Stationary Tetrolet Transform: an Improved Algorithm for Tetrolet Transform

In order to get an efficient image multi-scale geometrical representation, the basic principle of tetrolet transform is studied and an efficient stationary tetrolet transform algorithm based on Haar wavelet transform is proposed. Tetrolets are Haar-type wavelets whose supports are tetrominoes which are shapes made by connecting four equal-sized squares. Tetrolet transform is divide the image into 4 × 4 blocks in the horizontal and vertical direction, there is no overlap between the sub-blocks. Because there is no overlap between the images blocks, so the image decomposition coefficients in image processing is easy produce Gibbs phenomenon. Stationary tetrolet transform is a new adaptive Haar-type wavelet transforms which the block overlaps method in image decomposition process is inserted into the middle of the original coefficients in tetrolet transform. The corresponding filter bank algorithm is simple but enormously effective. Compare with standard two dimensional wavelet transform, stationary tetrolet transform is a novel tetrominoes based multi-scale geometrical transform tool, which can capture image anisotropic geometrical structures information efficiently by multi-direction selection. In this paper, the decomposition and reconstruction algorithms of the stationary tetrolet transform are described in detail, and the simulation and analysis of the decomposition of the image using the stationary tetrolet transform is carried out. Experimental results show that compared with traditional algorithm, the proposed algorithm can get better sparse representation and eliminate the blocking artifacts in image processing resulted from tetrolet transform algorithm.