Improved quadtree algorithm based on joint coding for piecewise smooth image compression

We are present a novel coding algorithm based on the tree structured segmentation, which achieves oracle like rate-distortion (R-D) behavior for a simple class of signals, namely piecewise polynomials in the high bit rate regime. We consider a R-D optimization framework, which employs optimal bit allocation strategy among different signal segments to achieve the best tradeoff between description complexity and approximation quality. First, we describe the basic idea of the algorithm for the 1-D case. It can be shown that the proposed compression algorithm based on an optimal binary tree segmentation achieves the oracle like R-D behavior (D(R) ~ c₀2^-c1R) with the computational cost of the order O(N log N). We then show the extension of the scheme to the 2-D case with the similar R-D behavior without sacrificing the computational ease. Finally, we conclude with some experimental results.