The convolution theorem for two-dimensional continuous wavelet transform

In this paper, application of two-dimensional continuous wavelet transform to image processes is studied. We first show that the convolution and correlation of two continuous wavelets satisfy the required admissibility and regularity conditions, and then we derive the convolution and correlation theorem for two-dimensional continuous wavelet transform. Finally, we present numerical example showing the usefulness of applying the convolution theorem for the two-dimensional continuous wavelet transform to perform image restoration in the presence of additive noise.