Dextractor:Deformation Extractor Framework for Monitoring-Based Ground Radar

Abstract

The radio frequency (RF) data generated from a single-chip millimeter-wave (mmWave) ground-based multi-input multi-output (GB-MIMO) radar can provide a highly robust, precise measurement for deformation in harsh environments, overcoming challenges such as different lighting and weather conditions. Monitoring deformation is significant for safety factors in different applications, such as detecting and monitoring the ground stability of underground mines. However, radar images can experience different types of clutter and artifacts besides the spreading effects caused by the side lobes, resulting in the foremost challenge of suppressing clutter and monitoring deformation.In the state of the art, the introduced frameworks usually include many filters proposed for different types of noise, with commercial systems typically using an amplitude threshold. This paper proposes a framework for monitoring the deformation, where the essential process is to apply a data-driven threshold to the amplitude heatmap, detect the deformation, and eliminate noise. The proposed threshold is an iterative approach based on radar imagery statistics, and it performs well for the collected dataset. The principal advantage of our proposed framework is simplicity, reducing the burden of using different filters. We can consider the dynamic threshold based on data statistics as a data-driven machine learning tool. The results show promising performance for our method in monitoring the deformation and removing clutter compared to the benchmark method.

1. Introduction

Underground mines represent one of the high-risk settings for ground instability; consequently, monitoring deformation in such an application is an essential safety factor. Non-contact monitoring can be conducted using 3D laser scanners [1,2,3,4,5], photogrammetry [6,7,8] and space-borne interferometric synthetic aperture radar (InSAR) [9,10,11,12] technologies. The 3D laser scanners and the photogrammetry are susceptible to adverse weather conditions, lighting conditions, and dust. Terrain conditions, coverage area, and the operational cycle of the satellite influence the space-borne InSAR monitoring technology. The ground-based radar (GBR) [13,14,15] for deformation monitoring is a specialized application that operates from a stable ground platform as depicted in Figure 1. It offers real-time monitoring capability compared to airborne and space-borne InSAR sensors.

A dynamic deformation estimation approach using a ground-based multi-input multi-output (GB-MIMO) radar of a bridge structure is introduced in Zhao et al. [16]. The method includes several processes, such as improving the clutter suppression method and a two-step pixel extraction. Another study that monitors dam structural deformations using ground-based SAR (GB-SAR) data is chosen through a comprehensive spatial–temporal coherence analysis based on the permanent scatterer (PS) theory [17]. In their work, the authors [18] introduce a processing framework for differential SAR tomography (D-TomoSAR) based on region growth. Eventually, PS interferometry (PSI), accompanied by traditional ground-based monitoring techniques, is employed [19] to monitor mining activities.

In [20], the authors introduce a new processing chain for real-time GBSAR (RT-GBSAR) proposed based on the interferometric SAR small baseline subset (SBAS) concept. An alternative approach for real-time deformation monitoring is introduced in [21], where the PS network is updated using a dynamic Kalman filter [22] based on the PSs. In [23], a ground-based real aperture radar (GB-RAR) deformation information estimation method considering the effect of colored noise by using wavelet transform (WT) [24] is introduced. Lastly, in their study [25], the authors develop a GBSAR imaging system and interferometric processing framework for structural health monitoring (SHM).

The study [26] explores the feasibility and performance of a ground clutter removal technique that integrates slow-time multiple-input multiple-output (st-MIMO) waveforms with independent component analysis (ICA) in a ground-based MIMO radar system, explicitly targeting the detection of low, slow, and small (LSS) targets. In their research [27], the authors validate the separability of clutter and target signals in the frequency–wavenumber (F-K) domain through modeling, which leads to the proposal of a comprehensive clutter removal method based on the F-K domain for complex scenarios. In [28], the authors propose a clutter suppression scheme employs parallel principal skewness analysis (PPSA) to process the echo signals in the range domain, identifying the positions of moving targets. Subsequently, PPSA is applied again to process the moving targets in the Doppler domain, enabling the precise determination of their relative velocities. However, all of the above methods require applying several filters with an extensive computational cost.

