A time-of-flight camera images an object around a corner or through a diffuser. In the case of imaging around a corner, light from a hidden target object reflects off a diffuse surface and travels to the camera. Points on the diffuse surface function as a virtual sensors. In the case of imaging through a diffuser, light from the target object is transmitted through a diffusive media and travels to the camera. Points on a surface of the diffuse media that is visible to the camera function as virtual sensors. In both cases, a computer represents phase and intensity measurements taken by the camera as a system of linear equations and solves a linear inverse problem to (i) recover an image of the target object; or (ii) to compute a 3D position for each point in a set of points on an exterior surface of the target object.