WaveThresh
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sure
Computes coefficient that minimizes Stein's unbiased risk estimation
DESCRIPTION
Returns the (absolute) value of the coefficient that minimizes Stein's
unbiased risk (SURE) for a soft thresholded estimator.
USAGE
sure(x)
REQUIRED ARGUMENTS
- x
- Vector of (normalized) wavelet coefficients. Coefficients should be
supplied divided by their standard deviation.
OPTIONAL ARGUMENTS
None.
VALUE
The (absolute) value of the wavelet coefficient that minimizes SURE.
SIDE EFFECTS
None
DETAILS
SURE is a method for unbiasedly estimating the risk of an estimator.
Stein (1981) showed that for a nearly arbitrary, nonlinear biased
estimator, one can estimate its loss unbiasedly. See
the Donoho and Johnstone, 1995 for
further references and explanation. This function minimizes formula
(11) from that paper.
RELEASE
Version 3.9 Copyright Guy Nason 1998
SEE ALSO
threshold
EXAMPLES
#
# Let's create "pretend" vector of wavelet coefficients contaminated with
# "noise".
#
v <- c(0.1, -0.2, 0.3, -0.4, 0.5, 99, 12, 6)
#
# Now, what's sure of this?
#
sure(v)
#
# [1] 0.5
#
#
# I.e. the large significant coefficients are 99, 12, 6 and the noise is
# anything less than this in abs value. So sure(v) is a good point to threshold
# at.