7.2.1 DATA INPUT–OUTPUT AND TRAINING SAMPLES

In this demonstration, two neural network configurations were devised, with three input parameters for backscattering and four input parameters for bistatic scattering (see Table 7.1). The outputs of the network were normalized surface roughness (RMS height $k\sigma$, correlation length $k\ell$), and soil moisture $m_v$. Three roughness spectra—Gaussian, exponential, and 1.5-power—were all included in the simulation. The inputs are given in Table 7.1.

Backscattering: In this case, HH-, VV-, and HV (=VH)-polarized backscattering coefficients were simultaneously fed into the dynamic learning neural network. The incident angles were set at 10~60°.

Bistatic Scattering: In this setup, inputs are chosen from HH-, HV-, VH-, and VV-polarized bistatic scattering coefficients at different incident angles, scattering angles, and scattering azimuthal angle were fed into the network. Both the incident angles and scattering angle were selected at 10~60°. The scattering azimuthal angle was set for the forward region at 0~90° and for the backward region at 90~180°. For bistatic scattering, we devised three inputs (as in backscattering) for comparison of inversion performance under the same number of inputs.

It follows that the network configuration, after trial and error, was given with a predetermined threshold of 0.1% (see Table 7.2). A total of 10,450 data sets were selected randomly as training data from the 15,014 data sets for backscattering, with 4564 data sets used as testing data. As a rule of thumb, 70% of the total data sets were used for training (i.e., 127,240 data sets are chosen randomly as training data from the 181,770 data sets for bistatic scattering), and 54,530 data sets were used as testing data, from which the backward region and forward region cases each accounted for half of the data. The data sets are randomly selected from the database simulated by the AIEM model with the ranges of the surface and radar parameters listed in Table 7.3. The step size of the discretized scattering azimuthal angle was set to 10°, and the discretized incident and scattering angles were both set to 1°. The network training was accomplished by mapping input–output pairs that were randomly selected from the database simulated by the AIEM model with the range of surface and radar parameters listed in Table 7.3. As a rule of thumb, 70% of the data was selected, randomly, as the training set, with the rest as the testing set.

7.2.2 RETRIEVAL RESULTS USING BACKSCATTERING COEFFICIENTS

After completing the training, the DLNN entered the process stage. By randomly selecting 30% testing sample, the surface parameter retrieval was performed via the DLNN. This was indeed a highly nonlinear mapping of feature sets (by training) onto the surface domain (by process). The retrieval performance between the network-inverted result and the model-observed data, using backscattering data only (i.e., three-input), can be seen in Figure 7.9. For three surface parameters of interest, the normalized root-mean-squared errors (nRMSE) were 0.074, 0.075, and 0.070 for RMS height, correlation length, and soil moisture, respectively, and correlation coefficients were larger than 0.95, which was quite satisfactory; among the three parameters, the inversion of $k\ell$ was poorer. The reason for this is that, as discussed previously, the estimation of correlation length always poses higher errors due to a higher uncertainty of the functional form of the correlation function. Several samples of inversion results between the measured data (POLARSCAT) and the network inversion are presented in Table 7.4. As we can see, the retrieval performance of these three parameters can achieve satisfactory accuracy.

7.2.3 RETRIEVAL USING BISTATIC SCATTERING COEFFICIENTS

When it comes to inversion from bistatic scattering data, we can examine the performance of using forward, backward, and full (backward plus forward), respectively. This might be practically useful since, in setting up the bistatic observation, the transmitter and receiver may be in specular or off-specular geometries. The correlation between the network-inverted result and model-observed data is shown in Figure 7.10. The inversion results were relatively close to the 1:1 line, indicating a quite-favorable correlation between the inversion and the truth data. It is worth noting that retrieval from bistatic scattering data performed better than from backscattering, especially for soil moisture inversion. Interestingly, the inversion results performed better at the forward region than in the backward region. This can also be seen quantitatively in Table 7.5, from which we can read the nRMSE being 0.060, 0.088, and 0.044 in the backward region and 0.045, 0.071, and 0.018 in the forward region for RMS height, correlation length, and soil moisture, respectively. The overall nRMSE and correlation coefficient (r) for backscattering and bistatic scatter are also given in Table 7.5. Typically, among the three surface parameters being inverted, the soil moisture tended to experience the least error, regardless of retrieval from backscattering data or bistatic scattering data. Better inversion performance seems to have been gained by the use of scattering data from the forward region. Based on this point and compared to the backscattering, it is not surprising that if we combine the scattering data from the forward and backward regions, the best retrieval accuracy in terms of nRMSE and the correlation coefficient can be obtained. This is also evident from Table 7.5, where the smaller nRMSE and higher correlation coefficient can be read as “Full” when compared to those for backscattering. It is apparently a conviction that the dynamic learning neural network as presented is able to tackle a bulky volume of data, either the training stage or operational stage, and thus achieve superior retrieval accuracy.

