Discrete cosine transform(DCT) has been an international standard in Joint Photographic Experts Group (JPEG) format to reduce\nthe blocking effect in digital image compression. This paper proposes a fast discrete cosine transform(FDCT) algorithmthat utilizes\nthe energy compactness and matrix sparseness properties in frequency domain to achieve higher computation performance. For\na JPEG image of 8 Ã?â?? 8 block size in spatial domain, the algorithm decomposes the two-dimensional (2D) DCT into one pair of\none-dimensional (1D) DCTs with transform computation in only 24 multiplications.The 2D spatial data is a linear combination of\nthe base image obtained by the outer product of the column and row vectors of cosine functions so that inverse DCT is as efficient.\nImplementation of the FDCT algorithm shows that embedding a watermark image of 32 Ã?â?? 32 block pixel size in a 256 Ã?â?? 256 digital\nimage can be completed in only 0.24 seconds and the extraction of watermark by inverse transform is within 0.21 seconds. The\nproposed FDCT algorithm is shown more efficient than many previous works in computation.
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