Image Separation Using Particle Filters

In this work, we will analyze the problem of source separation in the case of superpositions of different source images, which need to be extracted from a set of noisy observations. This problem occurs, for example, in the field of astrophysics, where the contributions of various Galactic and extra-Galactic components need to be separated from a set of observed noisy mixtures. Most of the previous work on the problem performed blind source separation, assuming noiseless models, and in the few cases when noise is taken into account assumed Gaussianity and space-invariance. We present a novel technique, namely particle filtering, for the solution of the source separation problem: it is an advanced Bayesian estimation method which can deal with non-Gaussian and non-linear models, and additive space-varying noise, in the sense that it is an extension of the Kalman filter. Our simulations on realistic astrophysical data show that the particle filter provides significantly better results in comparison with one of the most widespread algorithms for source separation (FastICA), especially in the case of low SNR.