Learning Overcomplete Spatiotemporal Bubbles from Natural Image Sequences

Recently, bubble coding for natural image sequences has been proposed. This method unified three important statistical properties: sparseness, temporal coherence, and topographic dependencies. However, this approach does not consider the overcomplete case. It is widely believed that the overcomplete representation is more efficient than the complete representation. In this paper, we use Bayesian estimation to extend the bubble coding into overcomplete case. Based on a quasi-orthogonality in a high-dimensional space, the prior probability of the mixing matrix is derived. Instead of examining basis coefficient, we investigate the dot product between basis functions and whitened observed data vectors for their sparseness and the advantage in the Bayesian model. Based on the bubble detector definition, an approximation of the prior probability of this dot product is given. Simulation results suggest that the overcomplete bubble coding can be achieved by a Bayesian inference. The model is promising in a wide variety of applications, such as image processing and pattern recognition.