Training networks to compensate for irregular sampling

Abstract

A system with regular sampling at the photoreceptor level can reconstruct an accurate estimate of the original image by low-pass filtering the sampled image with a space-invariant filter. Quality reconstruction of images which are irregularly sampled demands space-variant filters. If the reconstruction is to be an interpolation (correct at the sample positions), the impulse response at each sample point must have zero response at all the other sample points. Two learning models are described that use spontaneous activity and lateral spread of activity to make a distance-preserving copy of the receptor arrangement at a higher level in the nervous system and construct a transformation network which converts lateral spread functions into interpolation functions. The learning models do not use external stimuli or reinforcement and can, therefore, be regarded as self-organizing processes, although the adjustment algorithms are error-correctihg rather than competitive in nature. The distance learning process is easily modified to allow variable magnification with eccentricity. The interpolation process provides a mechanism for adding effects of irregular discrete sampling to models of visual processes which take images as input.