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1 results

  • On the amount of detail that can be recovered from a degraded signal

  • Peter Hall
  • Journal:
    Advances in Applied Probability / Volume 19 / Issue 2 / June 1987
    Published online by Cambridge University Press:
    01 July 2016, pp. 371-395
    Print publication:
    June 1987

  • Motivated by applications in digital image processing, we discuss information-theoretic bounds to the amount of detail that can be recovered from a defocused, noisy signal. Mathematical models are constructed for test-pattern, defocusing and noise. Using these models, upper bounds are derived for the amount of detail that can be recovered from the degraded signal, using any method of image restoration. The bounds are used to assess the performance of the class of linear restorative procedures. Certain members of the class are shown to be optimal, in the sense that they attain the bounds, while others are shown to be sub-optimal. The effect of smoothness of point-spread function on the amount of resolvable detail is discussed concisely.