Filtering RI, QI with a 2-D Gaussian curve
November 16, 2009
Hello all,
Today’s major project is filtering the fields of RI and QI with a Gaussian filter in two dimensions (see last post for more info). We essentially need to do this because refractivity measurements are smoothed (due to phase noise on small spatial scales, e.g. gate-to-gate nosiness…smoothing reduces noise and makes retrieval possible) with an approximate smoothing radius of 4 km. Boonleng’s algorithm essentially smoothes to a radius of
, where σ is the standard deviation of a Gaussian curve. This means that the variance, σ², equals 4 km². We can then assume that σ is the same in both the x and y dimensions, meaning the 2-D Gaussian curve will be circular symmetric.
We also set the maximum range to be smoothed as 3σ, or 6 km. This is done to reduce computational complexity significantly. It turns out that doing this leaves out only 0.2707% of the outer edges of the 2-D Gaussian curve. This was determined through:
, where the integrals are 2-D integrals of the Gaussian curve (eliminating the redundant 2π coefficient in each term). This leaves us with approx. 575 points contributing their values to the central point.
The results of this so far include matrices of range from a point (x0,y0) to every other point in the domain, as well as the 2-D Gaussian function from (x0,y0) to every point with a range less than 6 km. Here are sample output plots:
Range of each Pixel from element (180,50)
2-D Gaussian Function [zoomed on Pixel (180,50)
The next step is to take this Gaussian function, iterate it over the entire refractivity domain so that we have a similar smoothing function for every pixel, sum the product of the function with the data to be smoothed (i.e. RI, QI) and divide by the sum of the function. This will give us a Gaussian-smoothed map of RI and QI, which will allow for direct comparison with fields of N and dN/dt in both time and space (since spatial scales will be roughly the same).
November 18, 2009 at 2:11 pm
That’s an interesting idea, and makes more sense than using a point value of RI/QI to represent phase measurements that cover a larger area. As far as the circular convolution, C will be much faster than MATLAB and you can probably just use Boonleng’s cconv function if you can write a basic mex function in MATLAB to interface with it. I can help you with that.
November 18, 2009 at 2:40 pm
David,
I think that’s a good idea, using the circular convolution. And yes, I would greatly appreciate any help you could give as far as creating a mex file. Thanks!
P.S. – For now I’ve figured out how to do this w/ a 2-D Gaussian curve but it’s slow-ish (~20-30 min) and rather clunky…I’d like to streamline it so I can process a bunch of scans in a row.