Adaptive deblurring of noisy images

This paper proposes a practical sensor deblur filtering method for images that are contaminated with noise. A sensor blurring function is usually modeled via a Gaussian-like function having a bell shape. The straightforward inverse function results in magnification of noise at the high frequencies. In order to address this issue, we apply a special window to the inverse blurring function. This special window is called the power window, which is a Fourier-based smoothing window that preserves most of the spatial frequency components in the pass-band and attenuates quickly at the transition-band. The power window is differentiable at the transition point which gives a desired smooth property and limits the ripple effect. Utilizing properties of the power window, we design the deblurring filter adaptively by estimating energy of the signal and noise of the image to determine the pass-band and transition-band of the filter. The deblurring filter design criteria are: a) filter magnitude is less than one at the frequencies where the noise is stronger than the desired signal (transition-band); b) filter magnitude is greater than one at the other frequencies (pass-band). Therefore, the adaptively designed deblurring filter is able to deblur the image by a desired amount based on the estimated or known blurring function while suppressing the noise in the output image. The deblurring filter performance is demonstrated by a human perception experiment which 10 observers are to identify 12 military targets with 12 aspect angles. The results of comparing target identification probabilities with blurred, deblurred, adding 2 level of noise to blurred, and deblurred noisy images are reported.