Tetrolet transform: A new adaptive Haar wavelet algorithm for sparse image representation

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 fast filter bank algorithm is simple but very effective. In every level of the filter bank algorithm we divide the low-pass image into 4x4 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 approximation.

[1]  Stéphane Mallat,et al.  Sparse geometric image representations with bandelets , 2005, IEEE Transactions on Image Processing.

[2]  Mauro Barni.  Document and Image Compression , 2006 .

[3]  Michael Robert Korn.  Geometric and algebraic properties of polyomino tilings , 2004 .

[4]  Feng Wu,et al.  Adaptive Directional Lifting-Based Wavelet Transform for Image Coding , 2007, IEEE Transactions on Image Processing.

[5]  Erik D. Demaine,et al.  Tetris is hard, even to approximate , 2002, Int. J. Comput. Geom. Appl..

[6]  Baltasar Beferull-Lozano,et al.  Directionlets: anisotropic multidirectional representation with separable filtering , 2006, IEEE Transactions on Image Processing.

[7]  Hartmut Führ,et al.  Efficient Moment Computation over Polygonal Domains with an Application to Rapid Wedgelet Approximation , 2007, SIAM J. Sci. Comput..

[8]  Jianwei Ma,et al.  Tetrolet shrinkage with anisotropic total variation minimization for image approximation , 2010, Signal Process..

[9]  D. Donoho.  Wedgelets: nearly minimax estimation of edges , 1999 .

[10]  E. Candès,et al.  New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities , 2004 .

[11]  Demetrio Labate,et al.  Optimally Sparse Multidimensional Representation Using Shearlets , 2007, SIAM J. Math. Anal..

[12]  Felix Friedrich,et al.  Beyond wavelets: New image representation paradigms , 2005 .

[13]  Bernd Girod,et al.  Direction-Adaptive Discrete Wavelet Transform for Image Compression , 2007, IEEE Transactions on Image Processing.

[14]  G. Plonka.  The Easy Path Wavelet Transform: A New Adaptive Wavelet Transform for Sparse Representation of Two-Dimensional Data , 2009 .

[15]  Minh N. Do,et al.  Ieee Transactions on Image Processing the Contourlet Transform: an Efficient Directional Multiresolution Image Representation , 2022 .