Regularized Reconstruction of Nonnegative Images Degraded by a Point-spread Function with a Band-limited Transfer Function

In the reconstruction of images obtained from diffraction-limited optical systems such as two and three-dimensional light microscopic images, the observed image can be modeled as the convolution of the actual image with a point spread function, whose transfer function is band limited [1]. In addition, such images are contaminated by additive noise, whose signal to noise ratio we assume can be estimated. To obtain a reconstruction which contains information about the actual images in the frequency region where the optical transfer function is zero, additional constraints, such as positivity must be imposed [2].