Estimation of Bandlimited Grayscale Images From the Single Bit   Observations of Pixels Affected by Additive Gaussian Noise
  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. 
Abhinav Kumar and Animesh Kumar
cs.CV math.ST stat.TH