Bayesian estimation of overcomplete independent feature subspaces for natural images

Authors:
Libo Ma;Liqing Zhang
Affiliations:
Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China;Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China
Venue:
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Year:
2007

Citing 3
Cited 1

Estimating Overcomplete Independent Component Bases for Image Windows

Journal of Mathematical Imaging and Vision
Topographic Independent Component Analysis

Neural Computation
Emergence of Phase- and Shift-Invariant Features by Decomposition of Natural Images into Independent Feature Subspaces

Neural Computation

Separation theorem for independent subspace analysis and its consequences

Pattern Recognition

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Abstract

In this paper, we propose a Bayesian estimation approach to extend independent subspace analysis (ISA) for an overcomplete representation without imposing the orthogonal constraint. Our method is based on a synthesis of ISA [1] and overcomplete independent component analysis [2] developed by Hyvärinen et al. By introducing the variables of dot products (between basis vectors and whitened observed data vectors), we investigate the energy correlations of dot products in each subspace. Based on the prior probability of quasi-orthogonal basis vectors, theMAP (maximum a posteriori) estimation method is used for learning overcomplete independent feature subspaces. A gradient ascent algorithm is derived to maximize the posterior probability of the mixing matrix. Simulation results on natural images demonstrate that the proposed model can yield overcomplete independent feature subspaces and the emergence of phase- and limited shift-invariant features--the principal properties of visual complex cells.