Sparse Source Separation Of Non-Instantaneous Spatially Varying Single Path Mixtures

We present a method for recovering source images from their non-instantaneous single path mixtures using sparse component analysis (SCA). Non-instantaneous single path mixtures refer to mixtures generated by a mixing system that spatially distorts the source images (non-instantaneous and spatially varying) without any reverberations (single path/anechoic). For example, such mixtures can be found when imaging through a semi-reflective convex medium or in various movie fade effects. Recent studies have used SCA to separately address the time/position varying and the non-instantaneous scenarios. The present study is devoted to the unified scenario. Given n anechoic mixtures (without multiple reflections) of m source images, we recover the images up to a limited number of unknown parameters. This is accomplished by means of correspondence that we establish between the sparse representation of the input mixtures. Analyzing these correspondences allows us to recover models of both spatial distortion and attenuation. We implement a staged method for recovering the spatial distortion and attenuation, in order to reduce parametric model complexity by making use of descriptor invariants and model separability. Once the models have been recovered, well known BSS tools and techniques are used in recovering the sources.