Blind deconvolution

In electrical engineering and applied mathematics, blind deconvolution is deconvolution without explicit knowledge of the impulse response function used in the convolution. This is usually achieved by making appropriate assumptions of the input to estimate the impulse response by analyzing the output. Blind deconvolution is not solvable without making assumptions on input and impulse response. Most of the algorithms to solve this problem are based on assumption that both input and impulse response live in respective known subspaces. However, blind deconvolution remains a very challenging non-convex optimization problem even with this assumption.

Blind deconvolution illustration
Top left image: NGC224 by Hubble Space Telescope. Top right contour: best fit of the point spread function (PSF) (a priori).[1] Middle left image: Deconvolution by maximum a posteriori estimation (MAP), the 2nd iteration. Middle right contour: Estimate of the PSF by MAP, the 2nd iteration. Bottom left image: Deconvolution by MAP, the final result. Bottom right contour: Estimate of the PSF by MAP, the final result.
  1. ^ Barmby, Pauline; McLaughlin, Dean E.; Harris, William E.; Harris, Gretchen L. H.; Forbes, Duncan A. (2007). "Structural Parameters for Globular Clusters in M31 and Generalizations for the Fundamental Plane" (PDF). The Astronomical Journal. 133 (6): 2764–2786. arXiv:0704.2057. Bibcode:2007AJ....133.2764B. doi:10.1086/516777. S2CID 58913061.