Imagery is collected much faster and in significantly greater quantities today compared to a few years ago. Accurate registration of this imagery is vital for comparing the similarities and differences between multiple images. Image registration is a significant component in computer vision and other pattern recognition problems, medical applications such as Medical Resonance Images (MRI) and Positron Emission Tomography (PET), remotely sensed data for target location and identification, and super-resolution algorithms. Since human analysis is tedious and error prone for large data sets, we require an automatic, efficient, robust, and accurate method to register images. Wavelet transforms have proven useful for a variety of signal and image processing tasks. In our research, we present a fundamentally new wavelet-based registration algorithm utilizing redundant transforms and a masking process to suppress the adverse effects of noise and improve processing efficiency. The shift-invariant wavelet transform is applied in translation estimation and a new rotation-invariant polar wavelet transform is effectively utilized in rotation estimation. We demonstrate the robustness of these redundant wavelet transforms for the registration of two images (i.e., translating or rotating an input image to a reference image), but extensions to larger data sets are feasible. We compare the registration accuracy of our redundant wavelet transforms to the critically sampled discrete wavelet transform using the Daubechies wavelet to illustrate the power of our algorithm in the presence of significant additive white Gaussian noise and strongly translated or rotated images.