CHAPTER 5 Frames

A signal representation may provide “analysis” coefficients that are inner products with a family of vectors, or “synthesis” coefficients that compute an approximation by recombining a family of vectors. Frames are families of vectors where “analysis” and “synthesis” representations are stable. Signal reconstructions are computed with a dual frame. Frames are potentially redundant and thus more general than bases, with a redundancy measured by frame bounds. They provide the flexibility needed to build signal representations with unstructured families of vectors.

Complete and stable wavelet and windowed Fourier transforms are constructed with frames of wavelets and windowed Fourier atoms. In two dimensions, frames of directional ...

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