In this research, we propose a framework, namely, the deformation extractor (Dextractor), to detect and monitor the deformation mainly depending on an iterative data-driven amplitude heatmap threshold, namely, the peak-to-trough mean-clipping (PTMC) algorithm. The PTMC iteratively filters out outliers to find the background where the background can be used to remove the clutter and other noises. Our algorithm is inspired by the background estimation, namely, $\sigma$ clipping introduced for astronomical images [29]. The algorithm keeps the clip using a clipping threshold based on the statistics of the amplitude heatmap, namely, the average of the mean of the minima and maxima. The clipping process iteratively measures the change in the standard deviation ($\sigma$) and stops when a remarkable change occurs.

The idea behind proposing a data-driven threshold based on radar data statistics is to overcome the challenge of selecting a fixed threshold where a low threshold retains both objects and clutter, while a high threshold suppresses both. Clutter can originate from various sources such as air reflection, vegetation, noise, and side lobes, each with distinct characteristics. Our iterative threshold method aims to find a background value that includes clutter but retains objects. We evaluate our framework using a dataset collected with a single-chip mmWave GB-MIMO radar in a tunnel environment, simulating underground mines.

The paper is structured as follows. Section 2 introduces the Dextractor framework. Section 3 mainly focuses on the data-driven PTMC filter. Further, in Section 4, the description of the dataset is presented. Finally, Section 5 and Section 6 show the experimental results and conclusion, respectively.

2. Dextractor Framework

Our proposed Dextractor framework is presented in Figure 2, where the GB-MIMO radar transmits mmWave into the target and receives the reflected signal using multiple transmitter and receiver antennas. The framework used is a standard framework for interferometric radar data processing, where our main contribution lies in proposing the data-driven PTMC algorithm to remove clutter and detect deformation. The received signal is in a complex form, where the amplitude and the phase of the signal can be computed. The first processing step is to apply a mean temporal filter by determining a window size where each number of scans located in the same window is averaged, obtaining a frame that represents those averages. This step aims to increase the signal-to-noise ratio (SNR) of the received data by reducing the noise level. The mean temporal filter can be expressed as

$$F={\displaystyle \frac{1}{W}}\sum _{s=1}^W{R}^s,$$

(1)

where F represents the frame, W indicates the window size, and $R^s$ denotes the radar scan s. The second processing is to apply the frequency-domain beam former for suppressing ambiguous beam pattern side lobes and improving the detection accuracy. The beam forming transforms the radar signal into the frequency domain and utilizes the phase information across different frequency components. Beam forming is a signal-processing technique combining signals from multiple antenna elements to form a beam of radiation or reception in a specific direction. This directionality enables enhanced signal reception or transmission in the desired direction while suppressing interference and noise from other directions.

Consider an array of N sensors receiving a signal $s\left(t\right)$ from a source located at an angle $\theta$. The received signal at the n-th sensor can be expressed as $x_n\left(t\right)=s(t-{\tau }_n)+n_n\left(t\right)$, where ${\tau }_n$ is the time delay corresponding to the source’s angle of arrival, and $n_n\left(t\right)$ is the noise. The received signals are transformed into the frequency domain using the Fourier transform. Let $X_n\left(f\right)$ be the Fourier transform of the received signal at the n-th sensor. The weights are designed to steer the beam toward the desired angle $\theta$. The output of the beamformer in the frequency domain is $Y(f,\theta )={\sum }_{n=1}^N{w}_n(f,\theta )X_n\left(f\right)$.

Afterward, we obtain the amplitude and the phase of the radar signal from the complex data. Then, we compute the accumulative deformation, which is proportional to the accumulative sum of the phase gradient of the time series data. In many GBR applications, such as deformation monitoring and topographic mapping, the 2-D phase unwrapping (PU) process becomes essential due to the measurement characteristics [30]. The GBR measurement of a target can be given as

$${\varphi }_u\left(x\right)={\varphi }_w\left(x\right)-\left(2\pi \times K\left(x\right)\right),$$

