Abstract: Spectral estimation and poly-energetic reconstructions methods and x-ray systems are disclosed. According to an aspect, a spectral estimation method includes using multiple, poly-energetic x-ray sources to generate x-rays and to direct the x-rays towards a target object. The method also includes acquiring a series of poly-energetic measurements of x-rays from the target object. Further, the method includes estimating cross-sectional images of the target object based on the poly-energetic measurements. The method also includes determining path lengths through the cross-sectional images. Further, the method includes determining de-noised poly-energetic measurements and de-noised path lengths based on the acquired poly-energetic measurements and the determined path lengths. The method also includes estimating spectra for angular trajectories of a field of view based on the de-noised poly-energetic measurements and the path lengths.