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This paper introduces a non-linear Polarimetric SAR data filtering approach able to preserve the edges and small details of the data. It is based on exploiting the data locality in both, the spatial and the polarimetric domains, in order to avoid mixing heterogeneous samples of the data. A weighted average is performed over a given window favoring pixel values that are close on both domains. The filtering technique is based on a modified bilateral filtering, which is defined in terms of spatial and polarimetric distances. These distances encapsulate all the knowledge in both domains for an adaptation to the data structure. Finally, the proposed technique is employed to process a real RADARSAT-2 dataset.

Polarimetric Synthetic Aperture Radar (PolSAR) is a multidimensional SAR type based on exploiting the vectorial nature of the electromagnetic waves. Different wave polarization states are employed for the transmitted and the received radar echoes in order to achieve a more comprehensive characterization of the target. Additionally, it allows the exploration of the complete space of polarization states allowing, for instance, optimization procedures [

Usually in SAR systems, the resolution cell dimensions are larger than the wavelength and, consequently, the measured echo is the coherent sum of all the individual target contributions. Since this contribution may be constructive or destructive, for distributed scatterers, the measured echo depends on the spatial distribution and importance of the individual targets within each resolution cell. As a result, homogeneous areas of the scene appear with a grainy appearance on SAR data, which is referred to as speckle. Note that the speckle is a true electromagnetic measure but, due to its complexity, it can only be characterized statistically.

In order to mitigate the effects of the speckle, some filtering is applied to the data. This speckle filtering process is needed for a proper target response estimation and for a reliable information extraction from PolSAR data. A classical Boxcar linear filter may be applied to the data to reduce the effect of the speckle but it results into spatial resolution loss and, additionally, it will not be valid near contours, for instance, due to the mixture of heterogeneous samples. Consequently, a proper filtering technique should employ only homogeneous samples of the data for speckle filtering. However, SAR images are strongly inhomogeneous, as they reflect the complexity of the scene and, therefore, some sort of spatial adaptation is needed. Recently, some state-of-the-art speckle filtering techniques have been developed in order to adapt to the spatial contours of the scene. In [

These techniques are based on identifying homogeneous samples for each pixel over the image. Note that this information is related with the scene itself, and, usually, we have no access to it, so this information should be inferred from the data. In this case, it is assumed that homogeneous pixels will have a similar radar response. Consequently, a distance or similarity measure has to be defined over the polarimetric space. In fact, this is an aspect in common with a wide number of techniques for PolSAR data processing as, for instance, classification [

This paper is organized as follows: Section 2 introduces the bilateral filtering modification based on distances that is proposed. Section 3 describes the iterative weight refinement process that will be employed to achieve a more reliable estimation of the filter weights. On Section 4 the proposed filtering technique is applied to RADARSAT-2 real data and it is evaluated and compared with other state-of-the-art speckle filtering techniques. Finally, Section 5 presents the conclusions.

PolSAR systems measure the complex reflectivity of the scene, collecting the scattering matrix

As mentioned before, the speckle is a true electromagnetic measure but it has to be characterized statistically. If the resolution cell is much larger than the wavelength, and there is no dominant scatterer within, then, by applying the central limit theorem, it may be assumed that the measured reflectivity is following a zero-mean complex Gaussian distribution [^{†} is the complex conjugate transpose of a vector and

In this case, the distribution _{i}^{†} represents the complex conjugate transpose. This estimated covariance matrix

However, the sample covariance matrix as defined in ^{ij}^{ij}_{s}_{p}

The keystone of the filter, then, is the definition of the _{s}_{p}

_{s}_{p}

Consequently, it is assumed that

As symmetry is assumed in data closeness, _{s}_{p}

Consequently, _{s}_{p}_{s}_{p}_{s}_{p}_{s}_{p}_{s}_{p}

Different similarity measures on the polarimetric space are defined and analyzed in [^{†} is singular, having rank equal to 1, and these measures need full-rank matrices. This problem also affects the Wishart distribution

In the proposed technique, diagonal measures are considered since it is focused on speckle filtering while also preserving the spatial resolution and small details of the image as much as possible. On the spatial domain the euclidean distance is proposed:

