DECONVOLUTION

Deconvolution is the mathematical operation to reverse convolution. The term is specifically used to refer to the process of reversing the optical distortion that takes place in a microscope or other optical 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.

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 takes through the instrument. 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. 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. Since the original convolution discards data, some algorithms use additional data acquired at nearby focal points to make up some of the lost information.