Some Mathematical Properties of a Scheme for Reducing the Bandwidth of Motion Pictures by Hadamard Smearing

The fact t h a t successive frames of a motion picture are often very nearly alike has led to the consideration of schemes which transmit, for each point of the picture, the difference between the amplitude of the present frame and the amplitude of the previous frame. Since 969 970 T H E 13ELL SYSTEM TECHNICAL JOURNAL, J U L Y - A U G U S T 1970 this differential picture* is frequently zero at many points, there is reason to hope t h a t the bandwidth required for transmission of the differential picture could be greatly reduced by appropriate coding. One such coding scheme which has been considered by W. K. P r a t t , J. Kane, and H. C. Andrews, 2 and refined by M. R. Schroeder 1 is the following: let the differential picture be represented by a real n-dimensional vector, v. (For example, if the picture is represented by a 100 X 100 grid, then n = 10000.) Let 3C be an n X n Haclamard matrix, which is a self-orthogonal real matrix all of whose entries are ± 1 , and let the smeared differential picture (or transformed differential picture), x, be defined by x = 3Cv/(?i)*. Let Q be the power-preserving clipping operator, defined by QX