Fast parametric reciprocal-orthogonal jacket transforms

Abstract

In this paper, we propose a new construction method for a novel class of parametric reciprocal-orthogonal jacket transform (PROJT) having 9 4 N parameters for a sequence length N = 2 r+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.

Fast Jacket-Haar Transform with Any Size

“…In the later aspect, block Jacket transforms have been tentatively applied to quantum signal processing [10], Big-Data processing [11], emerging new-generation mobile communication, and so on. In addition, new orthogonal transforms, such as complex Hadamard transform [12][13][14], fractional Hadamard or Jacket transforms [15], parametric transforms [16][17][18], hybrid transforms [7], and the generalized orthogonal transforms [14], have been gradually proposed while enriching the orthogonal transform family. Particularly, with advancement of digital systems and widespread availability in the recent few decades, there exist some urgent demands for seeking a scheme to achieve compromise between the generalization efficiencies of Hadamard or Haar transforms and their the extended transforms to adaptively meet the practical implementation requirements.…”