Gamma LAT: Reference Manual

polcoh

ANSI-C program: polcoh.c

NAME
polcoh - Calculate coherence matrix T elements from Pauli decomposition alpha, beta, gamma

SYNOPSIS
polcoh <SLC-1> <SLC-2> <SLC-3> <SLC1_par> <SLC2_par> <SLC3_par> <T> <T_par> <rlks> <azlks> [loff] [nlines]

<SLC-1>	(input) alpha single-look complex image (scomplex or fcomplex format)
<SLC-2>	(input) beta single-look complex image (scomplex or fcomplex format)
<SLC-3>	(input) gamma single-look complex image coregistered with SLC-1 (scomplex or fcomplex format)
<SLC1_par>	(input) alpha SLC image parameter file
<SLC2_par>	(input) beta SLC image parameter file of SLC-2 coregistered with SLC-1
<SLC3_par>	(input) gamma SLC image parameter file of SLC-3 coregistered with SLC-1
<T>	(output) root file name of coherence matrix elements (e.g. scene_id) output files have extensions .t11, .t22, .t33 (float), .t12, .t13, .t23 (fcomplex)
<T_par>	(output) MLI image parameter file associated with the coherence matrix element data
<rlks>	number of range looks for the averaging window
<azlks>	number of azimuth looks for the averaging window
[loff]	offset to starting line (default: 0)
[nlines]	number of SLC lines to process (enter - for default: entire file)

EXAMPLE

polcoh slc/20080409_alpha.slc slc/20080409_beta.slc slc/20080409_gamma.slc slc/20080409_alpha.slc.par slc/20080409_beta.slc.par slc/20080409_gamma.slc.par COH/20080409_pauli COV/20080409_pauli.coh_mli.par 3 6

This calculates the elements of the polarimetric coherence matrix T11, T22, T33, T12, T13, T23 and stores them in the files with the root file name COV/20080409_pauli and ending in .t11, .t22, .t33, .t12, .t13, .t23.

DESCRIPTION

The 3x3 coherence matrix [1] contains information on the averaged polarimetric signature of the illuminated scene and is the basis for polarimetric speckle filtering and classification. The coherence matrix elements are derived from the second-order statistics of the k-target feature vector composed of the elements of the Pauli decomposition calculated with the program pauli.

k = 1/SQRT(2) [HH + VV, HH - VV, 2 HV]^T

For monostatic radar data the coherence matrix elements are calculated from the Pauli decomposition [1] that generates the 3D k-target vector. The coherence matrix is formed by the outer product of the k-feature vector and the complex conjugate transpose of k. These 9 product terms are averaged over a spatial window that has dimensions rlks by azlks. Let the 3 terms of the k-target feature vector be denoted alpha, beta, and gamma respectively:

k = [

α, β, γ

]^T

The 3x3 covariance matrix T is given by:

T = <k · k^*T>

The <> operator denotes a spatial averaging over the window with dimensions rlks in range and azlks in azimuth:
T11: <

α α

^*>

      T22:

<

β β

^*>

      T33:

<

γ γ

^*>

          T12:

<

α β

^*>

T13: <

α γ

^*>

              T23:

β γ

^*>
      

      

      T21 = T12*

      T31 = T13*

      T32 = T23*

The coefficients on the diagonal T11, T22, and T33 are real-valued and are proportional to the power in the each of the 3 channels. The span is defined as the sum of the diagonal matrix elements of the T matrix and has the same value as the span of the covariance matrix C calculated by polcovar. and The off-diagonal elements are complex-valued. By construction, the coherence matrix is Hermetian.

[1] Lee, J. S., Eric Pottier, "Polarimetric Radar Imaging: from Basics to Applications," Chapter 3, CRC Press, Boca Raton, 2008

SEE ALSO
polcovar, pauli