On the polarimetric domain two different measures are proposed, one based on the Wishart distribution and other based on the hermitian positive definite matrix cone geometry. The revised Wishart dissimilarity measure [_{ij}

The geodesic similarity measure is based on the Riemannian geometry of the hermitian positive definite cone of matrices [

When dealing with real PolSAR data, consideration must be given to the system noise, caused by thermal noise, discretization errors, _{pt}

Consequently, the _{pt}

Note that an important property of the proposed filtering in

As stated in Section 1, usually SAR images are strongly contaminated by speckle noise. Then, a given pixel of the image will have a large component induced by the speckle that will also contaminate all the pixel-based comparisons of the filter defined in _{p}

In this diagram, “Img 0” represents the original image and “Img

It is worth noting that the proposed scheme shown in _{p}

The proposed filtering technique has been employed to process the real RADARSAT-2 image presented in Pauli RGB composition in _{pw}_{s}_{p}

To see clearly the edge and small detail preservation of the proposed technique,

As mentioned before, the iterative weight refinement scheme, presented on _{p}

In the previous examples only the Pauli RGB representation and the

Additionally, to make a quantitative evaluation, _{13} over

In order to compare the amount of speckle filtering among different techniques, the equivalent (or effective) number of looks (ENL) is a well-known parameter. It describes the amount of averaging performed to SAR data under the complex Gaussian assumption [

Usually, the ENL is estimated over an homogeneous area of the image, assuming that the speckle is fully developed and that no texture is present, that is, assuming a constant radar cross section [

However, this measure was defined for single polarization SAR data and, when employing PolSAR data, different ENL values are obtained for each polarimetric channel. Some extensions to PolSAR data were proposed and analyzed in [_{TM}_{ML}^{(0)}(·) refers to the digamma function [_{ML}

To asses quantitatively the effectiveness of the different filtering techniques in terms of speckle noise reduction, _{ii}_{TM}_{ML}_{ML}

As it may be seen, there are significant differences according to the distinct ENL estimators. The performance of these estimators has been studied in detail in [_{TM}_{ML}_{ML}_{p}_{pw}_{pg}

As mentioned in Section 2, the parameters _{s}_{p}_{s}_{p}_{s}_{p}_{s}_{p}_{s}_{p}

However, these parameters have a different impact on the filtering process, as they are referring to different domains. In order to analyze this impact, _{s}_{p}_{s}_{s}_{p}_{p}_{s}_{p}_{p}_{s}_{s}_{p}

In the previous examples, the proposed method has been analyzed from the point of view of the speckle filtering application. However, it may also be useful for other applications as, for instance, matrix regularization. As mentioned before, the sample covariance matrix for original pixels ^{†} has rank equal to one, whereas for distributed scatterers the covariance matrix defining their statistical distribution has full-rank. Moreover, the Wishart distribution, that describes the statistics of the sample covariance matrix

In order to see the benefits of employing the proposed method as a covariance matrix regularization instead of the 3 × 3 multilook, _{s}_{p}_{sg}_{p}

In this paper, a novel Polarimetric Synthetic Aperture Radar (PolSAR) speckle filtering technique is proposed by exploiting the polarimetric locality, as well as its spatial locality in terms of polarimetric and geometric distances, respectively. Then, the spatial averaging is replaced by a weighted averaging favoring similar pixels in both spatial and polarimetric domains. This approach is based on a modified bilateral filter where a new iterative scheme is introduced to mitigate the noise over the estimated weights, leading to a large filtering over homogeneous areas, comparable to the classical multilook filter, while also preserving contours and small spatial details of the scene. In addition, the use of a polarimetric distance depending only on the diagonal elements of the covariance matrix, allows to consider the proposed technique as a regularization pre-processing step for other applications that require full-rank matrices, producing better results than a small multilook filtering for this purpose.

The technique has been applied to process real RADARSAT-2 data, leading to a better preservation of the polarimetric and the spatial information than other polarimetric approaches. In terms of polarimetric information, the retrieved values of Entropy, Anisotropy and Mean Alpha Angle present, in general, a lower bias. Additionally, the proposed approach allows a better preservation of spatial details associated to point targets presenting low Entropy.

