Durden decomposition of (a) hybrid-Pol and (b) quad-Pol, and (c) shows the comparison between single bounce scattering contribution of both configurations. Durden decomposition of (a) hybrid-Pol and (b) quad-Pol, and (c) shows the comparison between volume scattering contributions for both configurations.
Polarimetric SAR remote sensing
- Remote sensing
- Microwave remote sensing
- Unique features of microwave remote sensing
- Evolution of SAR
- Synthetic aperture radar
- Polarimetric SAR
- Hybrid polarimetric SAR
- Use of polarimetric radar for remote sensing applications
The width of the antenna beam β defines the spatial resolution in the azimuth direction (Xa). Wiley work, where he noted that the resolution of a SLAR can be improved by using the information contained in the Doppler frequency shift of the echo [6].
A Mathematical background for polarimetric radar
Polarization descriptors
- Jones coherency matrix
- Stokes vector
Partially polarized waves arise when a fully polarized wave is scattered by a random or scattered target. The characterization of partially polarized waves in terms of real quantities is done by Stokes vector G.
Mathematical characterization of target scattering
- Scattering matrix
- Scattering target vector
- Kennaugh and Mueller matrices
- Target covariance and coherency matrices
In general, the elements of the distribution matrix are complex and uncorrelated with each other. Pure or deterministic targets can be described using either the S distribution matrix or the Mueller/Kennaugh matrix.
Objective of the thesis
Thesis organization
- Phenomenological Huynen decomposition
- Eigenvector-based decompositions
- Model-based decompositions
- Coherent target decomposition
The main motive of this thesis is to extract information from polarimetric SAR (PolSAR) images. A second class of target decomposition theorems are those based on eigenvector analysis of the coherence matrix [19, 26].
Landcover classification using PolSAR images
34] introduced the combined use of unsupervised classification based on H/α and a supervised maximum likelihood (ML) classifier based on the complex Wishart distribution to improve the classification accuracy. 37] proposed an unsupervised classification algorithm based on the combined use of this classification technique with an ML classifier based on the complex Wishart distribution.
Hybrid-PolSAR configurations
It is established in Section 1.1.5 that hybrid-Pol mode is the optimum configuration among different dual-Pol modes. In his work [12, 39] he showed that the analysis of hybrid-Pol data can be started from the Stokes parameters of the backscattered field for hybrid-Pol system. The four-element Stokes vector captures all the information of backscattered signals for hybrid-Pol system.
Raney in [12] proposes anm-δdecomposition of double Pol hybrid data to extract information from hybrid Pol data. In their work, they introduced a new coefficient known as the coherence coefficient, which can be estimated from the Hybrid-Pol data as:.
PolSAR image enhancement techniques
However, the SVA technique cannot be implemented on data sampled at non-integer multiples of the Nyquist frequency. To remove the remaining sidelobes in the case of non-integer SVA, a modified version of the non-integer SVA algorithm was developed in [63]. In the modified version of the algorithm, a constant phase pis was added to non-integer Nyquist aperture functions to remove the remaining side lobes in the non-integer SVA algorithm.
However, the modified version of the incomplete SVA algorithm could not completely remove all the remaining sidelobes. To overcome this, a new SVA implementation was proposed in [65] that is able to completely side-suppress the lobes in the faded SAR image.
Scope of the present work
Wishart-H/α classification technique
Additionally, it is possible for a group of clusters to be confined to the same area. Therefore, the combined use of unsupervised classification based on H/α and supervised algorithm based on coherence matrix statistics was introduced in [34] to improve the classification accuracy. This supervised algorithm is a maximum likelihood (ML) classifier based on the complex Wishart distribution for the coherence matrix.
The classified pixels in each zone of H/α plane are taken as an initial training set for classification based on complex Wishart distribution. Improvements in classification accuracy through each iteration have been observed as the cluster centers in the H/α plane are updated after each iteration.
Wishart-H/A/α classification technique
A Gini-index based landcover classification scheme
The proposed landcover classification scheme
- Results and observations
Analysis of different entropies based landcover classification schemes
Different forms of entropy
The name "entropy" comes from the Greek word en-trepein, which means that energy is turned into waste. Although originally a thermodynamic concept, entropy has been used in other fields of study, including information theory, psychodynamics, economics, and evolution. In information theory, entropy is a measure of the uncertainty associated with a random variable and is commonly referred to as the Shannon entropy.
