-distributed regression error to model the textures of the classes. A non-stationary multinomial logistic latent class label model is used as a mixture density to obtain spatially smooth class segments. The classification expectation-maximization algorithm is performed to estimate the class parameters and to classify the pixels. We resort to integrated classification likelihood criterion to determine the number of classes in the model. We present our results on the classification of the land covers obtained in both supervised and unsupervised cases processing TerraSAR-X, as well as COSMO-SkyMed data.

Adaptive Langevin sampler for separation of t-distribution modelled astrophysical maps.

We propose to model the image differentials of astrophysical source maps by Student's t-distribution and to use them in the Bayesian source separation method as priors. We introduce an efficient Markov Chain Monte Carlo (MCMC) sampling scheme to unmix the astrophysical sources and describe the derivation details. In this scheme, we use the Langevin stochastic equation for transitions, which enables parallel drawing of random samples from the posterior, and reduces the computation time significantly (by two orders of magnitude). In addition, Student's t-distribution parameters are updated throughout the iterations. The results on astrophysical source separation are assessed with two performance criteria defined in the pixel and the frequency domains.

Bayesian separation of images modeled with MRFs using MCMC.

We investigate the source separation problem of random fields within a Bayesian framework. The Bayesian formulation enables the incorporation of prior image models in the estimation of sources. Due to the intractability of the analytical solution, we resort to numerical methods for the joint maximization of the a posteriori distribution of the unknown variables and parameters. We construct the prior densities of pixels using Markov random fields based on a statistical model of the gradient image, and we use a fully Bayesian method with modified-Gibbs sampling. We contrast our work to approximate Bayesian solutions such as Iterated Conditional Modes (ICM) and to non-Bayesian solutions of ICA variety. The performance of the method is tested on synthetic mixtures of texture images and astrophysical images under various noise scenarios. The proposed method is shown to outperform significantly both its approximate Bayesian and non-Bayesian competitors.