Fast total-variation based image restoration based on derivative alternated direction optimization methods

The total variation (TV) model is one of the most successful methods for image restoration, as well as an ideal bed to develop optimization algorithms for solving sparse representation problems. Previous studies showed that derivative space formulation of the image restoration model is useful in improving the success rate in image recovery and kernel estimation performance in blind deconvolution. However, little attentions are paid on the model and algorithm for derivative space based image restoration. In this paper, we study the TV based image restoration (TVIR) by developing a novel derivative space-based reformulation together with an efficient derivative alternating direction method of multipliers (D-ADMM) algorithm. Thanks to the simplicity of the proposed derivative space reformulation, D-ADMM only requires four fast Fourier transform (FFT) operations per iteration, and is much more efficient than the other augmented Lagrangian methods. Numerical experiments show that, D-ADMM can obtain satisfactory restoration result and is much faster than the state-of-the-art TVIR algorithms.