A Measure-Theoretic Variational Bayesian Algorithm for Large Dimensional Problems

作者：Fraysse A^*; Rodet T

来源：SIAM Journal on Imaging Sciences, 2014, 7(4): 2591-2622.

DOI：10.1137/140966575

• ill-posed inverse problems
• variational Bayesian methodology
• sparse signal reconstruction
• infinite dimensional convex optimization

In this paper we provide an algorithm adapted to variational Bayesian approximation. The main contribution is to transpose a classical iterative algorithm of optimization in the metric space of measures involved in Bayesian methodology. Once given the convergence properties of this algorithm, we consider its application to large dimensional inverse problems, especially for unsupervised reconstruction. The interest of our method is enhanced by its application to large dimensional linear inverse problems involving sparse objects. Finally, we provide simulation results. First we show the good numerical performances of our method compared to classical ones on a small example. Then we deal with a large dimensional dictionary learning problem.

• 出版日期2014