A theory of generalized multiresolution structure and pseudoframes of translates

The notion of a Generalized Multiresolution Structure (GMS) in L-2(R) is in troduced. Basically. it consists of an increasing sequence of closed subspa ces of L-2(R), with a pseudoframe of translates at each level. Using their shift-invariance a frame-like decomposition is derived based on such a GMS. As a major new contribution the construction of affine frames for L-2(R) b ased on an GMS is presented. A fast algorithm for the GMS-based affine fram e decomposition and reconstruction using filter banks is presented as well.