Bounding pixels in computational imaging

We consider computational imaging problems where we have an insufficient number of measurements to uniquely reconstruct the object, resulting in an ill-posed inverse problem. Rather than deal with this via the usual regularization approach, which presumes additional information which may be incorrect, we seek bounds on the pixel values of the reconstructed image. Formulating the inverse problem as an optimization problem, we find conditions for which a system's measurements can produce a bounded result for both the linear case and the non-negative case (e.g., intensity imaging). We also consider the problem of selecting measurements to yield the most bounded results. Finally we simulate examples of the application of bounded estimation to different two-dimensional multiview systems.