Method and apparatus for spectral computed tomography (CT) with multi-material decomposition into three or more material components

An apparatus, comprising:

• an X-ray source configured to transmit X-rays;
• a plurality of detector elements, wherein the plurality of detector elements is configured to
• detect a plurality of energy components of the X-rays, which are transmitted from the X-ray source through an object and are detected at the plurality of detector elements, and
• generate projection data having a plurality of energy components for each detector element of the plurality of detector elements, the energy components representing radiation of a respective energy profile;
• and
• circuitry configured to
• reconstruct images for the projection data, each of the images corresponding to a respective component of the plurality of energy components,
• perform a material decomposition on the images to decompose attenuation values for the respective energy components of a voxel of the images into material components, wherein,
• to perform the material decomposition, the circuitry is further configured to
• determine whether the attenuation values of the voxel are consistent with a volume-fraction condition,
• when the attenuation values of the voxel are consistent with the volume-fraction condition, decompose the attenuation values into n material components, wherein n is a natural number of three or greater, and,
• when the attenuation values of the voxel are not consistent with the volume-fraction condition, project the attenuation values of the voxel onto a closest (n-2) dimensional space of n-1 material components to the attenuation values of the voxel to generate a projected point, and decompose attenuation values of the projected point into the n-1 material components.

A method, comprising:

• obtaining images corresponding to respective energy components, and
• performing a material decomposition on the images to decompose attenuation values for the respective energy components of a voxel of the images into material components, wherein the material decomposition includes
• determining whether the attenuation values of the voxel are consistent with a volume-fraction condition,
• when the attenuation values of the voxel are consistent with the volume-fraction condition, decomposing the attenuation values into n material components, wherein n is a natural number of three or greater, and,
• when the attenuation values of the voxel are not consistent with the volume-fraction condition, projecting the attenuation values of the voxel onto a closest (n-2) dimensional space of n-1 material components to the attenuation values of the voxel to generate a projected point, and decomposing attenuation values of the projected point into the n-1 material components.