We consider the non-line-of-sight (NLOS) imagingof an object using light reflected off a diffusive wall. The wallscatters incident light such that a lens is no longer useful toform an image. Instead, we exploit the four-dimensional spatialcoherence function to reconstruct a two-dimensional projectionof the obscured object. The approach is completely passivein the sense that no control over the light illuminating theobject is assumed, and is compatible with the partially coherentfields ubiquitous in both indoor and outdoor environments.We formulate a multi-criteria convex optimization problem for reconstruction, which fuses the reflected field’s intensity and spatial coherence information at different scales. Our formulation leverages established optics models of light propagation and scattering and exploits the sparsity common to many images in different bases. We also develop an algorithm based on the Alternating Direction Method of Multipliers to efficiently solve the convex program proposed. A means for analyzing the null space of the measurement matrices is provided, as well as a means for weighting the contribution of individual measurements to the reconstruction. This work holds promise to advance passive imaging in challenging NLOS regimes in which the intensity does not necessarily retain distinguishable features, and provides a framework for multi-modal information fusion for efficient scenere construction.
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