We present a general framework for analyzing the transport matrix of a real-world scene at full resolution, without capturing many photos. The key idea is to use projectors and cameras to directly acquire eigenvectors and the Krylov subspace of the unknown transport matrix. To do this, we implement Krylov subspace methods partially in optics, by treating the scene as a "black box subroutine" that enables optical computation of arbitrary matrix-vector products. We describe two methods - -optical Arnoldi to acquire a low-rank approximation of the transport matrix for relighting; and optical GMRES to invert light transport. Our experiments suggest that good quality relighting and transport inversion are possible from a few dozen low-dynamic range photos, even for scenes with complex shadows, caustics, and other challenging lighting effects.
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