Term: Coherency matrix

Definition:

A 3x3 or 4x4 real-valued matrix expressing the relation between the scattered signals in the channels in a quadrature polarization radar, thereby describing the scatterers in the scene.

Explanation:

The coherency matrix is a close relative of the covariance matrix – it contains the same information but in a different form. When the scattering matrix elements are arranged into a vector: V_C = 0.707 [S_xx + S_yy, S_xx - S_yy, S_xy + S_yx, j(S_xy - S_yx) ] ^T, the coherency matrix is defined as the expected value of V_CV_C*^T. If the radar is monostatic and the reciprocity assumption is valid, then S_xy = S_yx . In this case, V_C can be written as: 0.707 [S_xx + S_yy, S_xx - S_yy, 2S_xy ] ^T, with the three elements referred to as the Pauli components of the signal. In this case, the coherency matrix reduces to a 3x3 matrix.

Values at several samples are usually averaged to obtain estimates of the coherency matrix, resulting in a lower resolution image that is less noisy, and easier to classify. Even though the coherency matrix is derived from a power representation of the data, the average phase angles between the polarimetric channels are preserved in the representation.

The coherency matrix is positive semi-definite Hermitian, which means it has real non-negative eigenvalues. The eigenvalues are the same as the eigenvalues of the covariance matrix, and are used in target decomposition and image classification. The sum of the diagonal elements of the coherency matrix is proportional to the total received power from the four polarimetric channels, and is referred to as the “span” of the data.

Related Terms:

Scattering Matrix
Target Decomposition
Polarimetric Image Classification
Cloude decomposition
Covariance matrix
Target Decomposition
Total Power