Warped discrete cosine transform and its application in image compression

This paper introduces the concept of warped discrete cosine transform (WDCT) and an image compression algorithm based on the WDCT. The proposed WDCT is a cascade connection of a conventional DCT and all-pass filters whose parameters can be adjusted to provide frequency warping. Because only the first-order all-pass filters are considered, the WDCT can be implemented by a Laguerre network connected with the DCT. For the more efficient software implementation, we propose truncated and approximated FIR filter banks which can be used instead of the Laguerre network. As a result, the input-output relationship of the WDCT can be represented by a single matrix-vector multiplication, like the DCT. In the proposed image-compression scheme, the frequency response of the all-pass filter is controlled by a fixed set of parameters from which a specified warping parameter is used for a specified frequency range. Also, for each parameter, the corresponding WDCT matrices are computed a priori. For each image block, the best parameter is chosen from the set and the index is sent to the decoder as side information along with the result of corresponding WDCT matrix computation. At the decoder, an inverse WDCT is performed to reconstruct the image. The WDCT based compression outperforms the DCT based compression, for high bit rate applications and for images with high-frequency components. It results in 1.1-3.1-dB PSNR gain over conventional DCT at 1.5 bpp for natural images, and provides more gain for compound images with texts.