A simple design of sparse signal representations using overlapping frames

The use of frames and matching pursuits for signal representation are receiving increased attention due to their perceived potential in various signal processing applications. Good design algorithms for block oriented frames have recently been published. Viewing these block oriented frames as generalizations of block oriented transforms, it is natural to seek corresponding generalizations of critically sampled filter banks leading to overlapping frames. Here we show that a large class of overlapping frames can be decomposed into a critically sampled orthogonal filter bank-that can be chosen prior to the design-and a block oriented frame. Based on this, we show that excellently performing overlapping frames can be designed using the already established and simple theory for the design of block oriented frames.