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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 57, Iss. 3 — Mar. 1, 1967
  • pp: 297–303

Image Restoration by the Method of Least Squares

CARL W. HELSTROM  »View Author Affiliations

JOSA, Vol. 57, Issue 3, pp. 297-303 (1967)

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The restoration of optical images, as well as the unfolding of spectroscopic and other data that have been convolved with a window function or an instrumental impulse response, can be viewed as the solution of an integral equation. Solution of such an integral equation when the data are corrupted by noise or experimental error is treated as the problem of finding an estimate that is a linear functional of the data and minimizes the mean squared error between the true solution and itself. The estimate depends on assumptions about the spectral densities of the images and the noise, the choice of which is discussed. Coherent optical processing and digital processing are described.

CARL W. HELSTROM, "Image Restoration by the Method of Least Squares," J. Opt. Soc. Am. 57, 297-303 (1967)

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