Can redundancy improve coding efficiency? This research explores the concept of overcomplete representations, where the number of basis vectors exceeds the dimensionality of the input signal. The study investigates an algorithm for learning an overcomplete basis by framing it as a probabilistic model of observed data. Overcomplete codes have also been proposed as a model of some of the response properties of neurons in primary visual cortex. Overcomplete codes have also been proposed as a model of some of the response properties of neurons in primary visual cortex. Previous work has focused on finding the best representation of a signal using a fixed overcomplete basis (or dictionary). The authors reveal that overcomplete bases can better approximate the underlying statistical distribution of data, leading to improved coding efficiency. This approach can be viewed as a generalization of independent component analysis, offering a method for Bayesian reconstruction of signals in the presence of noise and blind source separation when there are more sources than mixtures. The findings have implications for neural coding and signal processing, paving the way for more robust and flexible representation schemes in various applications.
Published in Neural Computation, this research is well aligned with the journal’s focus on theoretical and computational neuroscience. By proposing an algorithm for learning overcomplete representations and demonstrating its potential for improved coding efficiency, the study contributes to the journal's scope by addressing fundamental questions in neural coding and information processing.