Reconstruction of low-light images by use of the vector Wiener filter

Abstract

Photon noise imposes severe limitations on the resolution of images detected under low-light conditions. These resolution limitations are typically more severe than those imposed by diffraction. Nonlinear iterative reconstruction techniques are available that can successfully process these images. Typical iterative methods are computationally expensive, incorporate ad hoc termination criteria, and may suffer convergence problems. The scalar Wiener filter is linear, computationally inexpensive, and noniterative. However, the scalar Wiener filter cannot improve the Fourier domain signal-to-noise ratio. We extend the vector Wiener filter to account properly for photon noise to provide a reconstruction technique that better complements nonlinear iterative methods. Our analysis confirms previous research [IEEE Trans. Signal Process.42, 156 (1994)] that showed that photon noise is correlated with respect to spatial frequency. The amount of correlation depends on the product of the mean optical transfer function (OTF) and the mean object spectrum at a difference frequency. We conduct computer simulations for a class of random Gaussian objects degraded by a known OTF. These results show the extended vector Wiener filter provides dramatic improvement in normalized mean squared error performance compared with that of the scalar Wiener filter. The vector Wiener filter can also provide a superresolution capability that is due to knowledge of the object spatial frequency statistics for frequencies beyond the OTF cutoff.