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
Convolution, LUCY, Maximum Entropy Method, Wiener FilterExplore with Wolfram|Alpha
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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.Referenced on Wolfram|Alpha
DeconvolutionCite this as:
Weisstein, Eric W. "Deconvolution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Deconvolution.html