Performance bounds for computational imaging

A number of computational imaging techniques have been introduced to improve image quality by increasing light throughput. These techniques use optical coding to measure a stronger signal level. However, the performance of these techniques is limited by the decoding step, which amplifies noise. While it is well understood that optical coding can increase performance at low light levels, little is known about the quantitative performance advantage of computational imaging in general settings. Existing analyses are limited in two ways: (1) most analyses assume a signal independent noise model and ignore signal dependent noise and (2) most analyses neglect to model scene priors. Accurate analysis of multiplexing imaging systems requires us to explicitly consider the effect of both signal dependent photon noise and scene priors. In this work, we perform a careful analytical characterization of the effects of multiplexing under (a) a noise model incorporating both signal dependent and signal independent noise and (b) scene priors modeled both as a Gaussian and as a mixture of Gaussians (GMM). We then discuss the implications of these bounds for several real-world scenarios (illumination conditions, scene properties and sensor noise characteristics).