Gauss-Newton-Krylov for Reconstruction of Polychromatic X-Ray CT Images

Most lab-based X-ray sources are polychromatic, making the imaging process follow a non-linear model. However, widespread reconstruction algorithms, such as filtered back projection and the simultaneous iterative reconstruction technique, assume the reconstruction to be a linear problem, leading to artifacts in the reconstructions from polychromatic data. We propose to use quasi-Newton methods to minimize a polychromatic objective function, without the need of segmenting the image into different material regions. The objective function can also easily be extended with regularisation terms in a mathematically sound framework. We will show that these methods can outperform other statistical or algebraic reconstruction techniques. Reconstruction quality and projection error for reconstructions of both Monte-Carlo simulated data and experimental data are investigated. From the considered quasi-Newton methods, we find Gauss-Newton-Krylov to perform best. Compared to a recently proposed polychromatic algebraic reconstruction technique, quasi-Newton solvers reach a lower reconstruction error and have increased convergence speed.