The goal of this project is to explore mathematical properties of a
particularly novel concept, shiftability, and provide new results which can
be further developed or applied. Shiftability is a concept which needs
research to move from compactly supported and orthogonal bases to frames,
which are similar to unconditional bases, but functions that span the space
(i.e. frame functions) do not need to be linearly independent.
This research field has been found important in many applications utilizing
multiresolution analysis (MRA) methods, such as in pattern recognition, and
thus, strong knowledge on frames may improve these methods and applications.
Research is performed in a close co-operation between Laboratory of Applied
Mathematics and Laboratory of Information Processing in Deparment of Computer
Science in Lappeenranta University of Technology.