Deconvolution

To answer a recent question on the meaning of the term "deconvolution," I'll refer you to several texts referenced in the following citation from the world's greatest on-line source of information: "In optics and imaging, the term "deconvolution" is specifically used to refer to the process of reversing the optical distortion that takes place in an optical microscope, electron microscope, telescope, or other imaging instrument, thus creating clearer images. It is usually done in the digital domain by a software algorithm, as part of a suite of microscope image processing techniques. Deconvolution is also practical to sharpen images that suffer from fast motion or jiggles during capturing. Early Hubble Space Telescope images were distorted by a flawed mirror and could be sharpened by deconvolution.

The usual method is to assume that the optical path through the instrument is optically perfect, convolved with a point spread function (PSF), that is, a mathematical function that describes the distortion in terms of the pathway a theoretical point source of light (or other waves) takes through the instrument.[3] Usually, such a point source contributes a small area of fuzziness to the final image. If this function can be determined, it is then a matter of computing its inverse or complementary function, and convolving the acquired image with that. The result is the original, undistorted image.

In practice, finding the true PSF is impossible, and usually an approximation of it is used, theoretically calculated[4] or based on some experimental estimation by using known probes. Real optics may also have different PSFs at different focal and spatial locations, and the PSF may be non-linear. The accuracy of the approximation of the PSF will dictate the final result. Different algorithms can be employed to give better results, at the price of being more computationally intensive. Since the original convolution discards data, some algorithms use additional data acquired at nearby focal points to make up some of the lost information. Regularization in iterative algorithms (as in expectation-maximization algorithms) can be applied to avoid unrealistic solutions.

When the PSF is unknown, it may be possible to deduce it by systematically trying different possible PSFs and assessing whether the image has improved. This procedure is called blind deconvolution.[3] Blind deconvolution is a well-established image restoration technique in astronomy, where the point nature of the objects photographed exposes the PSF thus making it more feasible. It is also used in fluorescence microscopy for image restoration, and in fluorescence spectral imaging for spectral separation of multiple unknown fluorophores. The most common iterative algorithm for the purpose is the Richardson–Lucy deconvolution algorithm; the Wiener deconvolution (and approximations) are the most common non-iterative algorithms."

1. O'Haver T. "Intro to Signal Processing - Deconvolution". University of Maryland at College Park.
2. Wiener N (1964). Extrapolation, Interpolation, and Smoothing of Stationary Time Series. Cambridge, Mass: MIT Press. ISBN 0-262-73005-7.
3. Cheng PC (2006). "The Contrast Formation in Optical Microscopy". Handbook of Biological Confocal Microscopy (Pawley JB, ed.) (3rd ed. ed.). Berlin: Springer. pp. 189–90. ISBN 0-387-25921-X.
4. Nasse M. J., Woehl J. C. (2010). "Realistic modeling of the illumination point spread function in confocal scanning optical microscopy". J. Opt. Soc. Am. A 27 (2): 295–302. doi:10.1364/JOSAA.27.000295.