WITS: Tetrolet wavelets

The WITS (and the Virtue) honors today tetrolets, a breed of Haar-type wavelet transform based on tetrominoes. The preprint: "Tetrolet Transform: A New Adaptive Haar Wavelet Algorithm for Sparse Image Representation", may be found at J. Krommweh page (or local copy). The abstract reads:

In order to get an efficient image representation we introduce a new adaptive Haar wavelet transform, called Tetrolet Transform. Tetrolets are Haar-type wavelets whose supports are tetrominoes which are shapes made by connecting four equal-sized squares. The corresponding filter bank algorithm is simple but enormously effective. In every level of the filter bank algorithm we divide the low-pass image into 4 × 4 blocks. Then in each block we determine a local tetrolet basis which is adapted to the image geometry in this block. An analysis of the adaptivity costs leads to modified versions of our method. Numerical results show the strong efficiency of the tetrolet transform for image compression

Flat Noise Set - on Fast Noiselet transform

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