An apparatus and method of reconstructing a computed tomography (CT) image using multiple datasets of projective measurements, wherein the method of image reconstruction favors spatial correlations among the images respectively reconstructed from each of the corresponding multiple datasets. The multiple data sets each contain projective measurements of the same object taken in close temporal proximity, but taken with different detector type or configurations (e.g., different spectral components in spectral CT or different detector types in hybrid 3rd- and 4th-generation CT scanners). Reconstructed images minimizing a vectorial total variation norm satisfies the criteria of favoring images exhibiting spatial correlations among the reconstructed images and favoring a sparse gradient-magnitude image (i.e., edge enhancing image) for each reconstructed image.