Name

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POSITIVITY

Purpose

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Map an image uniquely and smoothly into all positive values.

Explanation

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Take unconstrained x (usually an image), and map it uniquely and
smoothly into positive values. Negative values of x get mapped to
interval ( 0, sqrt( epsilon )/2 ], positive values go to
( sqrt( epsilon )/2, oo ) with deriv approaching 1. Derivative is
always 1/2 at x=0. Derivative is used by the MRL deconvolution
algorithm.

Calling Sequence

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result = POSITIVITY( x, [ /DERIVATIVE, EPSILON = )

Inputs

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x - input array, unconstrained

Output

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result = output array = ((x + sqrt(x^2 + epsilon))/2
if the /DERIV keyword is set then instead the derivative of
the above expression with respect to X is returned

Optional Input Keywords

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DERIV - if this keyword set, then the derivative of the positivity
mapping is returned, rather than the mapping itself
EPSILON - real scalar specifying the interval into which to map
negative values. If EPSILON EQ 0 then the mapping reduces to
positive truncation. If EPSILON LT then the mapping reduces to
an identity (no change). Default is EPSILON = 1e-9

Revision History

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F.Varosi NASA/GSFC 1992, as suggested by R.Pina UCSD.
Converted to IDL V5.0 W. Landsman September 1997