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2 results

  • Toward a signal-processing foundation for computational sensing and imaging: electro-optical basis and merit functions

  • David G. Stork
  • Journal:
    APSIPA Transactions on Signal and Information Processing / Volume 6 / 2017
    Published online by Cambridge University Press:
    01 August 2017, e8
    Print publication:
    2017
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      • Open access
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  • We highlight the need for – and describe initial strategies to find – new digital-optical basis functions and performance merit functions to serve as a foundation for designing, analyzing, characterizing, testing, and comparing a range of computational imaging systems. Such functions will provide a firm theoretical foundation for computational sensing and imaging and enhanced design software, thereby broadly speeding the development of computational imaging systems.

  • ORTHOGONAL FUNCTIONS AND ZERNIKE POLYNOMIALS—A RANDOM VARIABLE INTERPRETATION

  • Part of
  • C. S. WITHERS
  • Journal:
    The ANZIAM Journal / Volume 50 / Issue 3 / January 2009
    Published online by Cambridge University Press:
    03 November 2009, pp. 435-444
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  • There are advantages in viewing orthogonal functions as functions generated by a random variable from a basis set of functions. Let Y be a random variable distributed uniformly on [0,1]. We give two ways of generating the Zernike radial polynomials with parameter l, {Zll+2n(x), n≥0}. The first is using the standard basis {xn,n≥0} and the random variable Y1/(l+1). The second is using the nonstandard basis {xl+2n,n≥0} and the random variable Y1/2. Zernike polynomials are important in the removal of lens aberrations, in characterizing video images with a small number of numbers, and in automatic aircraft identification.