Wavelength-Resolution SAR Change Detection
Using Bayes’ Theorem
Dimas Irion Alves
, Bruna Gregory Palm
, Hans Hellsten, Senior Member, IEEE,
Viet Thuy Vu
, Senior Member, IEEE, Mats I. Pettersson
, Renato Machado
, Member, IEEE,
Bartolomeu F. Uchôa-Filho
, Senior Member, IEEE, and Patrik Dammert, Senior Member, IEEE
Abstract—This article presents Bayes’ theorem for wavelength-resolution synthetic aperture radar (SAR) change detection method development. Different change detection methods can be derived using Bayes’ theorem in combination with the target model, clutter-plus-noise model, iterative implementation, and nonitera-tive implementation. As an example of the Bayes’ theorem use for wavelength-resolution SAR change detection method development, we propose a simple change detection method with a clutter-plus-noise model and noniterative implementation. In spite of simplicity, the proposed method provides a very competitive performance in terms of probability of detection and false alarm rate. The best result was a probability of detection of 98.7% versus a false alarm rate of one per square kilometer.
Index Terms—Bayes’ theorem, CARABAS, change detection, synthetic aperture radar (SAR), wavelength resolution.
I. INTRODUCTION
S
YNTHETIC aperture radar (SAR) plays an important role in surveillance, geoscience, and remote sensing applica-tions. The capabilities to provide broad coverage and effectively operate in all weather conditions are major advantages of SAR in comparison to other sensor systems. SAR change detection has been researched for many decades and it is an important research area used for different applications, such as detection of concealed targets [1], ground scene monitoring [2], polarime-try [3], and even GMTI [4]. Generally, the changes between two Manuscript received February 13, 2020; revised June 23, 2020 and August 14, 2020; accepted September 9, 2020. Date of publication September 18, 2020; date of current version September 28, 2020. This work was supported in part by the Brazilian National Council for Scientific and Technological Development (CNPq), in part by the Swedish-Brazilian Research and Innovation Centre (CISB), in part by Coordination for the Improvement of Higher Education Personnel (CAPES), and in part by Saab AB. (Corresponding author: DimasIrion Alves.)
Dimas Irion Alves is with the Federal University of Pampa, Alegrete 97546-550, Brazil, and also with the Federal University of Santa Catarina, Florianópolis 88040-900, Brazil (e-mail: dimasalves@unipampa.edu.br).
Bruna Gregory Palm and Renato Machado are with the Aeronautics In-stitute of Technology, São José dos Campos 12228-900, Brazil (e-mail: brunagpalm@gmail.com; renatomachado@ieee.org).
Hans Hellsten and Patrik Dammert are with the Saab Surveillance, Saab AB, 412 89 Gothenburg, Sweden (e-mail: hans.hellsten@saabgroup.com; patrik.dammert@saabgroup.com).
Viet Thuy Vu and Mats I. Pettersson are with the Blekinge Institute of Technology, 37179 Karlskrona, Sweden (e-mail: viet.thuy.vu@bth.se; mats.pettersson@bth.se).
Bartolomeu F. Uchôa-Filho is with the Federal University of Santa Catarina, Florianópolis 88040-900, Brazil (e-mail: bart.uchoa@gmail.com).
Digital Object Identifier 10.1109/JSTARS.2020.3025089
acquisitions separated in time can be found in SAR images with a change detection method.
Among these applications, it is possible to highlight the detection of concealed targets in foliage-penetrating (FOPEN) applications, which has been of great interest for a long time [5]. However, when change detection is employed in conventional microwave SAR images for FOPEN applications, a large number of false alarms are observed. Ultrahigh frequency and very high frequency SAR systems are excellent options to overcome this limitation [5].
The usage of low frequencies for FOPEN applications is associated with large fractional bandwidth and a wide antenna bandwidth. Systems with such characteristics have resolutions in the order of the radar signal wavelengths. That is the reason why those are frequently named wavelength-resolution SAR systems [6]. The images generated by wavelength-resolution SAR systems do not suffer from the speckle noise. The scattering process is related to scatterers with dimensions in the order of the signal wavelengths, which, for low-frequency SAR, are related to big objects (tree trunk, house, trucks) that are stable in time, and tend to be less affected by weather conditions [7]. These characteristics indicate that wavelength-resolution SAR images are adequate for change detection in FOPEN applications.
