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The estimation of grayscale images using their single-bit zero mean Gaussiannoise-affected pixels is presented in this paper. The images are assumed to bebandlimited in the Fourier Cosine transform (FCT) domain. The images areoversampled over their Nyquist rate in the FCT domain. We propose anon-recursive approach based on first order approximation of CumulativeDistribution Function (CDF) to estimate the image from single bit pixels whichitself is based on Banach's contraction theorem. The decay rate for meansquared error of estimating such images is found to be independent of theprecision 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 FCTdomain.

Estimation of Bandlimited Grayscale Images From the Single Bit Observations of Pixels Affected by Additive Gaussian Noise