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

TL;DR

This paper introduces a non-recursive method for estimating bandlimited grayscale images from single-bit noisy pixel observations, achieving an error decay rate of O(1/N) independent of quantizer precision.

Contribution

It proposes a novel non-recursive estimation approach based on CDF approximation and Banach's contraction theorem for single-bit noisy image data.

Findings

Error decay rate is O(1/N)

Estimation accuracy is independent of quantizer precision

Method is effective for oversampled bandlimited images

Abstract

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.