Coherent non-orthogonal expansions reencouraged

The authors understand “coherent families” as systems of functions which arise from a single function by a family of natural transformations. They point out that despite the success of orthogonal wavelet expansions various nonorthogonal expansions still hold some promises, in particular for cases where one can have fast algorithms and the coefficients have a natural interpretation. Recent achievements concerning Gabor expansions are presented as an example to make the case, but radial basis function approximations or oversampled affine frames are other examples