Fast Integer Sine-Cosine Transforms of Order 4 and Simplified Sine-Cosine Transforms of Order 8

Introduction. A matrix method for constructing one-norm sine-cosine transforms of type II of order 4 has been developed, which has better efficiency compared to the known sine transform of type II. An integer one-norm sine-cosine transform of type II of order 4 has been proposed, and on its basis an integer one-norm simplified sine-cosine transform of order 8 of low computational complexity has been developed. Fast calculation algorithms for the proposed transforms have been considered. The computational complexity of the simplified sine-cosine transform of type II of order 8 is only 40 operations, which is three times less than the computational complexity of the known sine transform of type VII of order 8, and the compression ratio is 1.5-2.3% lower, as shown by the presented experimental results. The proposed integer one-norm simplified sine-cosine transform of order 8 can be used for image and signal analysis and coding tasks, in particular for separable adaptive transforms as an alternative to the sine transform of type VII for high-speed and extreme coding modes. Two simplified modes for adaptive separable transforms are proposed: mode A, which uses two combinations out of four total, namely 2D cosine and split cosine/sine; mode B, which uses three combinations out of four, excluding the sine/sine variation. As an alternative to the type VII sine transform in the separable transform scheme for adaptive application in high-speed modes, a modified type II sine transform is proposed, which consistently compresses 0.3 % better than the classic type II sine transform, and lags behind the type VII sine transform by 1.2–1.4 %. Keywords: discrete sine-cosine transform, integer sine-cosine transform, simplified sine-cosine transform, adaptive separable transforms, factorization, computational complexity, Hadamard transform, Haar transform, Haar-Hadamard transform, hybrid transforms.