Various methods and systems are provided for multi-material decomposition for computed tomography. In one embodiment, a method comprises acquiring, via an imaging system, projection data for a plurality of x-ray spectra, estimating path lengths for a plurality of materials based on the projection data and calibration data for the imaging system, iteratively refining the estimated path lengths based on a linearized model derived from the calibration data, and reconstructing material-density images for each material of the plurality of materials from the iteratively-refined estimated path lengths. By determining path-length estimates in this way without modeling the physics of the imaging system, accurate material decomposition may be performed more quickly and with less sensitivity to changes in physics of the system, and furthermore may be extended to more than two materials.