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Most signals are smooth, but running medians assume they have no curvature.
An alternate expression of this assumption is that the signal
has minimal curvature
;in other words,
.Thus we propose to create the cleaned-up data from the observed data with the fitting problem
| |
(18) |

where is a diagonal matrix with weights sprinkled along the diagonal,
and where is a matrix
with a roughener like (1,-2,1) distributed along the diagonal.
This is shown in Figure with .Experience showed similar performances
for and .Better results, however, will be found later in Figure
,
where the operator is replaced
by an operator designed to predict this very predictable signal.

** Next:** MEDIAN BINNING
** Up:** NOISE BURSTS
** Previous:** De-spiking with median smoothing
Stanford Exploration Project

4/27/2004