A Fixed Point Algorithm for Noisy Time-Dependent Processes Using AR Source Model

Independent component analysis (ICA) is a fundamental and important task in unsupervised learning, that was studied mainly in the domain of Hebbian learning. In this paper, we consider the estimation of the data model of ICA when Gaussian noise is present and the independent components are time dependent. The temporal dependencies are explained by assuming that each source is an autoregressive (AR) process and innovations are independently and identically distributed (i.i.d). A fixed-point algorithm to estimation of the noisy time-dependent processes by maximizing negentropy of innovation when the noise covariance matrix is known. Computer simulations show that the fixed-point algorithm achieves better separation of the noisy mixed signals and noisy mixed images which are difficult to be separated by the basic independent component analysis algorithms, and comparison results verify the fixed-point algorithm converges faster than the existing gradient algorithm and, it is more simple to implement due to it does not need any learning rate.