Deconvolution

The inversion of a Convolution equation, i.e., the solution for $f$ of an equation of the form

$$f*g = h+\epsilon,$$

given $g$ and $h$, where $\epsilon$ is the Noise and $*$ denotes the Convolution. Deconvolution is ill-posed and will usually not have a unique solution even in the absence of Noise.

Linear deconvolution Algorithms include Inverse Filtering and Wiener Filtering. Nonlinear Algorithms include the CLEAN Algorithm, Maximum Entropy Method, and LUCY.

See also CLEAN Algorithm, Convolution, LUCY, Maximum Entropy Method, Wiener Filter

References

Cornwell, T. and Braun, R. ``Deconvolution.'' Ch. 8 in Synthesis Imaging in Radio Astronomy: Third NRAO Summer School, 1988 (Ed. R. A. Perley, F. R. Schwab, and A. H. Bridle). San Francisco, CA: Astronomical Society of the Pacific, pp. 167-183, 1989.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Convolution and Deconvolution Using the FFT.'' §13.1 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 531-537, 1992.