(2)

where ${\varphi }_u\left(x\right)$ denotes the unwrapped phase of the pixel located at x, ${\varphi }_w\left(x\right)$ is the wrapped phase, and $K\left(x\right)$ is the integer ambiguity number of the pixel located at x. Using Equation (2) is insufficient for obtaining a unique estimation of the absolute phase; consequently, all conventional 2-D PU methods rely on the phase continuity assumption, often referred to as the Itoh condition [31]. The phase continuity assumption is based on the idea that the absolute phase difference between adjacent pixels should not exceed $\pi$ [32]. This principle is a fundamental concept in 2-D PU, ensuring that phase values are consistent and continuous across the image. The phase continuity assumption can be defined as

$$\begin{array}{cc}\hfill \Delta {\varphi }_u\left(x\right)& =\left\{\begin{array}{cc}\Delta {\varphi }_w\left(x\right),\hfill & \Delta {\varphi }_w\left(x\right)\le \pi \hfill \\ \Delta {\varphi }_w\left(x\right)-2\pi ,\hfill & \Delta {\varphi }_w\left(x\right)>\pi \hfill \\ \Delta {\varphi }_w\left(x\right)+2\pi ,\hfill & \Delta {\varphi }_w\left(x\right)<-\pi \hfill \end{array}\right.\hfill \\ \hfill & \Delta {\varphi }_w\left(x\right)=\varphi \left(x\right)-\varphi (x-1),\hfill \end{array}$$

(3)

where $\Delta {\varphi }_u\left(x\right)$ is the estimated absolute phase gradient of pixel x, whereas $\Delta {\varphi }_w\left(x\right)$ is the phase difference between two pixels, x and $x-1$. We use the same approach by unwrapping the phase in the temporal dimension to ensure phase preservation and that the information remains coherent and consistent between radar acquisitions. We rely on the most common unwrapping method because of the short acquisition time of data collecting. The selection of a phase unwrapping technique depends upon the SNR levels, where simpler methods are sufficient for medium to high SNR radar signals. Conversely, low SNR conditions require more complex algorithms. In our study, we evaluate the SNR of the radar data in the following section, revealing a medium SNR ranging from 14.5 to 16.5 dB.

The last process is reducing clutter by filtering the pixels since the direction of deformation of those pixels is reversed from one scan to another. Our main objective is to detect and monitor the deformation of objects where the deformation does not fluctuate, i.e., moving in the same direction. Correspondingly, the diverse moving objects are out of interest in the current research. The deformation is computed directly by substituting with the estimated absolute phase gradient as [33]

$$d\left(x\right)=\lambda {\displaystyle \frac{\Delta {\varphi }_u\left(x\right)}{4\pi }}\times {10}^3\left(\mathrm{mm}\right),$$

(4)

where $d\left(x\right)$ represents the deformation in millimeter (mm) of pixel x, and $\lambda$ is the operating wavelength of the radar sensor. The accumulative deformation is the sum of each frame deformation of the time series data, which can be expressed as

$$D_{\mathrm{t}}\left(x\right)=\sum _{i=1}^{\mathrm{t}}{d}_i\left(x\right),$$

(5)

where $D_{\mathrm{t}}\left(x\right)$ is the accumulative deformation of pixel x at time t, and $d_i\left(x\right)$ is the deformation of pixel x at time i.

3. Peak-to-Trough Mean-Clipping Algorithm

One of our main contributions to this research is to propose a data-driven amplitude heatmap threshold to remove the clutter and precisely detect the deformation, namely, the PTMC algorithm. The clutter has different amplitude values, where the air reflection has a low value, whereas the noise has a high value. Air reflection in the context of radar data refers to the radar signals that are reflected off the air or atmospheric particles rather than solid objects or surfaces. It is typically seen as low-amplitude values in the radar data. As a result, the threshold selection process is challenging, where the low-value threshold preserves the objects and the clutter. However, the high threshold can suppress the clutter and the objects. Accordingly, a dynamic threshold is essential to remove the clutter and retain the objects.

The proposed adaptive PTMC algorithm, shown in Algorithm 1, iteratively eliminates outliers, aiming to find the value representing the background. The principle is that the radar amplitude consists of foreground objects and background clutter, and we aim to estimate the background value to remove the clutter. We then use the obtained background value as a threshold, where the objects that are less than it are considered clutter, and the deformation of those pixels is removed. However, the pixels with higher values are considered objects.

Algorithm 1: PTMC algorithm.

