Adaptive deblurring of noisy images.

We propose a practical sensor deblurring 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 the magnification of noise at high frequencies. To address this issue, we apply a special spectral 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 passband 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 the properties of the power window, we design the deblurring filter adaptively by estimating the energy of the signal and the noise of the image to determine the passband and the transition band of the filter. The deblurring filter design criteria are (a) the filter magnitude is less than 1 at the frequencies where the noise is stronger than the desired signal (the transition band), and (b) the filter magnitude is greater than 1 at the other frequencies (the passband). 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 in which 10 observers are to identify 12 military targets with 12 aspect angles. The results of comparing target identification probabilities with blurred and deblurred images and adding two levels of noise to blurred and deblurred noisy images are reported.