A possible drawback of the proposed technique is that, as opposed to the multilook filter, it is employing a different number of averaged samples for each pixel of the image. However, this information is related to the

This work has been funded by the MICINN TEC Project MUSEO (TEC2011-28201-C02-01) and the CUR of the DIUE of the Autonomous Government of Catalonia and the European Social Fund. Flevoland data were provided by ESA in the frame of the AgriSAR 2009 campaign.

The authors declare no conflict of interest.

Iterative weight refinement approach diagram.

Original (

Optical image of the scene with the acquisition area marked in red [

Pauli RGB (|

Evolution of the

Number of averaged pixels (the

Entropy (H) and averaged alpha angle (

Pauli RGB (|_{s}_{p}_{pw}, σ_{s}_{p}_{pw}, σ_{s}_{p}_{pg}, σ_{s}_{p}_{pw}, σ_{s}_{p}_{pw}, σ_{s}_{p}_{pg}, σ_{s}_{p}

Histograms of the number of averaged pixels _{s}_{p}_{pw}, σ_{s}_{p}_{pw}, σ_{s}_{p}_{pw}, σ_{s}_{p}_{pw}, σ_{s}_{p}_{pw}, σ_{s}_{p}_{pw}, σ_{s}_{p}_{pg}, σ_{s}_{p}_{pg}, σ_{s}_{p}_{pg}, σ_{s}_{p}

Pauli RGB (|

Mean estimated values over homogeneous areas for different filtering techniques. For the proposed technique, an 11 × 11 local window has been employed with 5 weight refinement iterations and _{s}_{p}

Region | Filtering | _{11} |
_{22} |
_{33} |
|_{13}| |
arg(_{13})(°) |
H | A | |
---|---|---|---|---|---|---|---|---|---|

Original | 2.302 × 10^{−1} |
1.125 × 10^{−1} |
1.906 × 10^{−1} |
- | - | - | - | - | |

Z1 | 7 × 7 Multilook | 2.305 × 10^{−1} |
1.130 × 10^{−1} |
1.933 × 10^{−1} |
0.4194 | 1.670 | 0.8504 | 0.2599 | 42.87 |

Forest | Refined Lee | 1.879 × 10^{−1} |
9.965 × 10^{−2} |
1.623 × 10^{−1} |
0.3971 | 2.873 | 0.8442 | 0.3063 | 44.51 |

5,000 | IDAN | 1.471 × 10^{−1} |
7.353 × 10^{−2} |
1.252 × 10^{−1} |
0.2993 | 2.339 | 0.8878 | 0.2513 | 46.03 |

pixels | Proposed _{pw} |
2.227 × 10^{−1} |
1.090 × 10^{−1} |
1.869 × 10^{−1} |
0.3865 | 1.569 | 0.8698 | 0.2244 | 43.46 |

Proposed _{pg} |
2.210 × 10^{−1} |
1.082 × 10^{−1} |
1.853 × 10^{−1} |
0.3869 | 1.550 | 0.8661 | 0.2290 | 43.52 | |

| |||||||||

Original | 1.787 × 10^{−2} |
1.280 × 10^{−3} |
2.552 × 10^{−2} |
- | - | - | - | - | |

Z2 | 7 × 7 Multilook | 1.801 × 10^{−2} |
1.271 × 10^{−3} |
2.552 × 10^{−2} |
0.7443 | 3.088 | 0.4351 | 0.6407 | 19.30 |

Water | Refined Lee | 1.492 × 10^{−2} |
1.255 × 10^{−3} |
2.099 × 10^{−2} |
0.7062 | 2.535 | 0.4701 | 0.6438 | 21.89 |

3,900 | IDAN | 1.158 × 10^{−2} |
8.901 × 10^{−4} |
1.667 × 10^{−2} |
0.6263 | 2.473 | 0.5248 | 0.6967 | 24.32 |

pixels | Proposed _{pw} |
1.749 × 10^{−2} |
1.263 × 10^{−3} |
2.479 × 10^{−2} |
0.7094 | 2.872 | 0.4689 | 0.6381 | 20.59 |

Proposed _{pg} |
1.732 × 10^{−2} |
1.254 × 10^{−3} |
2.458 × 10^{−2} |
0.7079 | 2.871 | 0.4693 | 0.6392 | 20.75 | |

| |||||||||

Original | 1.862 × 10^{−1} |
3.195 × 10^{−2} |
1.771 × 10^{−1} |
- | - | - | - | - | |

