PSPEDHT

Description

PSPEDHT creates a raster of pedestal height at every pixel of a fully polarimetric SAR (POLSAR) data set. The pedestal height is the minimum value of intensity at the maximum copolarization response and is an indicator of the intensity of the depolarized backscattering. The output image contains the floating-point pedestal-height values in linear or decibel scaling.

Parameters

Name	Type	Caption	Length	Value range
FILI*	String	Input polarimetric SAR image	1 - 192
FILO*	String	Output pedestal-height raster	1 - 192
SCALETYP	String	Scaling	0 - 7	Linear | Decibel Default: Linear
STEPPSI	Integer	Orientation angle step size (degrees)	0 - 1	1 - 90 Default: 10
STEPCHI	Integer	Ellipticity angle step size (degrees)	0 - 1	1 - 45 Default: 10
MONITOR	String	Monitor mode	0 - 3	ON, OFF Default: ON

* Required parameter

Parameter descriptions

FILI

The name of the input polarimetric SAR data set, which must be either non-symmetrized or symmetrized fully polarimetric (quad-polarization) complex data. The input data set must be in covariance, coherence, or Kennaugh matrix format. Polarization signatures computed from a single observation represent a fully polarized wave, even though multiple scattering mechanisms are present in the return. Therefore, the input data set should have an equivalent number of looks (ENL) of at least 25, which can be achieved by applying a polarimetric filter, such as boxcar, when the input data set is single-look complex.

The input data set must have already been imported into the PCIDSK (.pix) format with SARINGEST. For more information, including a complete list of supported SAR sensors and data products, follow the link to SARINGEST at the end of this topic.

FILO

The name of the output pedestal-height raster file. The output file has the same dimensions as the input, and one channel that contains the pedestal-height raster, stored in floating-point pixel values. The physical quantity (beta0, sigma0, or gamma0) represented by pixel values is the same as that of the input SAR data set, but its values can be scaled to be either linear or decibel.

The file name you specify must not already exist.

SCALETYP

The scaling (decibel or linear) of pixel values in the output image.

This parameter is optional.

STEPPSI

The increment, in degrees, for the orientation angle (psi) used in the search for the copolarization-response minimum. The computation is repeated for each increment started at -90 degrees successively until +90 degrees is reached. The specified value for the step size must be between 1 and 90 degrees; the default value is 10 degrees.

This parameter is optional.

STEPCHI

The step, in degrees, for the ellipticity angle (chi) used to search for the copolarization-response minimum. The computation is repeated for each increment started at -45 degrees successively until +45 degrees is reached. The specified value must be between 1 and 45 degrees; the default is 10 degrees.

This parameter is optional.

MONITOR

The program progress can be monitored by printing the percentage of processing completed. A system parameter, MONITOR, controls this activity.

Available options are:

• ON: Turns the monitor ON (default)
• OFF: Turns the monitor OFF (recommended if running in batch or background mode)

Details

PSPEDHT creates a raster that contains the pedestal height of the polarization response for a fully polarimetric SAR data set. The pedestal height is defined as the minimum value of the copolarization response (normalized to unity) and is based on the polarization synthesis at each pixel. It indicates the intensity of the depolarization for each pixel within the image.

The input file must represent a non-symmetrized or symmetrized, fully polarimetric (quad-polarization) data set in one of the following matrix formats: covariance (c4r6c or C3r3c), coherency (t4r6c or T3r3c), or Kennaugh (k16r or K9r).

The input data set must have already been imported into the PCIDSK (.pix) format with SARINGEST. For more information, including a complete list of supported SAR sensors and data products, follow the link to SARINGEST at the end of this topic.

For a fully polarized plane electromagnetic (EM) wave, the tip of the electric field vector traces an ellipse on a plane perpendicular to the wave-propagation direction. There are two parameters that define the polarization ellipse: orientation and ellipticity. The orientation of the ellipse, psi, can range from -90 degrees to +90 degrees. The ellipticity angle, chi, can range from -45 degrees to +45 degrees.

