Compressive Inverse Light Transport

A forward light transport simulates global illumination in a scene given direct lighting or corresponding light source emission. It embodies the forward rendering process, a cornerstone of computer graphics, which aggregates the effect of light bouncing in a scene. An inverse light transport reverses the forward process; it enables undoing of interreflections and separation of light bounces in a real scene. In all current work, an inverse light transport matrix (i-LTM) is obtained by inverting a forward light transport matrix (f-LTM). For a projector-camera setup, a f-LTM can easily exceed the size of 105 × 105. Acquiring such a large f-LTM can take hours or days while inverting the f-LTM requires various forms of approximation which compromises on the accuracy of the inverse light transport. In this work, we propose a way of computing i-LTM directly from the measurements without the need for a prior and explicit reconstruction of the f-LTM. We show that within the framework of compressive inverse theory, i-LTM can be obtained by compressed sensing directly without additional computational cost and aggregated error from matrix inversion. This is done by computing the response of each pixel by projecting patterned illumination. We probe the light transport matrix by m illumination conditions L = [l0, ..., lm] to obtain their corresponding observations C = [c0, ...,cm], which is,