X-ray CT is widely used, both clinically and preclinically, for fast, high-resolution, anatomic imaging; however, compelling opportunities exist to expand its use in functional imaging applications. For instance, spectral information combined with nanoparticle contrast agents enables quantification of tissue perfusion levels, while temporal information details cardiac and respiratory dynamics. Common implementations of spectral and temporal (spectro-temporal) CT discretely sample the time points and energies to be reconstructed, proportionally increasing acquisition time and ionizing radiation dose with data dimensionality. Here, we propose and develop an integrated framework for spectro-temporal CT data acquisition, reconstruction, and analysis which drastically reduces the sampling time and radiation dose associated with spectro-temporal CT imaging. Specifically, we exploit the latent, gradient sparse and low rank structure of spectro-temporal CT data sets to recover their full dimensionality from highly undersampled projection measurements. We achieve reliable, high fidelity results through a novel combination of hierarchical projection sampling, the split Bregman optimization method, and piecewise-constant kernel regression. The integrated framework generalizes to arbitrary spectral and temporal CT reconstruction problems, while maintaining or even improving upon the sampling time and radiation dose associated with anatomic imaging protocols. We believe that this integrated framework will serve as the basis for a new generation of routine, functional CT imaging protocols.
