Multiresolution analysis frames with applications

A generalization of multiresolution analysis (MRA) to arbitrary affine frames, and the constructions of affine frames based on MRAs are considered and characterized. The authors define a frame multiresolution analysis (FMRA) and provide a necessary and sufficient condition for constructing frames of translates. Conditions for constructing FMRAs and associated frames are derived. The results are part of the theoretical background for multiscale signal processing problems including filter bank design, where redundancy and robustness play a role.<>