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Regarding the adaptation scheme, an anisotropic geometric error estimate based on a bound of the interpolation error is proposed.
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They are a very good choice of points for polynomial interpolation, and as it was indicated in Section 1, they give the smallest upper bound for the interpolation error of polynomial interpolation.
Under some hypotheses, bounds of the interpolation error for function and derivatives are obtained.
An optimization function which is composed of the interpolation error and the constraint items of the vertical scaling factors in the fractal interpolation iterated function system is designed.
The former is very well suited to the control of the interpolation error.
The large difference stems from the dependence of the interpolation error on the width of the interpolation interval, e.g. for the BDF and the Adams-Moulton formula, this interval is four times larger.
This gives the L2 upper bound of the approximation error.
(Lower bound of the error) [9, 10].
The equations for minimum required sampling frequency are derived by balancing the interpolation error against Cramer Rao lower bound.
The shoulder artifacts are due to the interpolation error as the frequency of the interference fringes of measured OCT signal approaches Nyquist rate, where local interpolation algorithm fails to resample the data with the correct value [ 18].
It is shown that the interpolation error can be eliminated through the use of first-order accurate centered interpolation operators with mesh-independent weights.
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