1: Input: $\mathrm{{\rm Y}}$                          ▹ Amplitude heatmap 2: Output: $\beta$                          ▹ Background value 3: $[\Re ,\mathsf{\Theta }]\leftarrow \mathrm{size}\left(\mathrm{{\rm Y}}\right)$                       ▹ Amplitude size 4: // Calculate the mean and median of the amplitude 5: ${\mu }^{\mathrm{{\rm Y}}}\leftarrow \mathrm{mean}\left(\mathrm{{\rm Y}}\right)$                       ▹ Calculate mean (${\mu }^{\mathrm{{\rm Y}}}$) 6: ${ð}^{\mathrm{{\rm Y}}}\leftarrow \mathrm{med}\left(\mathrm{{\rm Y}}\right)$                        ▹ Calculate median (${ð}^{\mathrm{{\rm Y}}}$) 7: $\Delta \leftarrow 0$                          ▹ Initialize difference 8: // Eliminate values larger than the clipping threshold 9: while  $\Delta \le 20$  do 10:  ${\sigma }_{\mathrm{o}}\leftarrow {\sigma }_{\mathrm{{\rm Y}}}$                     ▹ Initial standard deviation 11:  $\mathbf{T}={\displaystyle \frac{{\mu }_{\mathrm{minima}}+{\mu }_{\mathrm{maxima}}}{2}}$             ▹ Calculate $\mathbf{T}$ using Equation (7) 12:  for each x within ℜ do                 ▹ Radar range (ℜ) 13:     for each y within $\mathsf{\Theta }$ do               ▹ Radar azimuth ($\mathsf{\Theta }$) 14:                 if $\mathrm{{\rm Y}}\left(x,y\right)\ge \mathbf{T}$ then              ▹ Compare to threshold 15:           $\mathrm{{\rm Y}}\left(x,y\right)\leftarrow 0$                 ▹ Amplitude clipping 16:                 end if 17:     end for 18:  end for 19:  ${\sigma }_{\mathrm{n}}\leftarrow {\sigma }_{\mathrm{{\rm Y}}}$                    ▹ Update standard deviation 20:  $\Delta \leftarrow \left|{\displaystyle \frac{{\sigma }_{\mathrm{n}}-{\sigma }_{\mathrm{o}}}{{\sigma }_{\mathrm{o}}}}\right|\times 100$                   ▹ Find difference 21: end while 22: // Calculate the background based on the clipping 23: if$max\left(\mathrm{{\rm Y}}\right)\ne 0$  then 24:  $\beta \leftarrow \mathrm{mean}\left(\mathrm{{\rm Y}}\right)$                  ▹ Mean of clipped amplitude 25: else 26:  $\beta \leftarrow C_{\mathrm{d}}\times {ð}^{\mathrm{{\rm Y}}}-C_{\mathrm{n}}\times {\mu }^{\mathrm{{\rm Y}}}$                   ▹ Initial amplitude 27: end if

The algorithm starts by computing the amplitude heatmap’s mean $\mu$ and standard deviation $\sigma$ in the spatial domain for each amplitude heatmap and the clip threshold, computed based on the data statistics, namely, the mean of minima and maxima. Then, the PTMC iteratively clips pixels representing objects by comparing them with the clipping threshold. The amplitude values greater than the clip threshold are assumed to represent objects, and they are clipped. The algorithm measures the clipping process’s effect depending on the difference $\Delta$ between the $\sigma$ before clipping and the updated one, computed after clipping. If $\Delta$ is greater than 20%, the change is considered remarkable, and the clipping process stops. Then, the background is estimated and used to remove the clutter. Otherwise, the clipping process continues, aiming to clip more values representing objects and reach the value representing the background.