Z3 | 7 × 7 Multilook | 1.855 × 10^{−1} |
3.170 × 10^{−2} |
1.758 × 10^{−1} |
0.7489 | 8.423 | 0.5444 | 0.2998 | 22.87 |

Crop | Refined Lee | 1.434 × 10^{−1} |
2.862 × 10^{−2} |
1.393 × 10^{−1} |
0.7059 | 7.478 | 0.5781 | 0.3653 | 25.86 |

2,200 | IDAN | 1.020 × 10^{−1} |
1.948 × 10^{−2} |
1.006 × 10^{−1} |
0.6187 | 8.641 | 0.6514 | 0.3783 | 27.84 |

pixels | Proposed _{pw} |
1.765 × 10^{−1} |
3.087 × 10^{−2} |
1.679 × 10^{−1} |
0.7062 | 8.474 | 0.5880 | 0.2933 | 24.50 |

Proposed _{pg} |
1.757 × 10^{−1} |
3.058 × 10^{−2} |
1.671 × 10^{−1} |
0.7072 | 8.470 | 0.5808 | 0.2987 | 24.53 |

Estimated equivalent number of looks (ENL) for different filtering techniques. For the proposed technique, an 11 × 11 local window has been employed with 5 weight refinement iterations and _{s}

_{11}) |
_{22}) |
_{33}) |
_{TM} |
_{ML} | ||
---|---|---|---|---|---|---|

Original | 0.9070 | 0.8309 | 0.9111 | 0.9241 | - | |

7 × 7 Multilook | 15.61 | 11.40 | 16.45 | 16.54 | 17.24 | |

Z1 | Refined Lee | 12.04 | 7.982 | 12.23 | 12.25 | 12.45 |

Forest | IDAN | 8.417 | 6.565 | 8.975 | 15.92 | - |

5,000 | Proposed _{pw}, σ_{p} |
8.610 | 7.764 | 10.20 | 13.24 | 18.52 |

pixels | Proposed _{pw}, σ_{p} |
20.20 | 15.04 | 23.24 | 24.31 | 26.57 |

Proposed _{pg}, σ_{p} |
7.860 | 6.993 | 9.090 | 11.97 | 17.19 | |

Proposed _{pg}, σ_{p} |
15.92 | 12.68 | 18.50 | 20.73 | 24.12 | |

| ||||||

Original | 1.018 | 0.9865 | 1.075 | 1.053 | - | |

7 × 7 Multilook | 23.25 | 15.67 | 21.63 | 22.73 | 20.74 | |

Z2 | Refined Lee | 15.54 | 11.06 | 15.09 | 15.23 | 13.66 |

Water | IDAN | 8.407 | 8.180 | 9.027 | 10.30 | - |

3,900 | Proposed _{pw}, σ_{p} |
7.297 | 17.32 | 7.516 | 8.085 | 21.48 |

pixels | Proposed _{pw}, σ_{p} |
28.96 | 22.89 | 26.44 | 29.09 | 33.81 |

Proposed _{pg}, σ_{p} |
6.631 | 14.29 | 6.845 | 7.375 | 19.73 | |

Proposed _{pg}, σ_{p} |
18.52 | 20.55 | 17.73 | 19.40 | 29.79 | |

| ||||||

Original | 0.7275 | 0.7319 | 0.8457 | 0.8090 | - | |

7 × 7 Multilook | 8.372 | 7.522 | 15.27 | 11.97 | 15.00 | |

Z3 | Refined Lee | 6.798 | 6.364 | 9.467 | 8.526 | 10.62 |

Crop | IDAN | 5.348 | 5.707 | 7.364 | 8.285 | - |

2,200 | Proposed _{pw}, σ_{p} |
2.947 | 4.889 | 4.464 | 4.254 | 12.97 |

pixels | Proposed _{pw}, σ_{p} |
6.810 | 8.061 | 12.93 | 10.59 | 19.77 |

Proposed _{pg}, σ_{p} |
2.911 | 4.561 | 4.308 | 4.134 | 12.55 | |

Proposed _{pg}, σ_{p} |
5.540 | 7.164 | 9.755 | 8.425 | 17.84 |