Extension of the concept of wavelet to vector functions
S. G. Rafayelyan, Edward Danielian, Jaakko T. Astola, Karen Egiazarian · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2002
Let Ln2 equals L2 (R) X L2 (R) X ... X L2 (R)/n. It is shown how to construct a system of functions {(phi) k (x)} equals {(phi) k(1) (x), (phi) k(2) (x), ..., (phi) k(n) (x)} from Ln2 which satisfies the following conditions: (1) After normalization it forms a Riesz basis in Ln2; (2) For any given set of functions [f1(x), f2(x), ..., fn(x)] (summation) Ln2 the representations fj(x) equals (Sigma) /k ck (DOT) (phi) k(j) (x), x (summation) R, j equals 1,n, hold, where the coefficients ck are defined from {(phi) k (x)} and [f1(x), f2(x),..., fn(x)].