After first try to provide some code for the noiselet transform matrix, which yields a flat noise set of coefficients from the Haar system (and to obtain nice pictures), a valuable implemetation has been made public. No lie, fastest Matlab code for noiselets is now available from Laurent Jacques (direct link). David Donoho(*) recently recalled that the compressed sensing litterature shared similarities with concepts in other fiels (an oft essential remark). For instance in data stream processing, as for “heavy hitters” or “Iceberg queries”. The Fast Noiselet is not the nastiest floe in this ocean of litterature.
(*) David L. Donoho, Compressed Sensing, IEEE Transactions on Information Theory, April 2006 (pdf copy).
On complex hadamard matrices