An X-ray imaging system for reconstructing X-ray spectra includes an integrating detector and a measurement mask, including at least one physical filter, positioned between the integrating detector and an X-ray source spectrum. The integrating detector receives a masked X-ray spectrum after the source spectrum has been filtered in accordance with the measurement mask. As a result of the measurement mask containing one or more physical filters being combined, a measurement mask having energy band-pass regions can be generated, to cover the source spectrum. Measured data, based on the masked X-ray spectrum and characteristics of the measurement mask, is collected from the integrating detector. The X-ray imaging system reconstructs an X-ray spectrum and generates the reconstructed X-ray spectrum based on applying a predetermined algorithm, such as total variation minimization reconstruction, to the measured data.