In this paper equations for the output mean and variance of the intensity-dependent spread (IDS) filter and its reconstruction are derived for images corrupted by white Gaussian and white Poisson noise. These equations are then used to compute the signal-to-noise ratio (SNR) in both the filtered image and the reconstructed image. We show that for additive Gaussian noise the SNR in the reconstructed image varies as the square root of the mean intensity and for additive Poisson noise the SNR is constant. We compare the SNR in the reconstructed image with that of the linear-shift-invariant Gaussian filter, and we show that the IDS filter can achieve a specified minimum SNR over the image with substantially less blur than a Gaussian. We also derive a formula to trade off blur for SNR by adjusting the spread factor of the IDS kernel.
© 1998 Optical Society of America
Shahriar Najand, Douglas Blough, and Glenn Healey, "Signal-to-noise ratio of the intensity-dependent spread filter and its reconstruction," J. Opt. Soc. Am. A 15, 1059-1067 (1998)