Representing Laplacian pyramids with varying amount of redundancy

The Laplacian pyramid (LP) is a useful tool for obtaining spatially scalable representations of visual signals such as image and video. However, the LP is overcomplete or redundant and has lower compression efficiency compared to critical representations such as wavelets and subband coding. In this paper, we propose to improve the rate-distortion (R-D) performance of the LP by varying its redundancy through decimation of the detail signals. We present two reconstruction algorithms based on the frame theory and the coding theory, and then show them to be equivalent. Simulation results with various standard test images suggest that, using suitable quantization parameters, it is possible to have better R-D performance over the usual or the dual frame based reconstruction.