June 18, 2009

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