New classes of quaternary linearly independent arithmetic transforms

New quaternary linearly independent arithmetic (QLIA) transforms are presented in this paper. The new transforms are recursive and they are classified into two classes according to their recursive equations. Fast flow graphs and relations for the transforms are presented. Computational cost for the calculation of the QLIA spectral coefficient vector is also derived. Experimental results in terms of the minimum number of nonzero spectral coefficients based on the QLIA transforms for a set of quaternary test functions are also given and compared with the corresponding numbers for quaternary fixed polarity arithmetic (QFPA) transforms. The comparison shows that for the set of quaternary test functions the average number of minimum number of nonzero spectral coefficients based on the introduced QLIA transforms is 39.28% and 16.29% smaller than that for the polarity zero and optimal polarity QFPA transforms, respectively.