Nonlinear Approximation and Image Representation using Wavelets

We address the problem of finding sparse wavelet representations of high-dimensional vectors. We present a lower-bounding technique and use it to develop an algorithm for computing provably-approximate instance-specific representations minimizing general p distances under a wide variety of compactly-supported wavelet bases. More specifically, given a vector f ∈ Rn , a compactly-supported wavelet basis, a sparsity constraint B ∈ Z, and p ∈ [1, ∞], our algorithm returns a B-term representation (a linear combination of B vectors from the given basis) whose p distance from f is a O(log n) factor away from that of the optimal such representation of f. Our algorithm applies in the one-pass sublinear-space data streaming model of computation, and it generalize to weighted p-norms and multidimensional signals. Our technique also generalizes to a version of the problem where we are given a bit-budget rather than a term-budget. Furthermore, we use it to construct a universal represen...

• Type: Conference
• Year: 2007
• Where: DAGSTUHL
• Authors: Sudipto Guha, Boulos Harb
• Keywords: Compactly-supported Wavelet, Compactly-supported Wavelet Bases, DAGSTUHL 2007, Software Engineering, Sparse Wavelet Representations