Assessment of noise in a digital image using the join-count statistic and the Moran test

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Abstract
We assume that the data bits of a pixel in digital images can be divided into signal and noise bits. The signal bits occupy the most significant part of the pixel and the noise bits the least significant part. The signal part of each pixel are correlated while the noise parts are uncorrelated. Two statistical methods, the Moran test and the join-count statistic, are used to examine the noise parts. Images from three digital modalities--computerized tomography, magnetic resonance and computed radiography--are used for the evaluation of the noise bits. A residual image is formed by subtracting the original image from its smoothed version. The noise level in the residual image is then identical to that in the original image. Both statistical tests are then performed on the bit planes of the residual image. The results show that most digital images contain only 8-9 bits of correlated information. Both methods are easy to implement and fast to perform.

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