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The present study introduces the four-component scattering power decomposition (4-CSPD) algorithm with rotation of covariance matrix, and presents an experimental proof of the equivalence between the 4-CSPD algorithms based on rotation of covariance matrix and coherency matrix. From a theoretical point of view, the 4-CSPD algorithms with rotation of the two matrices are identical. Although it seems obvious, no experimental evidence has yet been presented. In this paper, using polarimetric synthetic aperture radar (POLSAR) data acquired by Phased Array L-band SAR (PALSAR) on board of Advanced Land Observing Satellite (ALOS), an experimental proof is presented to show that both algorithms indeed produce identical results.

With increased quality of synthetic aperture radar (SAR) systems utilizing polarimetric information recently, the development and applications of polarimetric SAR (POLSAR) are one of the current major topics in radar remote sensing. While conventional SAR systems handle only single polarimetric information, data acquired through POLSAR systems contain fully polarimetric information on the shift in polarization between the transmitted and received microwave. Thus, they have potential to increase further the ability of extracting physical quantities of the scattering targets. Therefore, they are used in broad fields of study such as visualization for classification [

Several decomposition techniques have been proposed along with the utilization of fully polarimetric data sets provided by POLSAR platforms. Most of them can be categorized into either of two main groups. One is based on eigenvalue analysis [

The four-component scattering power decomposition (4-CSPD) [

According to [

To overcome this problem, the concept of rotation in the 4-CSPD has recently been proposed by Yamaguchi

In the present article, we introduce the 4-CSPD algorithm with rotation of covariance matrix and compare rotation of coherency and covariance matrices. This is because, although both approaches should yield a same result [

Since the detail of rotation of coherency matrix can be found in [_{HH}_{HV}_{V H}_{V V}_{22}(

Now, we are going to minimize _{22}(_{22}(

Therefore, when _{22}(

An extreme value can be derived from applying

The algorithm of the 4-CSPD analysis using rotation of covariance matrix is summarized in this section.

Once _{0}) > 0 is used for determining which scattering power, _{0} can be defined in terms of the covariance matrix elements as:

As a result, all of the four scattering components are determined. If

Since covariance matrix and coherency matrix are mutually interchangeable by unitary transformation, the output of this algorithm should exactly be the same as the output from the rotation of coherency matrix as long as the same angle, the one which optimally minimizes cross-polarized component, is chosen. This can easily be proven mathematically that both

The algorithm is applied to ALOS-PALSAR data, and the results and discussions are presented in this section.

The effect of the size of the moving window (

The central area in

In this study, the four-component scattering power decomposition (4-CSPD) algorithm with rotation of covariance matrix is introduced. We demonstrated that the algorithm is correct by showing that the result of covariance matrix rotation is identical to that of coherency matrix rotation utilizing ALOS-PALSAR quad-polarization data. Although it is well known that the both matrices should produce the same result based on the theory of unitary transformation, experimental proof with rotation of the matrices has not been done before. We clarified that different types of areas react to the rotation algorithm differently. Urban or industrial areas showing strong double-bounce scattering with the original 4-CSPD (without rotation) are little affected by rotation. Forested areas show random distribution in rotation angles because of their randomness in polarization. Sea or smooth ground surface areas are moderately affected by rotation. Urban or industrial areas which have oblique structures to radar illumination show peaks of rotation angle distribution away from zero degree (center) unlike the other areas, and the degree seems to correspond to the angle between the radar illumination and the structures. We also showed that the rotation can improve the classification of man-made objects such as ships and bridges on the sea.

We would like to thank Japan Aerospace Exploration Agency (JAXA) for cordially providing ALOS-PALSAR data. We also thank anonymous reviewers for constructive comments to improve the paper.

4-CSPD algorithm using rotation of covariance matrix (the structure of entire flowchart mainly comes from [

ALOS-PALSAR decomposition images of Tokyo Bay, Japan. The central coordinate of each image is approximately at (139°52′E, 35°20′N). The upper row (

Optical photograph of the image corresponding to the area in

Rotation Angle distribution of selected areas in

Tokyo Bay Aqua-Line (Highway) near the area of

Tokyo Bay Aqua-Line (Highway) near the area of

Relative contribution to total power of Tokyo Bay area before and after rotation.

Method (Rotation Range, Approach) | _{d} |
_{v} |
_{s} |
_{c} |
---|---|---|---|---|

4-CSPD without rotation | 26.26% | 30.63% | 40.06% | 3.05% |

4-CSPD with rotation | 36.34% | 17.53% | 43.68% | 2.45% |