Orthogonal wavelet transform with compact support filter design method and an algorithm of image perfect decomposition and reconstruction

A novel method to design the Daubechies filter is introduced. Based on this, an algorithm of the image perfect decomposition and reconstruction is proposed. In fact, for orthogonal wavelet transform, the padding approach to the boundary condition is periodic. The approach is derived from the design method of Daubechies filter. When the signal length is more than the length of the filter, the signal can be decomposed and reconstructed perfectly.