In this paper, we propose novel algorithms for total variation (TV) based image restoration and parameter estimation utilizing variational distribution approximations. Within the hierarchical Bayesian formulation, the reconstructed image and the unknown hyperparameters for the image prior and the noise are simultaneously estimated. The proposed algorithms provide approximations to the posterior distributions of the latent variables using variational methods. We show that some of the current approaches to TV-based image restoration are special cases of our framework. Experimental results show that the proposed approaches provide competitive performance without any assumptions about unknown hyperparameters and clearly outperform existing methods when additional information is included.

This paper addresses the issue of estimating underwater vehicle trajectories using Gyro-Doppler (body-xed velocities) and acoustic signals (earth-xed positions). The approach consists of diffusion-based observers processing a whole trajectory segment at a time, allowing to consider important practical problems such as different information update rates, outages, and outliers in a very simple framework. Results of [10] are used to prove that the observers are contracting, i.e. convergent in the sense of contraction analysis. Simulation and experimental results are presented to illustrate the potential of application of the method.