Lapped Transforms: A Graph-based Extension

Abstract

Lapped transforms are transform coding tools with basis functions that overlap across blocks in order to reduce blocking artifacts. In this work, we take the uniform line graph model interpretation of the discrete cosine transform (DCT) and extend it to lapped transforms. We first extend the conditions of perfect reconstruction and orthogonality to lapped transforms on graphs, where different transforms are allowed for different blocks. Then, with the focus on line graphs, we design a lapped graph Fourier transform (LGFT) that has these properties, with significantly reduced blocking artifact. Experimental results show that the proposed LGFT can achieve improved transform coding gain as compared to other existing transforms.