Wavelength-resolution SAR has been a research area since 2002, and this time instance is marked by the measurement campaign in Vidsel, Sweden [8], [9]. The goal of the measure-ment campaign was to provide data to evaluate the performance of change detection for targets obscured by foliage. Different passes with distinct flight headings have been tested. In the ground scene, the targets (vehicle) have been deployed at differ-ent locations and with distinct oridiffer-entations. One of the measure-ment campaigns’ outcomes is 24 SAR images (calibrated and coregistered) that are available for the wavelength-resolution SAR change detection research as a challenging problem [10]. A significant number of wavelength-resolution SAR change de-tection methods have been developed. A common aspect among them is that they are designed with the processing sequence: information extraction, thresholding, and false alarm minimiza-tion. The information extraction can simply be achieved by a subtraction followed by a filter, e.g., adaptive noise canceler [11] and smoothing filter [12]. This is possible thanks to the dominant thermal noise present in wavelength-resolution SAR images. The information extraction can also be achieved but a likeli-hood ratio test with the help of clutter and noise models. The This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
simplest models for clutter and noise are the bivariate complex normal distribution for coherent change detection [8], and, con-sequently, bivariate Rayleigh distribution for incoherent change detection [13].
Oppositely as the current trend of using machine learning and neural networks in change detection [14]–[16], several change detection methods available in the literature are related to prob-ability theory in general and Bayes’ theorem in particular [17]– [20]. These methods do not require the training stage, resulting in less computational complexity and fewer application require-ments. They also tend to provide good detection performance for wavelength-resolution SAR image applications [11]–[13]. An example of Bayes-based technique can be found in [18], where an unsupervised change detection method with thresholding is presented. The method consists of a Bayes-based estimator, which combines prior and current data knowledge for improving the change detection performance. Another example is presented in [20], where the authors proposed a change detection method for polarimetric images using a Bayes classifier. In this article, we use Bayes’ theorem for wavelength-resolution SAR change detection method development. Based on Bayes’ theorem, the probability of change in a SAR scene can be estimated from the data histogram of reference and surveillance images and either a target model or a clutter-plus-noise model. This results in two directions for change detection method development: one is based on the target model and the other on the clutter-plus-noise model. From the implementation point of view, the probability of change in a SAR scene can be estimated either noniteratively or iteratively. For the iterative implementation, the method will detect one by one target and update the data histogram iteratively until no new target is found. On the contrary, the noniterative implementation helps to detect all possible targets at the same time without updating the data histogram.
It is worth mentioning that part of this article has been published in [21] and [22], focusing on the target model and the iterative implementation. Initial evaluation of the change detection performance considered very few images and targets, e.g., only two targets and two images in [22]. For this reason, the clutter and noise model and the noniterative implementation are focused on this article. The evaluation of the change detection performance is discussed in detail. The dataset for the assess-ment consists of 24 SAR images and 600 targets [10]. Since the dataset is available, it is easier to compare the change detection performance of different methods that use the same dataset.
The remainder of this article is organized as follows. Section II presents Bayes’ theorem for change detection method develop-ment. Two possible expressions that can be used for change detection probability calculation are derived using Bayes’ theo-rem. One is based on the target model, and the other is based on the clutter-plus-noise model. Two possible ways to implement the change detection methods: iterative and noniterative are also discussed in this section. A change detection method is devel-oped in Section III using a clutter-plus-noise model, bivariate Rayleigh, and the noniterative implementation. Section IV gives the data description, experimental results with CARABAS data, and experimental evaluation. Concluding remarks are provided in Section V.
II. BAYES’ THEOREM FORCHANGEDETECTION METHODDEVELOPMENT
In this section, we present Bayes’ theorem in the SAR change detection scenario. The development of change detection meth-ods based on Bayes’ theorem is also provided.
