Blind deconvolution in model-based iterative reconstruction for CT using a normalized sparsity measure

Model-based iterative reconstruction techniques for CT that include a description of the noise statistics and a physical forward model of the image formation process have proven to increase image quality for many applications. Specifically, including models of the system blur into the physical forward model and thus implicitly performing a deconvolution of the projections during tomographic reconstruction, could demonstrate distinct improvements, especially in terms of resolution. However, the results strongly rely on an exact characterization of all components contributing to the system blur. Such characterizations can be laborious and even a slight mismatch can diminish image quality significantly. Therefore, we introduce a novel objective function, which enables us to jointly estimate system blur parameters during tomographic reconstruction. Conventional objective functions are biased in terms of blur and can yield lowest cost to blurred reconstructions with low noise levels. A key feature of our objective function is a new normalized sparsity measure for CT based on total-variation regularization, constructed to be less biased in terms of blur. We outline a solving strategy for jointly recovering low-dimensional blur parameters during tomographic reconstruction. We perform an extensive simulation study, evaluating the performance of the regularization and the dependency of the different parts of the objective function on the blur parameters. Scenarios with different regularization strengths and system blurs are investigated, demonstrating that we can recover the blur parameter used for the simulations. The proposed strategy is validated and the dependency of the objective function with the number of iterations is analyzed. Finally, our approach is experimentally validated on test-bench data of a human wrist phantom, where the estimated blur parameter coincides well with visual inspection. Our findings are not restricted to attenuation-based CT and may facilitate the recovery of more complex imaging model parameters.