Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations

We present algorithms for the type-IV discrete cosine transform (DCT-IV) and discrete sine transform (DST-IV), as well as for the modified discrete cosine transform (MDCT) and its inverse, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from ~2NlogN to ~(17/9)NlogN for a power-of-two transform size N, and the exact count is strictly lowered for all N > 4. These results are derived by considering the DCT to be a special case of a DFT of length 8N, with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split radix algorithm). The improved algorithms for DST-IV and MDCT follow immediately from the improved count for the DCT-IV.Comment: 11 page

Fast image decompression for telebrowsing of images

Progressive image transmission (PIT) is often used to reduce the transmission time of an image telebrowsing system. A side effect of the PIT is the increase of computational complexity at the viewer's site. This effect is more serious in transform domain techniques than in other techniques. Recent attempts to reduce the side effect are futile as they create another side effect, namely, the discontinuous and unpleasant image build-up. Based on a practical assumption that image blocks to be inverse transformed are generally sparse, this paper presents a method to minimize both side effects simultaneously