INVESTIGATION OF HYPERDISTRIBUTIONS FOR SIGNAL COMPRESSION

WE DEVELOP HERE A TECHNIQUE FOR SIGNAL COMPRESSION/DECOMPRESSION BASED ON NEW ADVANCES IN THE THEORY OF GENERALIZED FUNCTIONS. WE TERM THESE NEW MATHEMATICAL OBJECTS "GENERALIZED DISTRIBUTIONS" OR "HYPERDISTRIBUTION"/ WE PROPOSE TO DETERMINE THE COMPRESSION RATIOS WHICH MAY BE OBTAINED BY REPRESENTING IMAGE DATA IN TERMS OF A TRUNCATED HYPERDISTRIBUTION SERIES, RATHER THAN THE ORIGINAL COLLECTION OF PIXEL INTENSITIES. HYPERDISTRIBUTIONS EXHIBIT INTERESTING MATHEMATICAL PROPERTIES UNDER CONVOLUTION OPERATIONS, AND SO THE POSSIBILITY EXISTS THAT IMAGE PROCESSING OPERATIONS CAN BE COMBINED WITH SIGNAL COMPRESSION/DECOMPRESSSION, AND IN PARTICULARLY THAT PARTICULAR CLASSES OF IMAGE PROCESSING OPERATIONS MAY BE CARRIED OUT ON COMPRESSED DATA SETS, WITH CORRESPONDING GAINS IN PROCESSING TIME.