Nonlinear Restoration Of Filtered Images With Poisson Noise

A model for photon resolved low light level image signals detected by a counting array is developed. Those signals are impaired by signal dependent Poisson noise and linear blurring. An optimal restoration filter based on maximizing the a posteriori probability density (MAP) is developed. A suboptimal overlap-save sectioning method using a Newton-Raphson iterative procedure is used for the solution of the high dimensionality nonlinear estimation equations for any type of space-variant and invariant linear blur. An accurate image model with a nonstationary mean and stationary variance is used to provide a priori information for the MAP restoration filter. Finally, a comparison between the MAP filter and a linear space-invariant minimum mean-square error (LMMSE) filter is made.