The amount of uncertainty of the distribution P, that is, the amount of uncertainty regarding the outcome of an experiment whose possible outcomes have the probability p1, p2, .., pn, is called the entropy of the distribution P and is usually measured by the amount H[P] = H(p1, p2, .., pn) , is defined by [72]. In statistical mechanics, the Boltzmann-Gibb entropy has been used to provide a probabilistic definition of entropy [74].
Different entropies based landcover classification schemes
- Tsallis entropy based landcover classification
- R´enyi entropies based landcover classification schemes
- Comparison of different entropies based landcover classifi-
A comparison plot of T3 with entropy and a Wishart-T3/A/α classification map are shown in Figure 3.11. We can see that the scatterplot in Figure 3.11(a) shifts downward compared to the Gini entropy scatterplot in Figure 3.6. A comparison plot of R2 with entropy and a Wishart-R2/A/α classification map are shown in Figure 3.12.
From Figure 3.12(a), it can be observed that the scatter plot moves upwards compared to the Gini entropy scatter plot in Figure 3.6 and therefore most of the pixels now have Gini value smaller than entropy value. From Figure 3.13(a) it is observed that the scatter plot moves further upwards and therefore pushes pixels more towards the lower entropy value.
A Fully automated landcover classification scheme
Results
The values of the new and old entropy/alpha bounds for the Flevoland and San Francisco datasets are shown in Tables 3.4 and 3.5, respectively. First, for the Flevoland dataset, we obtained the H/α classification maps for the old and new boundary sets, as shown in Figure 3.18(a). Since this approach is expected to increase the effectiveness of the Wishart-based classifier, we obtained the Wishart-H/A/α result for the old and new boundary sets; as shown in Figures 3.19(a) and 3.19(b) respectively.
To evaluate the performance, these results are compared to the ground truth shown in Figure 3.10(d). The percentage of different crops correctly classified by the entropy-based Wishart classifier with the old and new threshold sets is shown in Table 3.6.
Summary
Using compact polarimetry scattering model
- Results and discussions
Here we discuss a technique to generate pseudo quad-Pol data from hybrid Pol data. The individual CHyb terms can be obtained from the quad-PolC covariance matrix. Thus, hybrid Pol data can be generated from four Pol data. To compare the information content of the two modes, we generate pseudo quad-Pol data from hybrid Pol data using compact polarimetric scattering models [38].
Therefore, an additional constraint is required to reconstruct the pseudo-quad-Pol data from the hybrid-Pol data. Then, the pseudo-quad-Pol data are constructed from the derived hybrid-Pol data using a compact scattering model.
Based on scattering information
- Results and discussions
We used NASA/JPL AIRSAR L quad-Pol data for the Flevoland region to compare the hybrid-Pol performance with the quad-Pol system. Figures 4.1(b)–4.1(d) show a comparison of the reconstructed pseudo quad-Pol data with the original quad-Pol data set. First, the pseudo quad-Pol data is generated from the hybrid Pol data as described in Section 4.1.1.
Then, the scattering contribution of each of the three fundamental scattering mechanisms is evaluated for both quad-Pol and pseudo quad-Pol data using the Freeman and Durden decomposition technique. In these figures, the abscissa represents the original quad-Pol values and the ordinate represents the pseudo-quad-Pol values.
Analysis of hybrid-PolSAR images
A unsupervised classification of hybrid-Pol data based on relative
It is observed that for single and double hop the δ values are +900 and −900, respectively, if RHCP is transmitted. The phase histogram of different land cover types corresponding to the three basic scattering mechanisms was studied and some observations were made as follows. Single jump (ocean and bare land): The phase histogram is Gaussian distributed with mean -880 and variance of 8 as shown in Figure 4.7(a).
Double bounce (urban area and semi-deciduous forest): The phase histogram is Gaussian distributed with a mean of 730 and a variance of 700, as shown in Figure 4.7(b). This result can be compared with the H/α classification of quad-Pol data shown in Figure 3.2(b).
H/α decomposition of hybrid-PolSAR images
The entropy role is the same as the quad-Pol data entropy, which takes into account the target randomness. Considering the same sets of boundaries for hybrid-Pol as for quad-Pol, a H/α classification map was obtained. We also obtained an aH/α classification map with new limits estimated using the procedure discussed in Section 3.4.