A. Bayes’ Theorem in the SAR Change Detection Scenario
Bayes’ theorem is used to describe the probability of an event, given some prior knowledge of conditions that could be related to this event. It can be stated as
P (A|B) = P (B|A)P (A)
P (B) (1)
where A and B are two events, P (A) and P (B) probabilities
of eventsA and B, respectively, and P (A|B) is the conditional
probability of eventA given that event B has occurred.
A common SAR change detection scenario is considered for an interpretation of Bayes’ theorem. This scenario is character-ized by the use of two complex images; one is the surveillance image, i.e., the image where it is desired to find the targets, and the other is the reference image, i.e., the image used to aid to characterize the clutter. By considering Bayes’ theorem, the probability of detecting a change in one pixel under test, given the complex value of the tested pixel in the surveillance imagezU and given the complex value of the tested pixel in the reference imagezR, can be expressed by
P (s ≡ sT|zU, zR) = P(zU|s ≡ sT, zR) P (s ≡ sT|zR )
P (zU|zR)
(2) wheres ≡ sTis the statement that the given image pixel contains a change and can write shortlysT. In the opposite case,s ≡ sT is the statement that the given image pixel contains no change and can write shortlysC. The conditional probabilityP (sT|zR) is the target probability and since zR is independent of the statement on change, it can be written by
P (sT|zR) = P (sT) = MK
N (3)
whereK is the number of detected changes, M is the number
of pixels that a change occupies, andN is the number of image
pixels.
The conditional probabilityP (zU|zR) can be described by two mutually exclusive events, which are based on a presence of a changesT or an absence of a changesC
P (zU|zR) = P (zU|sT, zR) P (sT|zR)
+ P (zU|sC, zR) [1 − P (sT|zR)] = P (zU|sT, zR) P (sT)
+ P (zU|sC, zR) [1 − P (sT)] . (4) We can also rearrange (4) in a new form as
P (zU|sT, zR) = P(zU|zR) − P (zU|sC, zR) [1 − P (sT )]
P (sT) . (5)
1) Case 1: The first case is straight ahead. If we insert (4) into
the denominator of (2) and then divide the numerator and de-nominator withP (zU|sT, zR)P (sT|zR), we get the conditional probability in the following form:
P (sT|zU, zR) =
1
1 +P (zU|sC, zR) [1 − P (sT|zR)]
P (zU|sT) P (sT)
. (6)
An approximate form of (6) is given by
P (sT|zU, zR) ≈
1
1 + P (zU|sC, zR)
P (zU|sT) P (sT)
(7)
due to the fact thatN M K and hence
1 − P (sT|zR) = 1 −M K
N ≈ 1. (8)
Apart from the number of targets assumed, the quotientη(z) = P (zU|sT)/P (zU|sC, zR) will decide the conditional probabil-ityP (sT|zU, zR). For this probability to be high, η(z) must be high and vice versa. The probability P (zU|sC, zR), so-called clutter change distribution, is estimated by the histogram anal-ysis of the SAR images, whereas the probabilityP (zT|sC, zR), so-called target change distribution, is shown to be
P (zT|sC, zR) = 1 4π2(zmax− zmin) Δϕ(zU,zR) dϕ z2U+ z2R− 2zUzRcos ϕ (9) wherezmaxandzminare the upper and lower magnitude limits,
and Δφ(zU, zR) is the angular span from arg(zU) to arg(zR).
2) Case 2: The second case is motivated by exploiting the
in-formation of the clutter-plus-noise statistical model into change detection. Substituting (5) into (2) results in
P (sT|zU, zR) = 1 − P (zU|sC, zR) P (sT )
P (zU|zR) .
(10) Applying Bayes’ theorem again to (10), we get the final expres-sion for (2) as
P (sT|zU, zR) = 1 − P (zU, zR|sC) P (sT )
P (zU, zR) .
(11) Considering (8), the approximation for (11) is derived by
P (sT|zU, zR) ≈ 1 −P (zU, zR|sC )
P (zU, zR) .