For each new iteration in the clipping process, the clip threshold is updated based on the statistics of the new data that are retained from the previous one, and $\sigma$ of the previous iteration is considered an old one, where 20% of the change is determined compared with it. When the clipping process stops, the mean of the pixels that are not clipped represents the background value of the amplitude heatmap. Conversely, the amplitude heatmap is regarded as a crowded area, and the background is computed as

$$\begin{array}{cc}\hfill \beta =& C_{\mathrm{d}}\times \mathrm{med}{\left\{\mathrm{Y}(x,y)\right\}}_{(x,y)\in (\Re ,\mathsf{\Theta })}\hfill \\ \hfill & -C_{\mathrm{n}}\times {\displaystyle \frac{1}{\Re \mathsf{\Theta }}}\sum _{x=1}^{\Re }\sum _{y=1}^{\mathsf{\Theta }}\mathrm{{\rm Y}}(x,y),\hfill \end{array}$$

(6)

where $\mathrm{{\rm Y}}(x,y)$ denotes the amplitude heatmap value located at position $(x,y)$, $\beta$ is the background value, and $C_{\mathrm{d}}$ and $C_{\mathrm{n}}$ are the median and mean coefficients, respectively. It is worth mentioning that the background estimation using Equation (6) is applied in the case of a crowded area where several objects exist, which is not the case for our case study dataset. The median and mean coefficients can be determined by varying the coefficient values and investigating the performance where, in our case, as the experiment does not include several moving objects, we rely on the values introduced in [29]. The estimated background value $\beta$ is then used as a threshold for the amplitude heatmap to suppress the clutter. In particular, we implement a mask where the pixels with values less than the estimated background $\beta$ are assigned to 0. Then, we multiply this mask with the estimated phase difference $\Delta {\varphi }_u$, suppressing the deformation of those pixels considered clutter.

The clipping threshold used within each iteration is the average of the mean of the minima and maxima. The idea is to regularly select samples (V) from the amplitude heatmap, where the selected samples can be considered matrix pooling, and then find the minima and maxima of those samples. Furthermore, the mean of the minima and the maxima are computed. Finally, the average of those statistics, namely, the mean of the minima (${\mu }_{\mathrm{minima}}$) and the mean of the maxima (${\mu }_{\mathrm{maxima}}$), is considered the clipping threshold ($\mathbf{T}$). We can express the clip threshold as

$$\begin{array}{cc}\hfill {\mu }_{\mathrm{minima}}& ={\displaystyle \frac{1}{n}}\sum _{i=1}^n\underset{(x,y)\in V_i}{min}\mathrm{{\rm Y}}(x,y),\hfill \\ \hfill {\mu }_{\mathrm{maxima}}& ={\displaystyle \frac{1}{n}}\sum _{i=1}^n\underset{(x,y)\in V_i}{max}\mathrm{{\rm Y}}(x,y),\hfill \\ \hfill \mathbf{T}& ={\displaystyle \frac{{\mu }_{\mathrm{minima}}+{\mu }_{\mathrm{maxima}}}{2}},\hfill \end{array}$$

(7)

where $i=1,2,3,\dots ,n$, and n is the number of samples.

4. Dataset

In this study, we apply the proposed Dextractor framework for a dataset collected using the tunnel experiment. Geobotica Pty Ltd. provides the GB-MIMO radar for acquiring the dataset and any other required experimental setup tools. The sensor, NanoRadar, monitors the sub-millimeter movement of rock in underground mines, providing early warning of potential collapses. The sensor, namely, NanoRadar, is a GB-MIMO that utilizes eight antennas operating in the GHz band, where the central frequency is 78.9 GHz. The robust, waterproof sensor design with no moving parts ensures it can withstand even the most demanding environments. More details about the sensor can be found in [34].

The experiment is set up inside a tunnel at a distance from the radar sensor. The environment is a reflection of rock tunnel surfaces as shown in Figure 3. We aim to evaluate the performance of the proposed Dextractor framework in an environment similar to the underground mines. It is worth mentioning that the amplitude heatmap, compared with the photograph, looks flipped because the flipping aligns with the original orientation of the data captured by the radar system. The hardware or data acquisition setup naturally results in a mirrored view, and maintaining this orientation ensures consistency with the source data.

Another alternative representation of the amplitude heatmap is plotting the image on the range–cross-range axis instead of the range–azimuth axis. The prime advantage of plotting on the range–cross-range axis is preventing any distortion in the image representation because it maintains the actual proportions, providing better image interpretation. Figure 4 shows the experiment’s amplitude heatmap, represented using the range–cross-range axis to maintain the actual proportions, which reveals the image interpretation. The figure precisely represents the tunnel rock surfaces and the overall experiment.

