Abstract
Discrete cosine transform (DCT) has been an international standard in Joint Photographic Experts Group (JPEG) format to reduce the blocking effect in digital image compression. This paper proposes a fast discrete cosine transform (FDCT) algorithm that utilizes the energy compactness and matrix sparseness properties in frequency domain to achieve higher computation performance. For a JPEG image of8×8block size in spatial domain, the algorithm decomposes the two-dimensional (2D) DCT into one pair of one-dimensional (1D) DCTs with transform computation in only 24 multiplications. The 2D spatial data is a linear combination of the base image obtained by the outer product of the column and row vectors of cosine functions so that inverse DCT is as efficient. Implementation of the FDCT algorithm shows that embedding a watermark image of 32 × 32 block pixel size in a 256 × 256 digital image can be completed in only 0.24 seconds and the extraction of watermark by inverse transform is within 0.21 seconds. The proposed FDCT algorithm is shown more efficient than many previous works in computation.
Highlights
Discrete cosine transform (DCT) has been widely used to convert a dynamic signal into frequency components so as to reduce digital image storage size, expedite data transmission, and remove redundant information
DCT is closely related to discrete Fourier transform with the advantage of concentrating the energy of transformed signal in low frequency range where human eyes are less sensitive in image processing [1]
DCT can map an original data into frequency domain by cosine waveform, and inverse discrete cosine transform (IDCT) transfers frequency domain data into spatial domain
Summary
Discrete cosine transform (DCT) has been widely used to convert a dynamic signal into frequency components so as to reduce digital image storage size, expedite data transmission, and remove redundant information. Numerous coding methods based on DCT have been presented for digital image processing; the associated memory size, bandwidth, and safety issues are of significant concern to real-time applications. Jridi et al [5] designed a low complexity DCT engine in digital video and image processing. Subband decomposition algorithms based on DCT have been used in transmitting image data of low resolution to rebuilt image of better quality [6–8], but they required high complexity and time-consuming computation. This paper proposes a fast DCT (FDCT) algorithm with significantly reduced number of multiplications to achieve higher computation efficiency in digital image processing. It is shown suitable for hardware implementation in DSP on digital watermarking applications
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