The present invention is directed to spatial-spectral filtering for multi-material CT decomposition. The invention includes a specialized filter that spectrally shapes an x-ray beam into a number of beamlets with different spectra. The filter allows decomposition of an object/anatomy into different material categories (including different biological types: muscle, fat, etc. or exogenous contrast agents that have been introduced: e.g iodine, gadolinium, etc.). The x-ray beam is spectrally modulated across the face of the detector using a repeating pattern of filter materials. Such spatial-spectral filters allow for collection of many different spectral channels using “source-side” control. However, in contrast to other spectral techniques that provide mathematically complete projection data, spatial-spectral filtered data is sparse in each spectral channel—making traditional projection-domain or image-domain material decomposition difficult to apply. Therefore, the present invention uses model-based material decomposition, which combines reconstruction and multi-material decomposition, and permits arbitrary spectral, spatial, and angular sampling patterns.