Directional Compactly Supported Tensor Product Complex Tight Framelets with Applications to Image Denoising and Inpainting

Compactly supported tight framelets are of great interest and importance in both theory and application. In this paper we discuss how to construct directional compactly supported tensor product complex tight framelets having varied directionality and good performance for applications in image processing. Our construction algorithms employ optimization techniques and put extensive emphasis on frequency response and spatial localization of their underlying one-dimensional tight framelet filter banks. Several concrete examples of directional compactly supported tensor product complex tight framelet filter banks are provided in this paper. Our numerical experiments show that such constructed directional compactly supported tensor product complex tight framelets have good performance for applications such as image denoising and inpainting compared with several other state-of-the-art transform-based methods.