At each pixel, PSPEDHT searches through the full range of the orientation and ellipticity angles with the search steps specified by the orientation and ellipticity step size parameters. For each combination of the two angles, PSPEDHT determines the copolarization-response (backscatter) value based on a polarization-synthesis algorithm. Copolarized response occurs when the received polarization is the same as the transmitted polarization. After each synthesized response is computed, the overall minimum at the pixel is stored in the output file.

Pedestal height in the output file is expressed in the same physical units (sigma0, gamma0, beta0) as the input data set. If scaling is set to 'decibel', the stored value is converted to the logarithmic scale before saving to the output file.

The values of the orientation and ellipticity search step parameters offer a trade-off between the processing speed and the accuracy of the computed pedestal height. Reducing values of step size for orientation and ellipticity increases the processing time, but makes the results more accurate. For example, changing the default values of 10 degrees to 5 degrees almost quadruples the processing time, but the pedestal height is determined more accurately at each pixel.

Example

Create the pedestal-height image for a RADARSAT-2 image that has already been ingested with SARINGEST. The single-look (SLC) image is first averaged by PSBOXCAR with a 5 x 5 window. You then use the averaged image as input to PSPEDHT, with 5-degree steps for each angle. The output pixel values are in the linear scale.

EASI>FILI="rsat2.pix" 
EASI>FILO="r2_avg5x5.pix"
EASI>FLSZ=5,5
EASI>run PSBOXCAR

EASI>FILI="r2_avg5x5.pix"
EASI>FILO="r2_ped_ht.pix"
EASI>SCALETYP=
EASI>STEPPSI=5
EASI>STEPCHI=5
EASI>run PSPEDHT
    

Algorithm

The polarimetric response (backscatter, B) is computed at every pixel in PSPEDHT from the polarimetric-synthesis equations. Each has a similar form for the three accepted input matrices: covariance c, coherency t, and Kennaugh k. The following expressions are shown for the non-symmetrized matrices. For symmetrized matrices, all symbols are capitalized.

The asterisk (*) denotes a complex conjugate of a vector. The y and z vectors are defined through the unit polarization x-vector in the horizontal-vertical basis, and Ft and Fr represent the transmit and receive Stokes vectors. The x-vector is defined as follows:

x = Transpose( h, v)
h = cos(psi) * cos(chi) - i * sin(psi) * sin(chi)
v = sin(psi) * cos(chi) + i * cos(psi) * sin(chi)

In the copolarization response, the orientation (psi) and ellipticity (chi) angles are the same for the transmit and receive polarizations; therefore, the y and z vectors are defined as follows:

y = Transpose( h*h, h*v, v*h, v*v )
z = Transpose( h*h+v*v, h*h-v*v, h*v+v*h, -i*(h*v-v*h) ) / sqrt(2)

The Stokes vectors Ft and Fr are identical for the copolarized response and are replaced by F. The common Stokes vector F is defined as follows:

F = Transpose( 1, cos(2*psi)*cos(2*chi), sin(2*psi)*cos(2*chi), sin(2*chi) )
For symmetrized data, the y and z vectors are replaced by the Y and Z vectors, but the same Stokes vector is used. The symmetrized Y and Z vectors are defined as follows: 
Y = Transpose( h*h, (h*v+v*h)/sqrt(2), v*v )
Z = Transpose( h*h+v*v, h*h-v*v, h*v+v*h ) / sqrt(2)

PSPEDHT loops over all lines and pixels of the input data set. The processing at every pixel proceeds as follows:

• Initialize the minimum response at a pixel: Rmin = MAX_FLOAT (the maximum floating-point number) and search for the minimum copolarization response:
  • For psi, from -90 degrees to +90 degrees, in STEPPSI-degree increments
  • For chi, from -45 degrees to +45 degrees, in STEPCHI-degree increments
    • Derive the copolarized response, Rco, for the current values of psi and chi as follows:

      Rco( psi, chi) = B( psi, chi, psi, chi )

      Of the preceding polarimetric-response equations, one is used according to the matrix type in the input data set.

    • If the computed response is less than Rmin, then Rmin = Rco( psi, chi )
• If output scaling to decibels is specified, convert the computed value as follows:

  Rmin_db = 10 * log10( Rmin )

• Store the computed value at the pixel.

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.