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Mathematics
Linear and Abstract Algebra
What is the difference between a complete basis and an overcomplete dictionary?
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[QUOTE="fog37, post: 6628879, member: 503639"] Hello again, I found this at resource on frame and dictionaries at [URL]https://www.egr.msu.edu/~aviyente/ece802lecture9.pdf[/URL] [ATTACH type="full" width="360px" alt="1651705420128.png"]301034[/ATTACH] In what sense are larger dictionary (overcomplete set of building vectors called atoms) more suitable for representing in a sparse way signals that have lots of structure? Could anybody providing some clarifications? I am stuck with the idea of a complete basis as the best choice to represent an arbitrary signal... Representing a signal using a frame, instead of a basis, leads us to several possible linear representations of the same signal which does not have a single unique representation. Apparently this is useful to create a simpler, more sparse representation of a signal...but why? [/QUOTE]
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Linear and Abstract Algebra
What is the difference between a complete basis and an overcomplete dictionary?
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