There is a much higher degree of freedom to test the inversion from bistatic scattering compared to backscattering, as well as to choose the inputs, depending on the physical feasibility of the measurements. We can have measurements at the backward, forward, or combined forward and backward regions to input to the DLNN. In terms of polarization, we can have four polarizations in bistatic—two co-polarizations, two cross-polarizations, two-polarizations, or one cross-polarization. Figure 7.11 shows the retrieval performance of surface roughness and soil moisture from bistatic scattering data (three-input). The simulation test confirms the inversion performance of the neural network in terms of training and operation. From Table 7.5, we can see that the retrieval accuracy is higher using forward bistatic data than backward. The impact of polarization for bistatic cases seems not as significant as that for backscattering cases. More importantly, for the bistatic case, three inputs do not necessarily produce higher retrieval accuracy than four inputs do. It is the number of features that determine the training effectiveness and thus the retrieval accuracy. It becomes clear at this point that under the same number of inputs, inversion accuracy is higher from bistatic scattering than from backscattering. This is likely due to the fact that the bistatic scattering measurements can better separate the coupling effect of roughness and dielectric constant. For this, the sensitivity analysis given in Chapter 5 is useful for feature selection to train the neural network.

At this point, it is of relevance to demonstrate the retrieval of soil surface parameters from bistatic radar measurements [6,11], including roughness and moisture content, using the model-trained DLNN. A bistatic measurement facility (BMF) [11] was designed and constructed consisting of a 10 and 35 GHz polarimetric radar system for the purpose of characterizing the 3D bistatic scattering response of rough dielectric surfaces. According to, [11] a measurement with 10 GHz from a Gaussian random rough surface, with a normalized RMS height of $k\sigma =0.2$ and a normalized correlation length of $kl=1.0$, was water-soaked bricks in which the real part of the dielectric constant was 62. The incident angle and scattering angle were both set as 45°, and the scattering azimuth angle was changed from 180° to −180°. A study in [11] gave the measurements of a rough soil surface with 35 GHz using an indoor bistatic measurement facility (IBMF). At 35 GHz, the surface was assumed to be an exponentially correlated function with the normalized RMS height and correlation length being 3.28 and 29.6, respectively. The effective soil permittivity was 3.5-j0.05. The measured bistatic scattering coefficient as a function of the scattering angle (0~70°) in the backward direction (${\varphi }_s={180}^{\circ }$) and forward direction (${\varphi }_s=0^{\circ }$), and the incident angle was 20°. Another data set is taken from [6,12], where the bistatic rough dielectric surface scattering was measured at the European Microwave Signature Laboratory (EMSL) at (−10~−50°) of incidence and scattering angles with 1.5–18.5 GHz of frequency. The surface was characterized by a Gaussian correlation function with surface roughness of $\sigma =2.5\mathrm{c}\mathrm{m},l=6\mathrm{c}\mathrm{m}$.

To assess the inversion performance and be more quantitative, we list the numeric results in Table 7.6, showing the measured $k\sigma$, $k\ell$, and $m_v$, along with the inverted data. Of the eight total test sets, the inverted results are in good agreement with the measured data. Relatively, the difference between the measured and inverted data is well within 20% error. The RMSE, nRMSE, and correlation coefficient (r) for each individual parameter, $k\sigma$, $k\ell$, and $m_v$, are also given. Of the three parameters, $k\ell$ had the largest RMSE. This is consistent with our previous discussion on the measurement uncertainty of the correlation length. Nevertheless, numeric values in Table 7.6 confirm the good performance of surface parameter inversion by model-trained DLNN with inputs from bistatic radar scattering measurements.

7.2.4 COMPARISON WITH IMAGE-BASED SURFACE PARAMETER ESTIMATION FROM POLARIMETRIC SAR IMAGE DATA

The trained DLNN is now applied to the measured data acquired at L-band (1.3 GHz) from E-SAR over the floodplain of River Elbe located in North-Eastern Germany [13–15] as shown in Figure 7.12. At L-band, the spatial resolution of the single look complex data is in azimuth about 0.75 m and in the range of about 1.5 m. The data were acquired in April and August of 1997 along with two 15 km long and 3.2 km wide strips. Ground data has been collected in August 1997 over agriculture test fields with different roughness conditions. Soil moisture measurements have been performed on five different locations at each test field. The fields were viewed with incidence angle ${\theta }_i$ ranging from 48° to 50°. Four fields were selected due to the vegetation-covered and the choices of them were constrained by the image-based model [13] (see Table 7.7).

The DLNN results show that the varied inversion results using different correlated surfaces in the AIEM model. All the retrieval results (mean value for each test area) are listed in Table 7.8. First, we can see the deviation of roughness ($k\sigma$) between the inversion results and ground truth values. The largest deviation occurs for the case of field A 5/16. Gaussian correlated surface matches best for the cases. It is interesting to note that 1.5 power correlated surfaces fall in between Gaussian and exponential correlated surfaces that represent two extremes of roughness spectra in terms of their bandwidth. For horizontal roughness scale, correlation length, there is no ground truth available, the comparison is excluded. Nevertheless, the inversion outputs are listed in Table 7.8 for reference. Next, we check the retrieved dielectric constants which may be related to moisture content. It is observed that the inversion results agree well with the ground truth. To indicate this point more clearly, we plot the inverted dielectric constants by model-based DLNN and image-based [13] along with ground truth values (0–4 and 4–8 cm), as shown in Figure 7.13. The image-based results and the model-based DLNN results reasonably fall within the range of two different depths [16]. A short note is that the neural network inversion can explain more closely the observed data and hence give a good inversion result.