Some problems were pointed out

which are easy to be confused and make mistakes in image processing using Mallat algorithem

and the correct restrained conditions using Mallat algorithem were also given. Image compressions based on subband coding has been studied by Haar and Daubechies wavelets

and three kinds of schemes for wavelet compression coding scheme were presented in this paper.The simulation experiments based on the restrained conditions were carried out and the results of the experiments can be used to effective schemes for image compression coding

therefore the Mallat algorithem can be applied correctly.