Fast DCT-domain filtering using frequency division processing

This paper presents a new scheme for the development of efficient DCT-domain algorithms based on frequency division processing (FDP). In this scheme, a manipulation in the DCT domain is decomposed into multiple simple operations, each of which is performed independently on certain sets of DCT coefficients. Using FDP we designed a fast DCT-domain algorithm for two-dimensional convolution. The algorithm, according to both theoretical analysis of computational complexity and experimental results, is more efficient than traditional spatial-domain convolution algorithms as well as other compressed-domain convolution algorithms. The performance is several times higher for kernel size beyond 5 and comparable for smaller kernel size. In addition, convolution performed directly in the compressed domain can achieve a slightly higher precision due to the removal of decompression artifacts.