Cropped incoherent (inverse) Fourier Dictionary

Generates small cropped (inverse) Fourier matrices with tight frames properties

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.