Compressed‐sensing‐based content‐driven hierarchical reconstruction: Theory and application to C‐arm cone‐beam tomography

Purpose: This paper addresses the reconstruction of x‐ray cone‐beam computed tomography (CBCT) for interventional C‐arm systems. Subsampling of CBCT is a significant issue with C‐arms due to their slow rotation and to the low frame rate of their flat panel x‐ray detectors. The aim of this work is to propose a novel method able to handle the subsampling artifacts generally observed with analytical reconstruction, through a content‐driven hierarchical reconstruction based on compressed sensing. Methods: The central idea is to proceed with a hierarchical method where the most salient features (high intensities or gradients) are reconstructed first to reduce the artifacts these features induce. These artifacts are addressed first because their presence contaminates less salient features. Several hierarchical schemes aiming at streak artifacts reduction are introduced for C‐arm CBCT: the empirical orthogonal matching pursuit approach with the ℓ0 pseudonorm for reconstructing sparse vessels; a convex variant using homotopy with the ℓ1‐norm constraint of compressed sensing, for reconstructing sparse vessels over a nonsparse background; homotopy with total variation (TV); and a novel empirical extension to nonlinear diffusion (NLD). Such principles are implemented with penalized iterative filtered backprojection algorithms. For soft‐tissue imaging, the authors compare the use of TV and NLD filters as sparsity constraints, both optimized with the alternating direction method of multipliers, using a threshold for TV and a nonlinear weighting for NLD. Results: The authors show on simulated data that their approach provides fast convergence to good approximations of the solution of the TV‐constrained minimization problem introduced by the compressed sensing theory. Using C‐arm CBCT clinical data, the authors show that both TV and NLD can deliver improved image quality by reducing streaks. Conclusions: A flexible compressed‐sensing‐based algorithmic approach is proposed that is able to accommodate for a wide range of constraints. It is successfully applied to C‐arm CBCT images that may not be so well approximated by piecewise constant functions.