(12) The conditional probability P (zU, zR|sC) can be calculated by using an appropriate statistical distribution for the clutter-plus-noise of the SAR images, whereas the joint probability
P (zU, zR) can get exact values from the SAR image histogram. Under the assumption of a correct statistical model choice for the clutter and noise in (11), it is expected that the occurrence of a change in the scene will lead toP (zU, zR) P (zU, zR|sC), resulting inP (sT|zU, zR) ≈ 1. Conversely, a situation with the absence of changes will lead to P (zU, zR) ≈ P (zU, zR|sC), resulting inP (sT|zU, zR) ≈ 0.
Fig. 1. Block diagram for iterative and noniterative implementation.
B. Implementation
(6) and (11) and their approximations (7) and (12) suggest to us two different ways to calculate the conditional probability
P (sT|zU, zR) for change detection: iterative and noniterative. In this part, we focus on the iterative and noniterative implemen-tation of (11) and (12) in Case 2. A similar description for the iterative and noniterative implementation of (6) and (7) in Case 1 can be included. Fig. 1 shows the block diagram for iterative and noniterative implementation.
For the iterative implementation, the number of assumed targets will increase in each iteration. In the first iteration,
K = 1 and the removal of the data surrounding the detected
change is ignored. The parameters required by the statistical distribution for the clutter-plus-noise of the SAR images to calculate P (zU, zR|sC) in Case 2 are estimated from whole reference and surveillance images. To form a histogram to find
P (zU, zR) in Case 2, we arrange the modulus and phase of the reference image pixels in bins. The same arrangement is applied to the surveillance image. The frequency of a bin indicates the simultaneous occurrence of a certain modulus and a certain phase of the reference image and of a certain modulus and a certain phase of the surveillance image. The value ofP (zU, zR) is given by the ratio of the frequency of the bin associated with
z = [zU, zR] to the sum of the frequency of all bins. We can get the values of the probability density function ofP (zU, zR) by scaling with the inverses of the bin sizes. With such, we can easily calculate the conditional probabilityP (sT|zU, zR) of each image pixel withK = 1 and the calculation results in
a matrix of probabilities with the same dimensions of the input images. Under the assumption that there is a single change in the SAR scene, the maximum value ofP (sT|zU, zR) is compared
with a defined thresholdλ. If max{P (sT|zU, zR)} ≥ λ, the first change is declared to be detected and we continue with the second iteration. In the second iteration,M pixels surrounding
the detected change in the first iteration are removed from both the reference and surveillance images based on the assumption on the size and the shape of the change. The parameters re-quired by the statistical distribution are updated due to the data removal. The histogram is also updated for the same reason. The conditional probability P (sT|zU, zR) is calculated with
K = 2, and new values of P (sT|zU, zR) and P (zU, zR|sC). If we still have max{P (sT|zU, zR)} ≥ λ, the second change is claimed to have been detected, and we continue with the next iterations. The same procedure is repeated for the next iterations until max{P (sT|zU, zR)} < λ.
For noniterative implementation, there is no assumption on the number of targets. We estimate one time the parameters required by the statistical distribution for the clutter-plus-noise of the SAR images to calculate P (zU, zR|sC) from whole reference and surveillance images. We also form a histogram one time to findP (zU, zR). With the values of P (zU, zR|sC) and P (zU, zR), we can achieve the conditional probability
P (sT|zU, zR) with (12). All the values of P (sT|zU, zR) are compared with a defined threshold λ. Only image pixels that meet the demandP (sT|zU, zR) ≥ λ will be considered to be the changes.
III. CHANGEDETECTIONMETHOD
In this section, we illustrate Bayes’ theorem for change detec-tion method development presented in the previous secdetec-tion. The illustration is given by developing a change detection method based on (12) and noniterative implementation for simplicity. According to (12) and the implementation, a statistical distribu-tion for the clutter-plus-noise of the SAR images is needed to calculateP (zU, zR|sC). A statistical distribution is, therefore, a prerequisite for the change detection method development. Bayes’ theorem for change detection method development pre-sented in Section II can be used for developing both coherent and incoherent change detection algorithms. For simplicity, we also limit this development with incoherent SAR change detection wherezU andzRonly represent the magnitude, i.e.,zU = |zU| andzR= |zR|.