To gain more insights into the dataset collected from the experiment conducted in the tunnel, we compute the SNR by first selecting two areas. The first is an area where objects are located, and the other represents the background. Then, we calculate the SNR by finding the power of the signal and the noise [35], which can be expressed as

$$\mathrm{SNR}=10{log}_{10}\left({\displaystyle \frac{P_{\mathrm{s}}}{P_{\mathrm{n}}}}\right)\left(\mathrm{dB}\right),$$

(8)

where $P_{\mathrm{s}}$ indicates the signal power, whereas $P_{\mathrm{n}}$ represents the noise power. Then, we verify the size of the selected area for the collected dataset as shown in Figure 5. We compute the SNR for five areas of sizes $15\times 8$, $25\times 8$, $35\times 8$, $45\times 8$, and $55\times 8$ pixels for the dataset. The results show that the SNR is moderate, suggesting that the signal is stronger than the noise, but there is still a noticeable noise presence. In addition, the results reveal that the SNR almost decreases as the area size increases in the dataset. It means that the noise level resulting from the clutter is significant and scattered throughout the image.

Figure 6 shows an example of the selected signal and noise areas for different area sizes. The used areas are of size $15\times 8$, $25\times 8$, $35\times 8$, $45\times 8$, and $55\times 8$ pixels. The figures indicate that different areas exhibit unique characteristics that influence signal quality. For instance, the $45\times 8$ area is positioned in a region that captures a more concentrated and significant portion of the signal’s energy than the $35\times 8$ area.

We aim to measure the change in the noise level through time by measuring the errors in the computed SNR time series for the different areas in the dataset. We rely on the standard error, which can be defined as

$${\daleth }_q^M={\displaystyle \frac{{\sigma }_q^M}{\sqrt{k^M}}},\forall q=1\cdots z,$$

(9)

where ${\daleth }_q^M$ represents the standard error of dataset M and area q, ${\sigma }_q^M$ is the standard deviation of the SNR time series of dataset M and area q, $k^M$ is the length of the SNR time series, and z is the number of areas. The standard error, which is also the standard error of the mean, differs from the standard deviation, where the standard deviation measures the variability or spread of data points; however, the standard error measures the accuracy with which a sample mean estimates the population mean.

Figure 7 reveals the standard error of the SNR time series presented in Figure 5. The results reveal that the error of the dataset is almost fixed through the different area sizes. The error is significantly high; however, it is more stable, demonstrating that the noise level in the case of the tunnel experiment is almost uniformly distributed through the image.

We compute the discrete index (DI) [17] for the dataset using windows with sizes of 15, 25, 35, and 45 pixels to quantify the variability of radar backscatter intensity within a local neighborhood of pixels. The windows with sizes of 15, 25, 35, 45, and 55 pixels correspond to 1.75, 2.91, 4.08, 5.25, and 6.42 m in the range axis and 11.56, 18.32, 25.18, 32.90, and 34.64 m in the cross-range axis, respectively. The DI is a measure of variability in the radar signal, which can give close insights into the environment. The DI is calculated as the standard deviation of backscatter intensity values within a local neighborhood, providing a measure of variability or texture. It is similar to the local variance [36] introduced to measure the image’s variability, which is computed as the variance of the image grey levels within a neighborhood of size $w_x$ × $w_y$ centered at $(x,y)$ but using the standard deviation. The DI can be defined as

$$\mathrm{DI}=\sqrt{{\displaystyle \frac{1}{\Re \mathsf{\Theta }}}\sum _{x=1}^{\Re }\sum _{y=1}^{\mathsf{\Theta }}{({\mathrm{{\rm Y}}}_v(x,y)-\overline{{\mathrm{{\rm Y}}}_v})}^2},$$

