Holographic Image Coding and Neurocomputer Architectures

Abstract

The development of more powerful computers in recent years has been driven by a seemingly unending thirst for automation, control issues, information availability, and a yearning for new understanding of the self-organization principles of ourselves and our environment. The challenges of the future force to create and study new concepts of adaptive information processing and to implement novel computer architectures based on synergetic principles. Up until now, the increased power has been driven largely by advancements in microelectronics, such as electronic switches (transistors) with higher switching speeds and integrated circuits (ICs) with increased levels of integration. Although the advancements in the IC wiring and packaging functions have been significant, their prospect for continuing at the same steady rates from very large scale integration (VLSI) to ultra large scale integration (ULSI) are being dimmed by physical limitations associated with further miniaturization.As a result, computer architects are turning to the design of parallel processors to continue the drive toward more powerful computers. The system of interconnections by which the processing elements can share information among themselves is one of the most important characteristics of any parallel computer. The massively parallel organization principles which distinguish analog neural systems from the small scale interconnection architectures of special-purpose parallel electronic processors and even more from the von Neumann architecture of standard digital computer hardware are one of the main reasons for the largely emerging interest in neurocomputers. Just as photonics is becoming the technology of the future for telecommunications, it also will affect communications within computers, especially for parallel computer architectures and even more for neurocomputer architectures. Not only does coherent light emitted by a laser have a much higher information capacity than electrical wires, but optical beams can pass through one another without interfering, leading to a very high packing density of free-space holographic optical interconnects. Holographic optical interconnect technology underlies the fundamental fact that in the quantized theory of the electromagnetic field the bosons (integral-spin particles) present in a beam of coherent light travelling in a well-defined direction are the photons. Based on a unified nilpotent harmonic analysis approach to artificial neural network models implemented with coherent optical, optoelectronic, or analog electronic neurocomputer architectures, the paper establishes a new identity for the matching polynomials of complete bichromatic graphs which connect neurons located in the neural plane. The key idea is to identify in a first step the hologram plane with the three-dimensional Heisenberg nilpotent Lie group quotiented by its one-dimensional center, then to restrict in a second step the holographic transform o ∼p H H(∼,∼p;.,.) to the holographic lattices which form two=dimensional pixel arrays inside the hologram plane, and finally to recognize in a thirdstep by canonical quantization the hologram plane as a neural plane. The quantum mechanical treatment of optical holography is imperative in microoptics and nanotechnology since atoms coherently excited by short laser pulses may be as large as some transistors of microelectronic ICs and the pathways between them inside the hybrid VLSI neurochips of amacronics.