An apparatus reconstructs an image using high energy-based data regarding a scene provides access to first image-capture data regarding the scene that is formed using a first image-capture modality and to second image-capture data that is formed using a second (different) image-capture modality. A control circuit executes an iterative image reconstruction process that establishes a first and a second image-representation channel, a fidelity error measure that measures inconsistency of the image as compared to first image-capture data and second image-capture data, and a prior-penalty term that scores the image based on a priori likelihood or desirability using, at least in part, for each of a plurality of pixels, a non-separable matrix-penalty of a Jacobian-matrix of the image at that pixel, such as nuclear norm. The control circuit further utilizes, in combination with the foregoing, an iterative process to generate a reconstructed image that at least approximately minimizes a combination of the fidelity error measure and the prior-penalty term.
