A CT system includes a gantry, an x-ray source, a detector, and a grating collimator that includes alternating first and second materials. The system includes a controller configured to emit a first beam of x-rays from a first focal spot and to a first detector pixel, wherein the first beam of x-rays passes along a ray and through one of the first materials of the grating collimator, and subsequently emit a second beam of x-rays from a second focal spot and to the first detector pixel, wherein the second beam of x-rays passes substantially along the ray and through one of the second materials of the grating collimator. The system includes a computer programmed to generate first and second kVp image datasets using data acquired from the first beam and second beams of x-rays, and reconstruct a basis material image of the object.