(10)

where

$$\begin{array}{cc}\hfill {\mathrm{{\rm Y}}}_v(x,y)=& {\displaystyle \frac{1}{w_x{w}_y}}\sum _{x=1}^{w_x}\sum _{y=1}^{w_y}{\left(\mathrm{{\rm Y}}(x,y)-\overline{{\mathrm{{\rm Y}}}_v}\right)}^2,\hfill \\ \hfill \overline{{\mathrm{{\rm Y}}}_v}=& {\displaystyle \frac{1}{w_x{w}_y}}\sum _{x=1}^{w_x}\sum _{y=1}^{w_y}\mathrm{{\rm Y}}(x,y),\hfill \\ \hfill \overline{{\mathrm{{\rm Y}}}_v}=& {\displaystyle \frac{1}{\Re \mathsf{\Theta }}}\sum _{x=1}^{\Re }\sum _{y=1}^{\mathsf{\Theta }}{\mathrm{{\rm Y}}}_v(x,y),\hfill \end{array}$$

where ℜ and $\mathsf{\Theta }$ represent the range and azimuth of the radar, which are the height and width of the amplitude heatmap matrix. Figure 8 shows the DI of the dataset using different window sizes. The results show that the DI decreases as the window size increases, which means the variability or texture within the radar data decreases as we consider larger spatial scales. As the window size increases, the radar backscatter values within the window are averaged over a larger area. This process smooths out local variations and reduces the apparent variability in the data. For instance, small-scale features like rocks, vegetation, or minor surface undulations that contribute to high texture variability at small scales become less distinct when averaged over a larger area. In other words, it means the variation on the larger scale is less than the lower one, which indicates that the radar data contain relatively homogeneous regions. It shows a more significant challenge to extracting only the deformation and rock surfaces from the entire image.

5. Experimental Results

In this research, we used the collected data from the experiment inside a tunnel surrounding rocks where a slider is used as a movable object. We used the GBR to monitor the slider deformation in the tunnel environment. We then applied our proposed Dextractor to the dataset. Figure 9 shows an example of the effect of the PTMC filter where the filter mask computed based on the amplitude heatmap statics shows that the filter almost removes the spread clutter and retains objects such as rocks and the slider.

Figure 10 shows the performance of using different amplitude thresholding, specifically, no threshold, low threshold, high threshold, and our proposed PTMC. We show the filter mask for each case and the corresponding deformation heatmaps. The results show that the no-thresholding results are a significant noise. Using low-threshold values results in retaining the slider in the deformation map while removing clutter failure. A high threshold results in removing clutter and the slider. Our proposed method retains the objects in the environment and removes most of the clutter.

Figure 11 reveals the deformation heatmap of applying the Dextractor framework to the dataset collected in the experiment inside the tunnel. The result shows that the proposed PTMC algorithm can remove most of the clutter, where most areas have no deformations, represented in the green color. Additionally, the only remarkable deformation in the heatmap is the blue color representing the slider movement. Furthermore, the deformation time series of the slider reveals the smooth movement of the slider where it is linearly increased. This result can show the deformation monitoring ability of the proposed method.

As mentioned, we used a mean temporal filter, averaging every 20 scans into one frame to reduce the noise impact. We used all the scans acquired by the sensor, where the radar hardware is designed to acquire 20 scans every three minutes. In Figure 12, we show the performance of the proposed Dextractor framework for different window sizes for the mean temporal filter, such as using a window size of 1, 5, 10, and 15 scans. The results reveal that for processing each scan, the deformation map remarkably includes clutter, and the deformation of the slider does not significantly appear. The clutter decreases as the window size increases, and the slider deformation appears. Lastly, it can be concluded that the window size of the mean filter of 20 scans can perform best when applying our proposed framework for the experiment dataset.

To evaluate the performance of the proposed PTMC algorithm compared to the benchmark method, we apply the constant false alarm rate (CFAR) [37] algorithm using the Dextractor framework to the dataset collected using the experiment in the tunnel. The primary goal of CFAR is to maintain a constant rate of false alarms, regardless of the environment’s varying noise or clutter levels. This is achieved by dynamically adjusting the detection threshold based on the local environment’s noise level. As a result, we select CFAR as the primary benchmark method for comparing the performance with our proposed method, PTMC. We compare the performance of our method with CFAR both qualitatively and quantitatively. The qualitative results can be represented by showing the different approaches’ deformation maps, highlighting each method’s impact on removing the clutter.

We use a false rate of 0.1, 12 training cells in the azimuth direction, and 6 and 2 guard cells in the range and azimuth directions, respectively, and we verify the range training cells from 50 to 80, respectively. Figure 13 shows the Dextractor’s performance using CFAR with 50, 60, 70, and 80 range training cells applied to the dataset. The results reveal that the threshold increases as the training cell value increases; the clutter removal performance improves correspondingly. However, increasing the threshold results in removing clutter and objects as well. Accordingly, the iterative threshold is promising for the deformation monitoring-based radar application.