A. Clutter-Plus-Noise Distribution Model
For low-frequency wavelength-resolution SAR images, the correlation between images (different illuminations) is very high in target-related pixels, and low for areas with the absence of a scatter (water, open fields, small trees) [7]. The reason is that scatterers at low frequencies are rather large (>3 m) and that
the resolution cell contains only one scatter. Thus, we only use single look images without using any type of clutter removal filtering technique. The large correlation is an effect of the high resolution in comparison to the wavelength and the fact that the CARABAS SAR system operates at low frequencies, namely, 20−90 MHz. The clutter-plus-noise distribution can be modeled by bivariate Rayleigh [13], bivariate Gamma [23], or K-distribution [24], which are usual distributions used for
Fig. 2. Simplified processing scheme for the proposed change detection method.
SAR magnitude images. Among the clutter-plus-noise distri-bution models for wavelength-resolution images, the bivariate Rayleigh distribution is the simplest one, since it belongs to a one-parameter family of probability distributions. It is worth mentioning that this distribution has already been used for CARABAS data and presented a good performance for change detection applications [13]. Although the Rayleigh distribution is not a perfect candidate for modeling the clutter-plus-noise of a wavelength-resolution SAR image, especially in the tail region, the model is still utilized due to its simplicity and efficiency in SAR applications [25]. For these reasons, we select the bivariate Rayleigh distribution here for SAR change detection method development.
The probability density function of a bivariate Rayleigh dis-tribution can be written as [26]
fZU,ZR(zU, ΩU; zR, ΩR|ρ) = Ω 4zRzU RΩU(1 − ρ) ×exp − 1 1 − ρ zR2 ΩR+ z 2 U ΩU × I0 2√ρ 1 − ρ zRzU √ ΩRΩU (13) where ΩR= zr2, ΩU = zU2,I0(·) is the modified Bessel
func-tion of the first kind with order zero, and ρ is the correlation
coefficient, which can be estimated by
ρ = cov(z 2 U, z2r) var(zU2)var(z2r) (14) where cov(., .) and var(.) represent the covariance and the
variance of random variables, and (.) represents the mean value. B. Processing Scheme
A simple processing scheme for the proposed change detec-tion method is presented in Fig. 2. According to the processing scheme, the input includes one surveillance image and one reference image that have been coregistered. The first processing block is given by the noniterative implementation given in Fig. 1. It consists of the statistical test based on (12), which is applied to each pixel position of the images. The conditional probability
P (zU, zR|sC) is calculated from the bivariate Rayleigh proba-bility density function (14), andP (zU, zR) is estimated from the data histogram. The output of the first processing block will be a binary data matrix. The value 1 is assigned toP (sT|zU, zR) ≥ λ and the value 0 toP (sT|zU, zR) < λ.
Two standard morphological operations, erosion and dilation are used in the second processing block. The first one aims to remove the small detections, e.g., less than the resolution of the SAR system, that might be false alarms. The latter merges the adjacent detections that are separated, e.g., less than the resolution of the SAR system or even less than four times the resolution of the SAR system. This avoids fragment of targets. The element structure for these morphological operations is, therefore, connected to the size of the system resolution cell. The output of the second processing block is the detected changes with false alarms (if any) presented by a binary data matrix.
There are also optional processing steps. For example, to avoid
P (sT|zU, zR) relating to isolated instances, we can calculate the average probabilities ofP (sT|zU, zR) using an averaging filter considering a window given by the size of the system resolution cell. Then, these average probabilities are placed to thresholding.
