Models in signal processing often deal with some notion of structure or conciseness suggesting that a signal really has “few degrees of freedom” relative to its actual size. Low-dimensional signal models support stable information-preserving dimensionality reduction. Each model has a particular geometrical structure that enables signal information to be stably preserved via a simple linear and no adaptive projection to a much lower dimensional space; in each case the projection dimension is independent of the signal's ambient dimension at best or grows logarithmically with it at worst.
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