Total variation based Fourier reconstruction and regularization for computer tomography

The paper develops a tomographic reconstruction and regularization method based on a total variation minimization constrained by the knowledge of the input intervals the Fourier coefficients belong to. Experiments show that the approach outperforms classical reconstruction methods such as direct Fourier method (DFM), filtered back-projection (FBP) and Tikhonov iterative method (TIM), both in terms of PSNR (an objective mean-square error) and visual quality, especially in the case of noisy or sparse data. In addition the resulting algorithm requires a number of operations of O(N² log N) only, and is therefore faster than ordinary iterative methods, such as space-based TIM.