Fast Reciprocal Jacket Transform With Many Parameters

In this paper, a novel class of element-wise inverse Jacket transforms (EIJT) with many parameters are proposed for signal length N = 3 × 2r. The EIJT has 2N-1 independent parameters. It is shown that the inverse transform of the proposed EIJT can be easily obtained by taking each reciprocal entry of the forward matrix of Jacket transform and then transposing the resulting matrix. Their fast transforms are also developed. Due to their simplicity, the proposed EIJT transforms may be used in many transform-based applications, where their independent parameters may provide more degrees of freedom such as affording an additional secret key in watermarking and encryption applications.