The Gamma Map filter was first proposed by Kuan. To apply it, the a priori knowledge of the probability density function of the scene is required. The scene reflectivity was assumed to be Gaussian distributed. However, this is not quite realistic since it implicitly assumes a negative reflectivity. Lopes modified the Kuan Map filter by assuming a gamma distributed scene and setting up two thresholds.
The gamma filter size ranges from 1 to 11. Different filter sizes will greatly affect the quality of processed images. If the filter is too small, the noise filtering algorithm is not effective. If the filter is too large, subtle details of the image will be lost in the filtering process. A 7x7 filter usually gives the best results.
The input text field for the number of looks specifies the number of looks of the radar image. This number is used to calculate the noise variance. The option menu allows the user to specify whether or not the Radar image is in intensity format or amplitude format.
GAMMA was based on the paper:
A. Lopes, E. Nezry, R. Touzi, and H. Laur, "Structure detection and statistical adaptive speckle filtering in SAR images", International Journal of Remote Sensing, Vol. 14, No. 9, pp. 1735-1758, 1993.The GAMMA filter performs spatial filtering on each individual pixel in an image using the grey level values in a square window surrounding each pixel. The dimensions of the filter must be odd, and can be from 3x3 to 11x11 pixels.
All pixels are filtered. In order to filter pixels located near edges of the image, edge-pixels are replicated to give sufficient data.
+----------+
| a1 a2 a3 |
| a4 a5 a6 | <--- Filter window 3 X 3
| a7 a8 a9 |
+----------+
Algorithm :The resulting grey level value R for the smoothed pixel is:
R = I for Ci less than or equal to Cu
R = (B*I + SQRT(D))/(2*ALFA) for Cu < Ci < Cmax
R = CP for Ci greater than or equal to Cmax
where:
NLOOK = Number of looks
VAR = Variance in filter window
CP = Centre pixel grey level value
I = Mean grey level in the filter window
Cu = 1/SQRT(NLOOK)
Ci = SQRT(VAR) / I
Cmax = SQRT(2)*Cu
ALFA = (1+Cu**2)/(Ci**2-Cu**2)
B = ALFA-NLOOK-1
D = I*I*B*B+4*ALFA*NLOOK*I*CP
For the amplitude image, each grey level will first be squared before
applying the algorithm, and the square root of the calculated pixel
is returned as the final result.
This parameter is specified via the option menu: The user can
either specify an amplitude image or a power (intensity) image.The NLOOK parameter is set via the Number of Looks input text field.
In addition, this program uses a method as described in P.994 of the following paper:
A. Lopes, R. Touzi, and E. Nezry, "Adaptive Speckle Filters and Scene Heterogeneity", IEEE Transactions on Geoscience and Remote Sensing, Vol 28, No. 6, November 1990.to remove isolated pixels (pixel of very high or very low value) in homogeneous areas.
PCI wishes to acknowledge the assistance of Ko B. Fung and Zhenghao Shi at Canada Centre for Remote Sensing for providing source code and assistance for their programs. Special thank to Dr. R. Touzi from Canada Centre for Remote Sensing for his helpful suggestions and comments.
For more information about comparison of different radar filtering methods, please refer to the following papers:
Zhenghao Shi and Ko B. Fung, 1994, A Comparison of Digital Speckle Filters, Proceedings of IGRASS 94, August 8-12, 1994.