  The estimation of grayscale images using their single-bit zero mean Gaussian
noise-affected pixels is presented in this paper. The images are assumed to be
bandlimited in the Fourier Cosine transform (FCT) domain. The images are
oversampled over their Nyquist rate in the FCT domain. We propose a
non-recursive approach based on first order approximation of Cumulative
Distribution Function (CDF) to estimate the image from single bit pixels which
itself is based on Banach's contraction theorem. The decay rate for mean
squared error of estimating such images is found to be independent of the
precision of the quantizer and it varies as $O(1/N)$ where $N$ is the
"effective" oversampling ratio with respect to the Nyquist rate in the FCT
domain.
