A sparsity-distortion-optimized multiscale representation of geometry

This paper describes the construction of a new multiresolutional decomposition with applications to image compression. The proposed method designs sparsity-distortion-optimized orthonormal transforms applied in wavelet domain to arrive at a multiresolutional representation which we term the Sparse Multiresolutional Transform (SMT). Our optimization operates over sub-bands of given orientation and exploits the inter-scale and intra-scale dependencies of wavelet co-efficients over image singularities. The resulting SMT is substantially sparser than the wavelet transform and leads to compaction that can be exploited by well-known coefficient coders. Our construction deviates from the literature, which mainly focuses on model-based methods, by offering a data-driven optimization of wavelet representations. Simulation experiments show that the proposed method consistently offers better performance compared to the original wavelet-representation and can reach up to 1dB improvements within state-of-the-art coefficient coders.