Fast 2D discrete cosine transform on compressed image in restricted quadtree and shading format

Given a compressed image in the restricted quadtree and shading format, this paper presents a fast algorithm for computing 2D discrete cosine transform (DCT) on the compressed grey image directly without the need to decompress the compressed image. The proposed new DCT algorithm takes O(K2 logK + N2) time where the decompressed image is of size N × N and K denotes the number of nodes in the restricted quadtree. Since commonly K < N , the proposed algorithm is faster than the indirect method by decompressing the compressed image first, then applying the conventional DCT algorithm on the decompressed image. The indirect method takes O(N2 logN) time.  2002 Elsevier Science B.V. All rights reserved.