The discretization problem for continuous frames

By Daniel Freeman, Darrin Speegle. Advances in Mathematics, 2016

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Abstract We characterize when a coherent state or continuous frame for a Hilbert space may be sampled to obtain a frame, which solves the discretization problem for continuous frames. In particular, we prove that every bounded continuous frame for a Hilbert space may be sampled to obtain a frame. We give multiple applications to different classes of frames such as scalable frames and Gabor frames.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/011f28af47f2e23225852dc4b660c7b55e656f77