Cropped incoherent (inverse) Fourier Dictionary

Generates small cropped (inverse) Fourier matrices with tight frames properties
Updated 15 Jan 2017

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Deterministically cropped (inverse) Fourier matrices with a incoherence near the Welch bound (theoretical minimum for [M,N] matrices) are useful in many applications involving Compressed Sensing, Sparse Coding, Dictionary Learning etc. This is an implementation according to the work reported in
"Deterministic construction of Fourier-based compressed sensing matrices using an almost difference set", Yu and Li, 2013 & 2015.
The result will be the closest match possible to a tight frame.
The algorithm works only if M=n==p^r with but allows to choose an N=L*(M+1) with L from [2, M-1].

This implementation is does not use yet the (i)fft(M+1) construction but crops a (i)fft(M^2-1) dictionary accordingly. However the calculation of row-indices is much more expensive and should be done only once if used in applications.

The current implementation is limited to M~160, since otherwise double overflows might occur, and is comparatively slow. It works however well for small M.

Cite As

Tobias Birnbaum (2024). Cropped incoherent (inverse) Fourier Dictionary (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2006a
Compatible with any release
Platform Compatibility
Windows macOS Linux
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