Perturbation Response of Model-based Material Decomposition with Edge-Preserving Penalties

Spectral CT permits material discrimination beyond the structural information in conventional single-energy CT. Model-based material decomposition facilitates direct estimation of material density from spectral measurements, incorporating a general forward model for arbitrary spectral CT system, a statistical model of spectral CT measurements, and flexible regularization schemes. Such one-step approaches are promising for superior image quality, but the relationship between regularization parameters, imaging conditions, and reconstructed image properties is complicated. More specifically, the estimator is inherently nonlinear and may include additional nonlinearities like edge-preserving regularization, making image quality metrics intended for linear system evaluation difficult to apply. In this work, we seek approaches to quantify the image properties of this inherently nonlinear process through an investigation of perturbation response - the generalized system response to a local perturbation of arbitrary shape, location, and contrast. Such responses include cross-talk between material density channels, and we investigate the application of this metric in a sample spectral CT system. Inspired by the prior work under assumptions of local linearity and shift-invariant we also propose a prediction framework for perturbation response using a perceptron neural network. The proposed prediction framework offers an alternative to exhaustive evaluation and is a potential tool that can be used to prospectively choose optimal regularization parameters based on imaging conditions and diagnostic task.