Directional Lapped Transforms for Image Coding

This paper presents a scheme to design directional lapped transforms. Lapped transforms can be factorized into lifting steps. By introducing directional operator into each lifting step, the directional lapped transform is constructed. The directional lapped transform proposed not only preserves the advantages of lapped transforms, it also can represent directional signals more efficiently. An image coding scheme using the directional lapped transform is also described. Compared to the state-of-the-art image coding using lapped transform, HD photo, the proposed scheme shows more than 20 dB's gain for artificial images with strong directional correlations. And for natural images, up to 1.5 dB's gain can also be observed.