Compressing the Laplacian Pyramid

The Laplacian pyramid (LP) is one of the earliest examples of multiscale representation of visual data. It is well known that an LP is overcomplete or redundant by construction, 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 through critical representation. We consider an LP with biorthogonal decimation and interpolation filters, and show that the detail signals lie in lower-dimensional subspaces. This allows them to be represented using fewer coefficients than the original spatial representations. We derive orthogonal bases for these subspaces and represent the detail signals in terms of their projections onto these bases. Simulation results suggest that higher compression ratios can be achieved with the critical representation than with the standard LP with usual or dual frame based reconstructions