Parallel optical arithmetic on images by a redundant binary number representation.

Quick and efficient processing of images is an important request of various disciplines and several applied fields. Many authors have studied specialized computing architectures (with electronic technology) devoted to image processing (see, for example, Refs. 1-5), but other authors have pointed out that optical computing architectures are more suitable for massive computation on images because of the 2-D inherent structure both of data (images) and DOC (digital optical computing) architectures. In recent works67 Huang et al. showed a complete formal approach to a 2-D binary algebra and related arithmetic oriented to 2-D objects. In the second work (regarding a parallel optical arithmetic on images, with emphasis on the symbolic substitution methods-") the use of redundant number representations is neglected in spite of several works about this subject related to optical computing systems. Redundant number systems can have important properties such as the carry-free addition (namely, the possibility to carry out addition in constant time independent of the bit strings length k).'2-'6 In optical image arithmetic a novel redundant binary (RB) number representations can be used. In the RB representation an integer D is given by