Cropped incoherent (inverse) Fourier Dictionary
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 p..prime 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 (https://www.mathworks.com/matlabcentral/fileexchange/61160-cropped-incoherent-inverse-fourier-dictionary), MATLAB Central File Exchange. Retrieved .
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1.0.0.0 |