IV. EXPERIMENTALRESULTS
To evaluate the proposed change detection algorithm, we used the same CARABAS II dataset used in [8] and [9]. This dataset was provided by the Swedish Defence Research Agency and is made available by AFRL in [10]. The dataset is composed of 24 magnitude images that are already calibrated, preprocessed, and geo-coded, according to the Swedish reference system RR92 [9]. Each magnitude image includes 3000×2000 pixels, contains 25 testing targets, and covers the same ground area of 6 km2 (3 × 2 km). The tested targets consist of ten TGB11 model vehicles, eight TGB30 model vehicles, and seven TGB40 model vehicles [9]. All target deployments were positioned in a forest to test the capability to detect concealed targets, i.e., FOPEN.
The 24 images consider four different target deployments (missions), divided into two geographically different forest sites. For each deployment, it was realized six image acquisition with different flight geometries (passes). All measurements adopted HH polarization used the strip map SAR mode, and adopted an incidence angle of 58◦, for a range of 12 km to a common aim point [9]. Also, the flights were conducted with the radar looking left. More details on the data can be obtained in [8] and [9]. For simplicity, we will follow the same image classification as given in [9]. To exemplify, Fig. 3 shows one CARABAS II image of the ground scene of interest.
A. Implementation Aspects
The experimental evaluation was performed using all the 24 images and considering the processing scheme provided in Fig. 2. Using an image pair, we can calculate the probabili-ties for all image pixels based on (12). However, to minimize the processing time and to reduce the number of evaluations of situations with a mismatch between model and data, only pixels with possible positive changes in the surveillance image are tested. One magnitude constraint is performed in the first processing block. If the change in the magnitude of an image pixel is too small, they are not considered to contain a change. Hence, the probabilityP (sT|zU, zR) is set to 0 if zU < zr+ Δz; otherwise, the conditional probability is calculated using (12). This constraint is based on prior knowledge from the evaluated
Fig. 3. CARABAS image of ground scene.
data, and it is similar to the one used in [13] or [23]. Throughout this article, we use the same set of values Δz ∈ [0.2, 0.3, 0.4] as
having been used in [23], in order to guarantee a fair comparison between the tested methods.
There might be mismatches between the selected distribution and the data histogram that lead (12) to negative values, i.e.,
P (sT|zU, zR) < 0. In this situation, we simply set the condi-tional probability to zero, i.e.,P (sT|zU, zR) = 0.
A fixed thresholdλ is applied to all the results of the statistical tests. The threshold should be selected according to the charac-teristics of each specific application and should lie in the range (0, 1). In this article, a wide range of thresholds is considered to obtain the receiver operating characteristic (ROC) curves.
To perform a fair comparison between the evaluated meth-ods, we apply similar morphological operations, such as those considered in [9], after the thresholding step. The morphological operations used herein are one erosion followed by two dilations. The erosion uses a square structuring element with the same size as the system resolution cell (3× 3 m). Hence, the operation removes the isolated detected changes. The dilations use square structuring elements whose sizes enable merging any detected samples that are separated by up to 10 m.
An example of change detection results presented by a binary data matrix with the detected changes and the false alarms is given in Fig. 4. The detected changes are marked with a rectangle, and the false alarms are marked with a circle.
B. Method Evaluation
The evaluation of the proposed method is realized in terms of the detection probabilityPd, i.e., the ratio of the number of detected targets to the known number of targets, and the number of false alarms per square kilometer (FAR). For results repro-ducibility, every object detected by the algorithm was considered as a change, even knowing that some of them could be related to structures caused by the back-lobes, which are associated with systems or image formation issues.
We compare the proposed method with an existing change detection method, which uses CARABAS II images [8]. For
Fig. 4. Change detection results with detected changes and false alarms.
Fig. 5. ROC performance for proposed and Ulander et al. [8] methods.
this evaluation, we considered the same 24 image pairs as used in [9] in comparison to the best ROC curve presented in [8]. Fig. 5 shows that the proposed method outperforms the reference method for Δz = 0.2, Δz = 0.3, and Δz = 0.4.
