Spectral estimation and poly-energetic reconstruction methods and X-ray systems

A spectral estimation system comprising:

• a plurality of poly-energetic x-ray sources configured to generate x-rays and to direct the x-rays towards a target object;
• detectors configured to acquire a series of poly-energetic measurements of x-rays from the target object;
• and
• a computing device comprising a memory and processor, wherein the processor is configured to:
• estimate cross-sectional images of the target object based on the poly-energetic measurements;
• determine path lengths through the cross-sectional images;
• determine de-noised poly-energetic measurements and de-noised path lengths based on the acquired poly-energetic measurements and the determined path lengths;
• and
• estimate spectra for angular trajectories of a field of view based on the de-noised poly-energetic measurements and the path lengths,
• wherein estimating spectra comprises using the following iterative algorithm:
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• and
• reconstruct a volume based on the angle dependent spectra by executing the iterative algorithm, whereby executing the iterative algorithm increases reconstruction and convergence speed at the processor.

A poly-energetic reconstruction method comprising:

• providing a plurality of acquired poly-energetic measurements, a reference energy for reconstruction, and an initialized reconstruction volume;
• providing one or more base material sets;
• generating a region map based on a current reconstruction volume;
• decomposing each voxel of the current reconstruction volume into a plurality of base materials in terms of based material path lengths based on the provided reference energy, a voxel value of the reconstruction volume, the region map, and the corresponding base material set;
• performing a forward poly-energetic, ray-tracing technique to estimate poly-energetic measurements based on the current reconstruction volume;
• subtracting estimated poly-energetic measurements from the acquired poly-energetic measurements to obtain error measurements;
• performing a backward updating technique to update the current reconstruction volume based on a difference between the estimated poly-energetic measurements and acquired poly-energetic measurements;
• iterating the steps of providing one or more based material sets, initializing, and generating for one of a predetermined number of iterations or until the reconstruction volume converges and meets predetermined criteria, whereby the iterating step increases reconstruction speed at the processor;
• and
• transforming a finalized reconstruction volume from the reference energy to the target energy.