Polarimetric Decomposition

Polarimetric Decomposition Operator

   This operator performs the following polarimetric decompositions for a full polarimetric SAR product:

Sinclair Decomposition

   Let 
   

    be the complex scatter matrix. The Sinclair decomposition produces (R, G, B) bands with the following intensities
   
    The main drawback of this decomposition is the physical interpretation of the resulting RGB image.

Pauli Decomposition

   The (R, G, B) bands produced by the Pauli decomposition correspond to the following intensities:

Freeman-Durden Decomposition

   The Freeman decomposition models the covariance matrix as the contribution of three scattering mechanisms:
  1. canopy scatter from a cloud of randomly oriented dipoles, forest for example;
  2. even- or double-bounce scatter from a pair of orthogonal surfaces with different dielectric constants;
  3. Bragg scatter from a moderately rough surface.
    The power scattered by the components of the above three scattering mechanisms are employed to generate a RGB image as the following:

Yamaguchi Decomposition

   The three-component Freeman-Durden decomposition can be successfully applied to SAR observations under the reflection symmetry assumption. However, there exists areas in an SAR image where the reflection symmetry condition does not hold. Yamaguchi et al. proposed, in 2005, a four-component scattering model by introducing an additional term corresponding to nonreflection symmetric cases. The fourth component introduced is equivalent to a helix scattering power. This helix scattering power term appears in heterogeneous areas (complicated shape targets or man-made structures) whereas disappears for almost all natural distributed scattering. Therefore, Yamaguchi decomposition models the covariance matrix as the following four scattering mechanisms:
  1. volume;
  2. double-bounce;
  3. surface; and
  4. helix scatter components.

H-A-Alpha Decomposition

   The H-A-Alpha decomposition is based on the eigen decomposition of the coherency matrix [T3]. Let λ1, λ2, and λ3 be the eigenvalues of the coherency matrix (λ1 > λ2 > λ3 > 0), and u1, u2 and u3 be the corresponding eigenvectors which can be expressed as the following:


 Then three secondary parameters are defined as the follows:
  1. Entropy:
  1. Anistropy: 
  1. Alpha:

Touzi Decomposition

   In 2007, for the monostatic scattering case, Ridha Touzi has proposed a new Target Scattering Vector Model (TSVM) [2]. Based on the Kennaugh-Huynen decomposition, this model allows to extract four roll-invariant parameters:
  1. Kennaugh-Huynen maximum polarization parameter: orientation angle (Ψ);
  2. Kennaugh-Huynen maximum polarization parameter: helicity (τ);
  3. Symmetric scattering type magnitude (α);
  4. Symmetric scattering type phase (Φ).
    The roll-invariant incoherent target decomposition, i.e. Touzi decomposition, is as the following:
  1. Compute target coherency matrix [T3] with a sliding window;
  2. Perform eigendecomposition on the coherency matrix;
  3. Apply the new target scattering vector model to each eigenvector to extract four parameters (Ψk, τk, αk, Φk, k = 1, 2, 3).
  4. Compute averaged parameters (Ψ, τ, α, Φ):

Van Zyl Decomposition

   The Van Zyl decomposition assumes that the reflection symmetry hypothesis establishes and the correlation between co-polarized and cross-polarized channels is zero. The assumption is generally true in case of natual media such as soil and forest. With such an assumption, the eigen decomposition of the averaged covariance matric C3 can be given  analytically  and C3 can be expressed in the following manner:


The van Zyl decomposition thus shows that the first two eigenvectors represent equivalent scattering matrices that can be interpreted in terms of odd and even numbers of reflections.

Input and Output

Parameters Used

   For all decompositions, the following processing parameter is needed (see Figure 1):


                                                       
                 Figure 1. Dialog box for Polarimetric Decomposition operator


For Freeman-Durden decomposition, an extra parameter is needed (see Figure 2):


                 Figure 2. Dialog box for Freeman-Durden decomposition


For Yamaguchi decomposition, the following parameters are needed (see Figure 3):


                 Figure 3. Dialog box for Yamaguchi decomposition

For H-A-Alpha decomposition, the following extra parameters are needed (see Figure 4):


                 Figure 4. Dialog box for H-A-Alpha decomposition


For Touzi decomposition, the following extra parameters are needed (see Figure 5):



                 Figure 5. Dialog box for Touzi decomposition

For Van Zyl decomposition, the following parameters are used (see Figure 6):


                 Figure 6. Dialog box for Van Zyl decomposition


Reference: 

[1] Jong-Sen Lee and Eric Pottier, Polarimetric Radar Imaging: From Basics to Applications, CRC Press, 2009

[2] R. Touzi, “Target Scattering Decomposition in Terms of Roll-Invariant Target Parameters,” IEEE Transactions on Geoscience and Remote Sensing, vol. 45, no. 1, pp. 73–84, January 2007.