It is important to highlight that the use of higher values for the magnitude constraint reduces the impact of the tail mismatch between the data and the model distribution, reducing the oc-currence of the false alarm. However, the combination of high magnitudes for the constraint and the erosion morphological operation could result in the erasure of some targets, making it impossible to obtain 100% of detection with any threshold. Although this phenomenon has not been observed for the con-straints used in Fig. 5, it is expected to occur for higher Δz
values. Finally, the possibility of this phenomenon’s occurrence can be reduced by selecting a better-matched distribution model or using different signal processing schemes.
Analyzing the results presented in Fig. 5, for the points with FAR = 100, the following probabilities of detection are observable:Pd= 90% for the reference method; Pd= 96.8% for Δz = 0.2; Pd= 98.2% for Δz = 0.3; and Pd= 98.7%
Fig. 6. ROC performance for proposed and Vu et al. [23] and Gomes et al. [27] methods.
for Δz = 0.4. Note that increasing Δz improves the detection
performance, but with diminishing returns. On the other hand, a large value of Δz may have the detrimental effect of removing
targets, as mentioned before. As observed, Δz = 0.4 is the
best option tested for characterizing the target-like pattern in this dataset, although the intermediate value of Δz = 0.3 has
also proved to be a good choice. Optimal values of Δz could
be achieved through an investigation about the statistics of the targets dataset. Thus, based on the numerical results, it is appropriate to state that prior knowledge about the targets in the dataset can be incorporated into the application constraints to improve the proposed method’s performance.
Also, we compare the proposed method with [23] and [27], in which the first presents one of the best, already published, detection performances for this dataset, and the second is one of the most recent results published using the CARABAS II dataset. The technique published in [23] consists of likelihood-based change detection method considering the clutter-plus-noise statistics modeled as a bivariate Gamma distribution. Sim-ilarly, the techniques published in [27] consists of a likelihood-based change detection methods considering the clutter-plus-noise statistics modeled as a bivariate Rayleigh distribution and k-distribution. For the sake of simplicity, only the results of the k-distribution are considered for the evaluation, given that it presented the best performances. Fig. 6 shows the performance comparison between the proposed method and the best ones presented in [23] and [27].
From the results presented in Fig. 6, it is observable that the proposed method excels in terms of false alarm rate and detection probability, the reference method [27] for all the evaluated scenarios. In this same figure of merit, we compare the proposed method with the reference method [23]. We can note that the proposed method with Δz = 0.4 outperforms
the reference method in all tested points with Δz = 0.3, and
outperforms the reference one with Δz = 0.4 for Pd> 95%. Moreover, the proposed method with Δz = 0.3 outperforms
TABLE I
PERFORMANCERESULTS OF THEPROPOSEDMETHOD FOR ATHRESHOLDλ = 0.5ANDΔz = 0.3
Note: The rows highlighted with gray color are related to images that contain back-lobe structures.
Pd> 92.5% and Pd> 96.3%, respectively. However, for the reference method, when Δz = 0.4, the algorithm was unable
to detect some targets, resulting in a maximum Pd< 100%. It is important to emphasize that these performance gains are directly related to the target/clutter statistics selected in the evaluated methods. Finally, considering the points with FAR = 10◦, the following probabilities of detection are obtained for the method proposed in [23]: Pd= 97.8% for Δz = 0.3 andPd= 97.6% for Δz = 0.4. For the proposed method, the following probabilities of detection are obtained:Pd= 98.2% for Δz = 0.3 and Pd= 98.7% for Δz = 0.4.
To further investigate the performance of the proposed de-tection method, we present the results for a specific test setup in Table I, where the gray highlighted rows refer to images that contain back-lobe structures. By comparison with the results pre-sented in [9], Table I reveals that the proposed method presents better performance for both detection probability (585 target detections against 579) and false alarm rate (76 false alarms against 96). Furthermore, Table I shows that the majority of false alarms 75% and a large number of the missed detections 46.66% are related to the pairs 18 and 20. In fact, these images were studied in [11] being characterized by the presence of some low amplitude targets and by high amplitude elongated structures, which may cause false alarms. Based on the study presented in [11], aiming to reduce false alarms in these image pairs, we can
say that more sophisticated techniques in the simple processing chain considered in this article are required. However, the results presented in Table I show that the proposed method works well with most of the experimental data without the aid of any other processing techniques.
