Inverse filtering

In a Fluorescence Microscope "we model the deterministic blurring as a Convolution of the image with the Point Spread Function . In the frequency domain a convolution transforms into a multiplication of the Fourier Transform of the sample with the Optical Transfer Function . The optical transfer function (OTF) is the Fourier transform of the point spread function. Therefore a naive form of Image Restoration is to divide the Fourier transform of the image by the OTF. This procedure is know as inverse filtering.

"... the result of inverse filtering is not usable due to large amplification of noise. This amplification is caused by the reconstruction by the inverse filter of the high frequencies in the Fourier spectrum of the image. Not only are these frequencies dominated by noise, but the OTF has low intensities at these frequencies as well. Therefore the inverse filter divides noise-dominated frequencies by low transfer values which result in a strong amplification of the noise in the restoration result.

"The inverse filter takes only the deterministic distortion, the blurring, into account, which results in an unacceptable performance on noisy images. Therefore we need more sophisticated algorithms that take both the deterministic and the stochastic distortions into account".

(From Image Restoration in Fluorescence Microscopy, G.M.P. van Kempen. Delf University Press, 1998. ISBN 90-407-1792-3 / CIP.)

For a practical example, see this link. To see the influence of noise, see this other link.

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