Chromotomographic spectral imaging techniques offer high spatial resolution, moderate spectral resolution and high optical throughput. However, the performance of chromotomographic systems has historically been limited by the artifacts introduced by a cone of missing information. The recent successful application of principal component analysis to spectral imagery indicates that spectral imagery is inherently redundant. We have developed an iterative technique for filling in the missing cone that relies on this redundancy. We demonstrate the effectiveness of our approach on measured data, and compare the results to those obtained with a scanned slit configuration.