Compressive inverse light transport

This paper explores the possibility of acquiring inverse light transport directly. The current strategy of obtaining an inverse light transport matrix involves two steps: First, acquire the forward light transport matrix (f-LTM) and then calculate the inverse of the f-LTM. Both steps of the strategy requires considerable computational power. In addition to computational cost, the measurement error incurred at the first step inevitably propagates to or potentially gets amplified in the matrix inversion step. In this paper, we propose a sensing strategy that acquires the inverse light transport matrix (i-LTM) directly, without reconstructing the f-LTM. Our direct strategy reduces both computational error and cost of acquiring i-LTM. For that, we propose a compres-sive inverse theory. Following the compressible property of i-LTM, a reconstruction condition for i-LTM is introduced. This new framework implies a trade-off between two factors: condition numbers of submatrices of f-LTM and the isometry constant of the illumination pattern. Our direct i-LTM reconstruction method is then demonstrated with a 2nd-bounce separation experiment on an M-shaped panel scene. Finally by quantitatively comparing our method with the existing two-stage approach, our method shows higher accuracy with lower complexity. The proofs of main theorem/lemma are contained in the supplementary material. The compressive inverse theory is general and potentially useful for wider application.