THEORY AND IMPLEMENTATION OF INFOMAX FILTERS FOR THE RETINA

In the first part of this paper we discuss a technical visual sensory system, which in analogy with the retina-includes some preprocessing o f visual information. In so doing, we use an information-theoretic cri terion, the infomax ansatz,; to: optimize the response of the sensory system. In particular, it is shown that the lattice structure of the p hotoreceptor array has to be taken into account. By a discrete Fourier transformation on a triangular lattice we derive the frequency respon se of the infomax filter within the first Brillouin: zone. To illustra te the response properties, infomax filters adapted to different noise levels are applied to images with different signal-to-noise ratios. T his clearly demonstrates the necessity of adaptation of the filter pro perties to the given noise level. Furthermore, it is shown how to effi ciently implement infomax-like filters by simple networks with only ne arest-neighbour interactions. A two-layered network topology proves to be very advantageous in implementing the desired high-pass or low-pas s properties. The network topology allows for adaption of the network to low and high noise levels by simply adjusting the nearest-neighbour couplings. In the second part of this paper, we compare the previousl y described information-theoretic requirements on a visual sensory sys tem with biological facts known from the vertebrate retina. The substa ntial physiological response properties of the vertebrate retina are i n agreement with the main features of the infomax filter. Since availa ble experimental data lacks information which is necessary for a more quantitative comparison, we present suggestions for future experiments . Some key anatomical features of the retina of many vertebrates compa re well with our two-layered implementation of the infomax filter. The analogy, in particular, concerns the adaption mechanism. To illustrat e this point, we summarize some recent experiments which demonstrate t hat in the retina of some species adaption is based on the release of the neuromodulator dopamine by the interplexiform cells. This causes t he horizontal cells to decouple. On the basis of recently gained under standing of the outer plexiform layer of the retina some further hypot heses about the functionality of the retina become obvious and possibl e future experiments To verify or refute them are suggested. Finally, we discuss the infomax approach from a more general point of view. In particular, we show that redundancy is essential to obtaining noise ro bustness of an internal representation of the environment as it is pro duced by a sensory system such as the retina.