The objective of this project is to develop the theory and algorithms of wave propagation and imaging in the wavelet domain for direct application to compressed seismic data. We will strive to find optimum algorithms for both compression and processing of which imaging is the heart. The newly developed fast wavelet transform (WT) is considered to be a revolutionary breakthrough in signal analysis/processing. In the same time frame, there has been significant progress in one-way wave propagation theory and algorithms, including the recently developed fast acoustic and elastic generalized screen propagators from our group. We will apply the wavelet transform to the generalized screen or other one-way wave propagation methods to develop efficient 3D imaging and modeling methods. The cross-breeding of these two new developments has the potential of revolutionizing modeling and imaging techniques for complex Earth media.