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 |
+----------+
The Lee Filter program FLE for different types of noise are
implemented as follows:Algorithm for ADDITIVE NOISE:
The resulting grey-level value R for the smoothed pixel is:
R = I + K * (CP - I)
where:
K = QVAR / (QVAR + AVAR)
Algorithm for MULTIPLICATIVE NOISE:The resulting grey-level value R for the smoothed pixel is:
R = I + K * (CP - U*I)
where:
(MVAR/U**2)
K = 1 - -----------
(QVAR/I**2)
Algorithm for combined ADDITIVE and MULTIPLICATIVE NOISE:The resulting grey-level value R for the smoothed pixel is:
R = I + K * (CP - U*I - W)
where:
K = (U*QVAR) / (QVAR*U**2 + I**2*MVAR+AVAR)
The multiplicative noise variance is calculated from local
statistics in the filter window:
MVAR = (SD / I)**2
The value of mean additive noise is usually 0. The value of mean
multiplicative noise is usually 1.
QVAR is the variance in filter window
I is the mean grey level in the filter window
U is the mean multiplicative noise
W is the mean additive noise
CP is the central pixel in filter window
MVAR is the multiplicative noise variance
AVAR is the additive noise variance
SD is the standard deviation of the noise
in the filter window
The parameter THRVAR (only for 7x7 and 9x9 windows) is introduced in
order to reduce noise in the edge areas (Improved Lee Filter). The
basic idea is to redefine the filter window near the high contrast
regions taking into account the orientation of edges. For each high
local variance (high contrast point) over the threshold (THRVAR), a
gradient will be computed to obtain the orientation of the edge.
Then the subset of pixels in the local area on either side of the
edge is defined; the local variance will be reduced, and hence the
noise along the edge will be removed.For further information on the Improved Lee Filter, refer to:
J.S.Lee, "Refined filtering of image noise using local statistics" Computer Graphic and Image Processing 15, 380-389 (1981)
Example of using 5x5 Lee Filter on 8x8 database image where NOISE = "BOTH", NOISEVAR = 300, ADDMEAN = 0, MULMEAN = 1.0, THRVAR = (default).
All pixels are filtered. In order to filter pixels located near the edges of the image, edge-pixel values are replicated to give sufficient data.
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 of their programs. For more information about the method, please refer the following papers:
Zhenghao Shi and Ko B. Fung, 1994, A Comparison of Digital Speckle Filters, Proceedings of IGRASS 94, August 8-12, 1994. Jong-Sen Lee, Digital Image Enhancement and Noise Filtering by Use of Local Statistics, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAM1-2, No. 2, March, 1980.