On non-orthogonal signal representation

In this chapter we present recent techniques for signal representation outside the traditional orthogonal basis setting. The appropriate setting for our purpose is provided by the general structure of frames. The highly non-linear problem arising in non-orthogonal signal approximation is addressed here by recourse to adaptive pursuit strategies. Forward and backward adaptive biorthogonalisation techniques are derived, which allow for an effective implementation of such strategies. A new motivation for the use of redundant representations is discussed. Namely, the possibility of using redundancy for the purpose of transmitting or storing hidden information. An approach for compressing redundancy is also advanced.