Elimination of Gibbs Phenomenon for Image Fusion in Tetrolet Transform Domain

In order to get an efficient image multi-scale geometrical representation, the basic principle of tetrolet transform is studied. 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 x 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 fusion processing is easy produce Gibbs phenomenon. In order to reduce the blocking artifacts resulted from tetrolet transform algorithm in image fusion. An efficient stationary tetrolet transform algorithm based on Haar wavelet transform is proposed. The block overlaps method in image decomposition process is introduced in tetrolet transform. The new overlap block is inserted into the middle of the original coefficients. Experimental results show that compared with tetrolet transform algorithm for image fusion, the proposed algorithm can get better sparse representation and eliminate the blocking artifacts in image fusion resulted from tetrolet transform algorithm.