A new transform of trinary vectors, called pseudo-Hadamard transform, is introduced. This transform is a one-to-one mapping in a trinary vector space and very similar to the Hadamard transform. To define the pseudo-Hadamard transform, the Good's formula for the fast Hadamard transform of N( = 2n ) dimension HN = T1T2...Tn is used, where the transform T. ( i = 1,2,...,n ) consists of N additions and subtractions. The pseudo-Hadamard transform'is defined by replacing the additions and the subtractions with kinds of trinary operations. This transform preserves some properties of the Hadamard transform and is also very easy to perform. As applications of the pseudo-Hadamard transform, examples of binary image processing are presented.
"Pseudo-Hadamard Transform For Image Processing", Proc. SPIE 0435, Architectures and Algorithms for Digital Image Processing, (9 January 1984); doi: 10.1117/12.936964; https://doi.org/10.1117/12.936964