PSWHITE

Description

PSWHITE detects coherent point targets in a single-look, fully polarimetric SAR data set. It uses a polarimetric whitening filter and threshold-based detection to discriminate bright point targets.

Parameters

pswhite(fili, filo, winsize, dtthrshl)

Name	Type	Caption	Length	Value range
FILI*	str	Input polarimetric SAR image	1 -
FILO*	str	Output coherent targets raster	1 -
WINSIZE	List[int]	Window size (pixels)	0 - 1	3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 31 | 33 Default: 5
DTTHRSHL	List[float]	Detection threshold	0 - 1	Default: 20

* Required parameter

Parameter descriptions

FILI

Specifies the name of the input polarimetric SAR data set. The input SAR image must contain either non-symmetrized or symmetrized, fully polarimetric (quad-polarization) single-look complex data in the scattering matrix format (s4c or S3c).

The input data set must have already been imported into the PCIDSK (.pix) format by SARINGEST. For more information and a complete list of supported polarimetric SAR sensors and data products, see the SARINGEST Help.

FILO

Specifies the name of the output coherent targets raster file. The file must not already exist. The output file will be generated to have the same dimensions as the input file. It will contain one bitmap segment and no raster channels. The 'on' pixels in the bitmap represent the detected bright targets. The overall Probability of False Alarm is stored as a ProbFalseAlarm metadata tag.

WINSIZE

Specifies the size of the square filter window that is moved across the input image. An odd integer between 3 and 33 must be specified; the default value is 5.

DTTHRSHL

Specifies the detection threshold. A float value greater than 0 must be specified; the default value is 20. Pixels with a value higher than this threshold will be determined as coherent point targets. For further information about this threshold, see the 'Details' section.

Details

PSWHITE uses a polarimetric whitening filter and a threshold-based detection to discriminate bright point targets.

The detected targets are marked as "on" pixels in a bitmap written to the output file.

PSWHITE optimally detects bright point targets in single-look complex, fully polarimetric SAR (POLSAR) data sets. The detection is performed in two stages. In the first stage the image is filtered to create a single-channel power image with reduced speckle and flattened backscatter. A threshold is then applied in the filtered image to detect small, bright targets. The pixels that contain detected targets are set to 1 in the output bitmap.

The number of detected targets depends on the window size and detection threshold. When the detection threshold value increases, the number of detected targets decreases. The relationship is not linear for window size and depends on the characteristics of the input data set. This detection threshold is computed by multiplying the average covariance matrix by the transposed symmetrized (or non-symmetrized, depending on the input data set) matrix at each pixel.

Example

Detect point targets in a RADARSAT-2 SLC data set that has already been ingested using SARINGEST. Use the default values for the two program parameters (WINSIZE=5, DTTHRSHL=20).

from pci.pswhite import *

fili	=	"rsat2.pix"
filo	=	"r2_white.pix"
winsize	=	[]
dtthrshl	=	[]

pswhite( fili, filo, winsize, dtthrshl )

Algorithm

PSWHITE is based on the article in the reference section. The processing involves the following steps.

• Derive several working parameters as follows:

  T = DTTHRSHL
  N = WINSIZE
  M = N^2 - 1
  n = (N - 1) / 2
  m = 4 for the non-symmetrized matrix, or
  m = 3 for the symmetrized matrix
                          

• Generate the covariance matrix image from the input scattering matrix. The c4r6c covariance matrix is created from a non-symmetrized input matrix s4c. The C3r3c matrix is created from a symmetrized input matrix S3c. In the following, the non-symmetrized matrix c4r6c is shown and is abbreviated as c.
• Generate the averaged covariance matrix image, c_hat. This requires looping over all image pixels (i,j), and all matrix elements. At every pixel, the filtered element is computed as an average over all pixels of the filtering window. The central pixel of the window is excluded from averaging, as follows:

               1      n     n
  c_hat(i,j) = - * ( Sum ( Sum ( c(i'+i,j'+j) ) ) - c(i,j) )
               M    i'=-n j'=-n
                          

• Loop over all lines and pixels (i,j) of the input data set. The processing at every pixel proceeds as follows:
  • Create a vector, w or W, from the scattering matrix elements as follows:

    w = Transpose( shh, shv, svh, svv ) for the non-symmetrized matrix, or
    W = Transpose( Shh, sqrt(2)*Shv, Svv ) for the symmetrized matrix.
                                    

  • Compute the inverse, Inv(c_hat), of the averaged matrix, c_hat.
  • Compute the filtered power value at the current pixel, y, as follows:

    y = Transpose(w*) * Inv(c_hat) * w
                                    

    The asterisk (*) represents the complex conjugate of the vector.

  • Compare the filtered power value, y, with the threshold, T. If y exceeds the threshold, set the corresponding bitmap pixel to 1.
• Compute the PFA, p, as follows:

                         m-1        M!
  p = (1 + T/M)^(-M) * ( Sum ( ----------- * (T/M)^k ) )
                         k=0   (M-k)! * k!
                          

  The exclamation mark (!) represents the factorial of the preceding number.

• Store the bitmap and the computed PFA in the output file.

Acknowledgements

PCI Geomatics gratefully acknowledges the financial support provided by the Canadian Space Agency through the Earth Observation Application Development Program (EOADP), contract number 9F028-034946.

References

Novak, L.M., and A.C. Burl. "Optimal speckle reduction in polarimetric SAR imagery", IEEE AES, 26 (1990): 293-305.