Nonlinear approximation of image based on monoscale orthonormal ridgelets frame

A new tight frame called as monoscale orthonormal ridgelet frame (MORF) is proposed. The localization principle and the orthonormal ridgelet constructed by Donoho are applied to construct the MORF, which are used to evaluate the order of nonlinear approximation for image with edge. Because the new tight frame not only has directionality but also bears orthonormality. It overcomes redundancy of Candes’s monoscale ridgelets and provides many excellent properties in practical application. Theoretical analysis and experiments demonstrate that the new frame has remarkable potential for image compression, image reconstruction, and image denoising with the simple refinement for MORF.