Multiresolutional piecewise-linear image decompositions: Quantization error propagation and design of `stable' compression schemes

A new approach to the design of stable tile-effect-free multiresolutional image compression schemes is introduced. The paper focuses on how quantization errors in decomposition coefficients affect the quality of the decompressed picture, how errors propagate in a multidimensional decomposition, and how to design a compression scheme where the effect of quantization errors is minimized (visually and quantitatively). Also introduced and analyzed is the simplest family of Laplacian pyramids which yield multiresolutional piecewise linear image decompositions. The error propagation analysis presented has lead to the discovery of particular Laplacian pyramids where quantizations errors do not amplify as they propagate but quickly decay.