This paper addresses the problem of finding a B-term wavelet representation
of a given discrete function f∈ℜn whose distance from f is
minimized. The problem is well understood when we seek to minimize the
Euclidean distance between f and its representation. The first known algorithms
for finding provably approximate representations minimizing general ℓp
distances (including ℓ∞) under a wide variety of compactly supported
wavelet bases are presented in this paper. For the Haar basis, a polynomial
time approximation scheme is demonstrated. These algorithms are applicable in
the one-pass sublinear-space data stream model of computation. They generalize
naturally to multiple dimensions and weighted norms. A universal representation
that provides a provable approximation guarantee under all p-norms
simultaneously; and the first approximation algorithms for bit-budget versions
of the problem, known as adaptive quantization, are also presented. Further, it
is shown that the algorithms presented here can be used to select a basis from
a tree-structured dictionary of bases and find a B-term representation of the
given function that provably approximates its best dictionary-basis
representation.Comment: Added a universal representation that provides a provable
approximation guarantee under all p-norms simultaneousl