Fast parametric reciprocal-orthogonal jacket transforms

In this paper, we propose a new construction method for a novel class of parametric reciprocal-orthogonal jacket transform (PROJT) having 4N parameters for a sequence length N = 2r+1 that is a power of two, based on the reciprocal-orthogonal parametric (ROP) transform and block diagonal matrices. It is shown that the inverse transform of the proposed PROJT is conveniently obtained by the reciprocal of each elements of the forward matrix and transpose operation. What is more, an efficient algorithm for the computation of the PROJT has been developed with the aid of the matrix decomposition and Kronecker product. Further, the experiments show that the independent parameters in the proposed PROJT are successfully used as additional secret keys for image encryption, watermarking, and error-correcting codes.