In this work we propose a fast, model-based restoration scheme for noisy or undersampled spec- tral CT data and demonstrate its potential utility with two simulation studies. First, we show how one can denoise photon counting CT images, post- reconstruction, by using a spectrally averaged im- age formed from all detected photons as a high SNR prior. Next, we consider a slow slew-rate kV switch- ing scheme, where sparse sinograms are obtained at peak voltages of 80 and 140 kVp. We show how the missing views can be restored by using a spectrally av- eraged, composite sinogram containing all of the views as a fully sampled prior. We have chosen these ex- amples to demonstrate the versatility of the proposed approach and because they have been discussed in the literature before3,6 but we hope to convey that it may be applicable to a fairly general class of spectral CT systems. Comparisons to several sparsity-exploiting, iterative reconstructions are provided for reference.