Re: Smoothing a time sequence of contour areas

On May 24, 9:08 am, ke <kateedward...@xxxxxxxxxxx> wrote:
Hello,

I have an interesting filtering problem that I could benefit from some
insight on.
I have a time sequence of 2D maps / images of ocean temperature, and
for each map I've contoured the same value and estimated the area
inside the contour.  The contour value was chosen to pick out a
natural high gradient that comes and goes in the maps.  The resulting
time sequence of contour areas is noisy due both to measurement noise
and to the real variability in temperature, which has unknown
timescale of variability (I tried calculating integral timescales but
the results look strange).

To reduce the noise in my time series of contour areas, it seems like
there's a couple of things I could do:
1) Spatially lowpass the maps before calculating the contours, but I
don't want to smooth out real high gradients which would introduce
errors into the contour area calculation
2) Temporally lowpass the temperature data before calculating the
contours, but I don't want to smooth out real variability in
temperature
3) Temporally lowpass the sequence of contour areas; same problem

Any suggestions on the best plan of attack?
Thanks,
Kate

Have you thought of using orthogonal wavelet decomposition?
It works well for problems such as yours, where the signal is non-
stationary.
For your option 3, you would decompose the signal into wavelet
coefficients (wavedec from the wavelet toolbox), then recompose into
wavelet details (wrcoef). Each detail represents the signal for a
range of timescales, with average timescales (from zero-crossing
analysis) given by 1.5*dt*2^i, i= 1, 2, 3,..... (for 'db5' mother
wavelet).
The wavelet details are orthogonal, so you can combine them in any
fashion you wish, while preserving the correct energy balance.
You can also de-noise by splitting each detail into noise and signal -
Matlab has a range of routines for doing this.
.

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