To compare our proposed method and the benchmark methods quantitively, we first create a ground-truth deformation heatmap for our experiment, as we have a deformation for the slider as shown in Figure 14. We compare the performance of our proposed method PTMC with the benchmark method CFAR based on several evaluation metrics, namely, mean square error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity index measure (SSIM). We use different range training ratios for the CFAR, where we compare the performance in the case of using 50, 60, 70, and 80 range resolution cells CFAR-50, CFAR-60, CFAR-70, and CFAR-80, respectively.

As our essential objective of this research is to propose a deformation monitoring approach and remove the clutter, the quantity comparison using the three metrics MSE, PSNR, and SSIM is based on the resulting deformation heatmap of different approaches compared with the ground-truth one. The different approaches, namely, PTMC, CFAR-50, CFAR-60, CFAR-70, and CFAR-80, are applied to the amplitude heatmaps, aiming to obtain a mask used to remove the deformation of pixels representing clutter. The results presented in Figure 15 show that the proposed method, PTMC, outperforms the benchmark methods for different evaluation criteria, where PTMC has the lowest error and the highest PSNR and SSIM.

Eventually, we aim to show that the computational cost of the proposed PTMC method is lower than other methods, where several filters are applied to the same dataset to remove the clutter. We compare our method with one of the direct filters to remove clutter using singular value decomposition (SVD) [38]. The computational time of applying PTMC to a frame is 0.001007 s, whereas the computational time of applying SVD to a frame is 0.007927 s. The results show the simplicity of the PTMC compared to SVD. In future work, we aim to collect more datasets from different environments, investigating the performance of our proposed method to remove the clutter in different case studies.

Drawbacks

The principal drawback of our proposed PTMC is the limitation on removing the side lobes effects. To show this limitation, we conduct a second experiment by locating the slider at 10 m from the radar sensor in an open park where vegetation covers the imaging area. The objective is to estimate the performance of the Dextractor framework in different case studies. Figure 16 shows the deformation heatmap obtained for the second experiment. The result shows that the proposed amplitude filter, namely, PTMC, can significantly reduce the effect of the clutter, where the green color, which indicates no deformation, is prevalent in the heatmap of experiment 2. However, it is noted that the vegetation affects the radar signal by being partially absorbed, scattered, or reflected, resulting in the appearance of a larger size slider; however, it does not affect the deformation time series.

6. Conclusions

In this research, we propose a framework for deformation monitoring, namely, Dextractor. The proposed framework aims to provide deformation monitoring to be used as a safety factor for some applications, such as mines. The framework mainly depends on the standard radar interferometry technique, such as our principle contribution to using a data-driven threshold to remove clutter. The framework consists of several processing steps. Initially, a mean temporal filter is applied to reduce the effect of the clutter and noises on the radar data. Then, the beam former is applied to form and direct the radar beam to achieve accurate range and angular resolution. Furthermore, a proposed data-driven amplitude filter, PTMC, is applied to remove the clutter. The proposed PTMC algorithm is an iterative threshold approach aiming to reach the value representing the background of the radar data, which includes clutter.

The approach keeps clipping outliers based on statistics, namely, the average of the mean of the minima and maxima, until the change in the $\sigma$ becomes larger than 20%, indicating a significant change. The mean of the pixels that are not clipped is used to present the background values where the clutter values are less than it. We apply our proposed framework to the dataset collected from the tunnel where rocks surround the slider. The deformation heatmap shows the ability of the proposed framework to remove the significant clutter besides monitoring the deformation.

We compare our proposed method quantitively and qualitatively with one of the most common clutter removal approaches, CFAR. The visual results show that as we increase the number of range training cells, the performance of the CFAR improves, removing more clutter and leading to the removal of the object. We compare the performance based on different evaluation metrics: MSE, PSNR, and SSIM. The results show that the performance of our proposed method significantly outperforms the CFAR of different training cells for the different evaluation metrics. Eventually, we show that our proposed method is less computational than the SVD.