Wavelet based image compression process were more commonly used in all types of compression. The images were decomposed using Redundant tree based wavelet transform(RTBWT). Arithmetic encoding is employed to the decomposed sequences and the values were saved in dictionary. The sparse coding and entropy coding were applied to the decomposed images. The images were reconstructed by reversing the encoding process. The performance of the process is measured. The redundant tree-based wavelet transform (RTBWT), which extends the redundant wavelet transform to scalar functions defined on high-dimen-sional data clouds, graphs and networks. This transform is obtained by modifying an implementation of the redundant wavelet transform, which was proposed, similarly to the way we modified the decomposition scheme of the orthonormal transform. This implementation employs a filter-bank decomposition scheme, similarly to the orthonormal discrete wavelet transform. However, in each level of this scheme none of the coefficients are discarded. We add in each decomposition level operators that reorder the approximation coefficients.