Natural image representation by redundancy reduction inspired by neuroscience
In my thesis, statistical modeling of natural images has been investigated. In recent years, several methods have been proposed for this problem which are mainly founded on the statistical independence among the components of the model. A principal assumption in these models is that the entire space of data is able to be described by a single coordinate frame.
In my thesis, a method based on mixture models is proposed to obtain a better understanding of the internal statistical structure of natural image. This method is able to separate image components and describe each component in a specific coordinate frame. To this aim, an analytical model of Independent Component Analysis (ICA) is extended to a mixture of Independent Component Analysis (MoICA) model and an efficient method is proposed to solve it. From the computational point of view, two methods are implemented and investigated for estimation the statistical model: one based on calculus of variations and the other based on manifold optimization. It is observed that the manifold optimization method shows a better performance with respect to time and local minima avoidance. Meanwhile, calculus of variation method is used as a tool for separating image components due to its flexibility in modeling the prior knowledge by imposing prior probabilities over parameters and hyper-parameters.
In mixture models, the issue of model selection and specifically determining the number of mixture components is of fundamental importance. Therefore, a specific season of this thesis is dedicated to this problem. This season proposes a more accurate approximation of marginal likelihood specifically to mixture models. Investigations and results of this season can be used in the model selection researches beyond my thesis.
Improved Bayesian information criterion for mixture model selection
Pattern Recognition Letters, 2016
Mixture of ICAs model for natural images solved by manifold optimization method
IKT2015 7th International Conference on Information and Knowledge Technology, 2015