Still image compression with multiple overlapping local cosine bases

This paper investigates several multiple overlapping transform based image coders. For better image representation, decorrelation and energy compaction the coders are based on new and powerful classes of multiple overlapping localized trigonometric bases (LCB-x, x>2). The compression results outperform the wavelet coders SPIHT [A. Said et al., June 1996] and JPEG2000 [S. Trautmann] for various test images in both objective and subjective coding performance. In the last years, much of the research activities in image coding have been focused on the discrete wavelet transform (DWT), which avoids blocking artifacts. Several new classes of multiple overlapping localized cosine bases [K. Bittner, 2002, A. Mali et al., 2003] can also eliminate completely blocking artifacts. Additionally unlike the wavelet transform, textures and oscillating patterns in a lot number of images are well preserved using trigonometric bases [F.G. Meyer, June 2002]. This provides significant improvements in reconstructed image quality over the discrete cosine transform and the discrete wavelet transform. First we recall the main results on multiple overlapping trigonometric bases. To solve the problem of infinite dual trigonometric bases, various sequences of new window functions for finite signals are introduced. Then, with aid of the generalized unfolding operator we propose fast algorithms for signal analysis and synthesis. Finally, we apply the transforms for image compression.