Optimal scheduling of capture times in a multiple-capture imaging system

Several papers have discussed the idea of extending image sensor dynamic range by capturing several images during a normal exposure time. Most of these papers assume that the images are captured according to a uniform or an exponentially increasing exposure time schedule. Even though such schedules can be justified by certain implementation considerations, there has not been any systematic study of how capture time schedules should be optimally determined. In this paper we formulae the multiple capture time scheduling problem when the incident illumination probability density function (pdf) is completely known as a constrained optimization problem. We aim to find the capture times that maximize the average signal SNR. The formulation leads to a general upper bound on achievable average SNR using multiple capture for any given illumination pdf. For a uniform pdf, the average SNR is a concave function in capture times and therefore well-known convex optimization techniques can be applied to find the global optimum. For a general piece-wise uniform pdf, the average SNR is not necessarily concave. The cost function, however, is a Difference of Convex (D.C.) function and well-established D.C. or global optimization techniques can be used.