A Fast Wavelet Multilevel Approach to Total Variation Image Denoising

In this paper we present an adaptive multilevel total variational (TV) method for image denoising which utilizes TV partial differential equation (PDE) models and exploits the multiresolution properties of wavelets. The adaptive multilevel TV method provides fast adaptive wavelet-based solvers for the TV model. Our approach employs a wavelet collocation method applied to the TV model using two-dimensional anisotropic tensor product of Daubechies wavelets. The algorithm inherently combines the denoising property of wavelet compression algorithms with that of the TV model, and produces results superior to each method when implemented alone. It exploits the edge preservation property of the TV model to reduce the oscillations that may be generated around the edges in wavelet compression. In contrast with previous work combining TV denoising with wavelet compression, the method presented in this paper treats the numerical solution in a novel way which decreases the computational cost associated with the solution of the TV model. We present a detailed description of our method and results which indicate that a combination of wavelet based denoising techniques with the TV model produces superior results, for a fraction of the computational cost.