The discrete cosine transform (DCT) is a technique for converting a signal into elementary frequency components. It is widely used in image compression. Here we develop some simple functions to compute the DCT and to compress images.
These functions illustrate the power of Mathematica in the prototyping of image processing algorithms. The rapid growth of digital imaging applications, including desktop publishing, multimedia, teleconferencing, and high-definition television (HDTV) has increased the need for effective and standardized image compression techniques.
Among the emerging standards are JPEG, for compression of still images, MPEG, for compression of motion video, and CCITT H.261 (also known as Px64), for compression of video telephony and teleconferencing. All three of these standards employ a basic technique known as the discrete cosine transform (DCT).
The DCT is a close relative of the discrete Fourier transform (DFT). Its application to will develop some simple functions to compute the DCT and show how it is used for image compression. We have used these functions to explore methods of optimizing image compression for the human viewer, using information about the human visual system .
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