# Four-Component Scattering Power Decomposition Algorithm with Rotation of Covariance Matrix Using ALOS-PALSAR Polarimetric Data

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Rotation of Covariance Matrix

_{HH}, S

_{HV}, S

_{V H}and S

_{V V}denote the complex scattering elements at HH, HV, VH, and VV polarizations respectively, 〈〉 denotes the ensemble average of an arbitrary window size, and * denotes complex conjugate. The covariance matrix after rotation can be expressed using a unitary rotation matrix as:

_{22}(θ) given by

_{22}(θ) because it is equivalent to minimizing volume scattering after the decomposition. Polarimetric matrices are rotated based on the angle which minimizes the cross-polarized component, so that the contribution of volume scattering power after the decomposition is suppressed. The derivative of C

_{22}(θ) with respect to θ is

_{22}(θ) = 0, the angle is

## 3. 4-CSPD Algorithm Using Rotated Covariance Matrix

_{0}) > 0 is used for determining which scattering power, Ps or Pd, is dominant. C

_{0}can be defined in terms of the covariance matrix elements as:

## 4. Experimental Results and Discussions

## 5. Conclusions

## Acknowledgments

## References

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**Figure 1.**4-CSPD algorithm using rotation of covariance matrix (the structure of entire flowchart mainly comes from [18]).

**Figure 2.**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 (

**a,b**): 4-CSPD (helix component excluded). The lower row (

**c,d**): 4-CSPD with rotation. The left column (a,c) shows results from coherency matrix and the right column (b,d) shows results from covariance matrix. The red, green, and blue colors represent double-bounce, volume, and surface scattering components respectively. Areas A, B, and C are mostly composed of urban, mountainous, and sea area respectively. Area D is an area which shows remarkable change after rotation.

**Figure 3.**Optical photograph of the image corresponding to the area in Figure 2. The central coordinate of the image is approximately at (139°52′E, 35°20′N).

**Figure 4.**Rotation Angle distribution of selected areas in Figure 2. Horizontal axis is rotation angle and vertical axis is frequency. (

**a**) Area A. (

**b**) Area B. (

**c**) Area C. (

**d**) Area D.

**Figure 5.**Tokyo Bay Aqua-Line (Highway) near the area of Figure 2. The central coordinate of each image is approximately at (139°53′E, 35°26′N). (

**a**) 4-CSPD image without rotation. (

**b**) 4-CSPD image with rotation. (

**c**) Difference of Pd component between the left and the middle image.

**Figure 6.**Tokyo Bay Aqua-Line (Highway) near the area of Figure 2. (

**a**) Rotation angle image. The central coordinate of the image is approximately at (139°53′E, 35°27′N). (

**b**) Rotation angle distribution of the left image. The peak around 30 degree represents the highway bridge.

Method (Rotation Range, Approach) | P_{d} | P_{v} | P_{s} | P_{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% |

## Share and Cite

**MDPI and ACS Style**

Sugimoto, M.; Ouchi, K.; Nakamura, Y.
Four-Component Scattering Power Decomposition Algorithm with Rotation of Covariance Matrix Using ALOS-PALSAR Polarimetric Data. *Remote Sens.* **2012**, *4*, 2199-2209.
https://doi.org/10.3390/rs4082199

**AMA Style**

Sugimoto M, Ouchi K, Nakamura Y.
Four-Component Scattering Power Decomposition Algorithm with Rotation of Covariance Matrix Using ALOS-PALSAR Polarimetric Data. *Remote Sensing*. 2012; 4(8):2199-2209.
https://doi.org/10.3390/rs4082199

**Chicago/Turabian Style**

Sugimoto, Mitsunobu, Kazuo Ouchi, and Yasuhiro Nakamura.
2012. "Four-Component Scattering Power Decomposition Algorithm with Rotation of Covariance Matrix Using ALOS-PALSAR Polarimetric Data" *Remote Sensing* 4, no. 8: 2199-2209.
https://doi.org/10.3390/rs4082199