A stopping criterion for iterative proton CT image reconstruction based on correlated noise properties

BACKGROUND: Whereas filtered back projection algorithms for voxel‐based CT image reconstruction have noise properties defined by the filter, iterative algorithms must stop at some point in their convergence and do not necessarily produce consistent noise properties for images with different degrees of heterogeneity. PURPOSE: A least‐squares iterative algorithm for proton CT (pCT) image reconstruction converges toward a unique solution for relative stopping power (RSP) that optimally fits the protons. We present a stopping criterion that delivers solutions with the property that correlations of RSP noise between voxels are relatively low. This provides a method to produce pCT images with consistent noise properties useful for proton therapy treatment planning, which relies on summing RSP along lines of voxels. Consistent noise properties will also be useful for future studies of image quality using metrics such as contrast to noise ratio, and to compare RSP noise and dose of pCT with other modalities such as dual‐energy CT. METHODS: With simulated and real images with varying heterogeneity from a prototype clinical proton imaging system, we calculate average RSP correlations between voxel pairs in uniform regions‐of‐interest versus distance between voxels. We define a parameter r, the remaining distance to the unique solution relative to estimated RSP noise, and our stopping criterion is based on r falling below a chosen value. RESULTS: We find large correlations between voxels for larger values of r, and anticorrelations for smaller values. For r in the range of 0.5–1, voxels are relatively uncorrelated, and compared to smaller values of r have lower noise with only slight loss of spatial resolution. CONCLUSIONS: Iterative algorithms not using a specific metric or rationale for stopping iterations may produce images with an unknown and arbitrary level of convergence or smoothing. We resolve this issue by stopping iterations of a least‐squares iterative algorithm when r reaches the range of 0.5–1. This defines a pCT image reconstruction method with consistent statistical properties optimal for clinical use, including for treatment planning with pCT images.