It is noted that several land features are poorly classified in both classification maps, while the new boundary classification map performs slightly better.
PCA decomposition of hybrid-Pol data
- Application of PCA to radar image dataset
- Application of PCA to hybrid-Pol dataset
To check the effectiveness of this approach, the PCA RGB image can now be compared with the Freeman-Durden RGB image, shown in Figure 4.11(b). The Freeman-Durden RGB image is obtained by applying Freeman-Durden decomposition to quad-Pol data. The reason may be that the Freeman-Durden decomposition of fully polarimetric SAR data may not be completely accurate.
For example, many of the urban areas in the Freeman RGB image (Figure 4.11(b)) appear green, which is the color assigned for volume scattering. The other reason may be that PCA decomposition is implemented on hybrid-Pol data which occupies half of the polarization information space provided by fully polarimetric data, which is used by the Freeman-Durden decomposition technique.
Summary
The composite function of the main lobe and the side lobes is called the impulse response (IPR) of a system. Consequently, the finiteness of the data causes spectral leakage and degradation of the spectral resolution in the transformed domain. Degradation in spectral resolution: The width of main lobe defines the spectral resolution of the system.
However, this method achieves a reduction in size of the side lobes at the expense of an increase in the width of the main lobe of the IPR and thus a loss of spectral resolution. The DA IPR appears to have the narrow main lobe of the uniform IPR and the lower side lobes of Hanning IPR.
A local gradient based NLA algorithm
Results and observations
The frequency spectrum of the unweighted data, the apodized SVA spectrum, and the spectrum of the LGNLA algorithm are shown in Figure 5.2. From this figure, it can be seen that the two components at 89 and 90 Hz are clustered in the Fourier and SVA spectra, but quite distinguishable in the proposed LGNLA algorithm spectrum. We also demonstrated the performance of the proposed LGNLA algorithm in the presence of noise.
However, as the SNR decreases, the LGNLA algorithm is unable to separate two closely spaced frequency components. To evaluate the performance of the proposed algorithm for 2-D cases, the Moving and stationary target acquisition and recognition (MSTAR) airborne SAR image public dataset is used.
An extended CDA technique
PolSAR image enhancement through NLA
Results and observations
Decomposition of apodized PolSAR images
Pauli decomposition of apodized PolSAR images
In a visual comparison, it was found that the proposed E2CDA and LGNLA algorithms outperform the classical SVA technique in sidelobe noise suppression of PolSAR images. Second, Pauli decomposition is applied to the same PolSAR images after side noise has been removed from them using NLA algorithms. The three components of the Pauli decay of the apodized PolSAR images are shown in Figure 5.12.
The color-coded image for the Pauli decomposition of apodized PolSAR images and its apodized version are represented in Figure 5.13. Therefore, it is argued that information extraction through target decomposition is better when sidelobe noise is removed from the PolSAR images.
PCA decomposition of apodized PolSAR images
- Results and observations
We have proposed three new approaches for hybrid-Pol data analysis. Durden, “A three-component scattering model for polarimetric SAR data,” IEEE Transactions on Geoscience and Remote Sensing, vol. Yamada, “Four-component scattering model for polarimetric SAR image decomposition,” IEEE Transactions on Geoscience and Remote Sensing, vol.
Mango, "Spikkelvermindering in multipolarisasie, multifrekwensie SAR-beelde," IEEE Transactions on Geoscience and Remote Sensing, vol. Mishra, “A Novel Algorithm for Apodization and Super-Resolution in Fourier Imaging”, Devices and Communications (ICDeCom), 2011 International Conference on, vol., no., pp Feb.
Geometry of a side looking aperture radar
A schematic of the thesis organization
Feasible region in H/α classification plane
Classifications results of (a) Wishart-H/α and (b) Wishart-H/A/α after two
Entropy H: San Francisco data
Gini-index G: San Francisco data
Pixels distribution in the Entropy/Gini space
Comparison of G/α and H/α Classification map. From top: (a) H/α Clas-
The distribution of pixels for Flevoland data in (a) H/α and (b) G/α seg-
Variation of entropy and Gini-index as a function of scattering order in vol-
