In this paper we propose a new approach for tomographic reconstruction with spatially varying regularization parameter. Our work is based on the SA-TV image restoration model proposed by Dong et al (2011 J. Math. Imag. Vis. 40 82–104) where an automated parameter selection rule for spatially varying parameters has been proposed. Their parameter selection rule, however, only applies if measured imaging data are defined in the image domain, e.g. for image denoising and image deblurring problems. By introducing an auxiliary variable in their model, we show here that this idea can indeed by extended to general inverse imaging problems such as tomographic reconstruction where measurements are not in the image domain. With a spatially varying regularization parameter, the new method can suppress artifacts due to limited data and noise while preserving more details. Using numerical simulations on synthetic and real data, we demonstrate the validity of the proposed approach and its effectiveness for computed tomography reconstruction, delivering reconstruction results that are significantly improved compared to the state-of-the-art.
- Computed tomography
- Inverse problems
- Variational methods
- Spatially varying parameter
- Total variation regularization