Finally, it is essential to mention that back-lobe structures are related to system and image formation issues, and they have a target-like pattern. Thus, detections related to back-lobe structures do not represent a method error and should not be counted as false alarms in our evaluation. By analyzing the results of the four image pairs, it is verified that only two of the ten previously observed false alarms are not associated with this type of structure. Disregarding false alarms related to back-lobe structures, the number of false alarms presented in Table I would drop to a total of 68, resulting in FAR = 0.47.
V. CONCLUSION
Bayes’ theorem for wavelength-resolution SAR change de-tection method presented in this article can be used for the development of new change detection algorithms. As an ex-ample, we have developed a simple change detection method using a clutter-plus-noise model with a noniterative approach. The bivariate Rayleigh distribution was considered for mod-eling the clutter-plus-noise in the used wavelength-resolution
images, due to its simplicity. Unlike the current trend of using machine learning-based change detection methods for SAR images, the proposed method is fully explainable and does not require training images. These characteristics enable the use of the proposed method for different applications, especially those with a reduced number of available images. The pro-posed method was evaluated in terms of detection probability and false alarm rate considering CARABAS incoherent data. Comparisons with change detection methods based on LRTs were provided, showing that the proposed method can achieve competitive performance in terms of the two evaluated metrics. The obtained probability of detection was up to 98.7%, whereas the false alarm rate was only 1 per square kilometer. Never-theless, better performance could be achieved using a clutter distribution with a better match between data and the statistical model.
REFERENCES
[1] L. M. H. Ulander, W. E. Pierson, M. Lundberg, P. Follo, P. -O. Frolind, and A. Gustavsson, “Performance of VHF-band SAR change detection for wide-area surveillance of concealed ground targets,” in Proc. SPIE
Algorithms Synthetic Aperture Radar Imagery XI, Orlando, FL, USA,
May 2004, vol. 5427, pp. 259–270.
[2] M. Cha, R. D. Phillips, J. W. Patrick, and C. D. Richmond, “Two-stage change detection for synthetic aperture radar,” IEEE Trans. Geosci. Remote
Sens., vol. 53, no. 12, pp. 6547–6560, Dec. 2015.
[3] A. Marino, S. R. Cloude, and J. M. Lopez-Sanchez, “A new polarimetric change detector in radar imagery,” IEEE Trans. Geosci. Remote Sens., vol. 51, no. 5, pp. 2986–3000, May 2013.
[4] T. K. Sjogren and V. T. Vu, “Detection of slow and fast moving targets using hybrid CD-DMTF SAR GMTI mode,” in Proc. IEEE 5th Asia-Pacific
Conf. Synthetic Aperture Radar, Singapore, Sep. 2015, pp. 818–821.
[5] W. L. Melvin and J. A. Scheer, Principles of Modern Radar: Volume
III—Radar Applications, 1st ed. Edison, NJ, USA: SciTech, 2014.
[6] H. Hellsten, L. M. H. Ulander, A. Gustavsson, and B. Larsson, “Develop-ment of VHF CARABAS II SAR,” in Proc. SPIE Radar Sensor Technol., Orlando, FL, USA, Jun. 1996, pp. 48–60.
[7] R. Machado, M. I. Pettersson, V. T. Vu, P. Dammert, and H. Hellsten, “The stability of UWB low-frequency SAR images,” IEEE Geosci. Remote Sens.
Lett., vol. 18, no. 3, pp. 1114–1118, Aug. 2016.
[8] L. M. H. Ulander, M. Lundberg, W. Pierson, and A. Gustavsson, “Change detection for low-frequency SAR ground surveillance,” IEE Proc. Radar
Sonar Navig., vol. 152, no. 6, pp. 413–420, 2005.
[9] M. Lundberg, L. M. H. Ulander, W. E. Pierson, and A. Gustavsson, “A challenge problem for detection of targets in foliage,” in Proc. SPIE
Algorithms Synthetic Aperture Radar Imagery XIII, vol. 6327, May 2006,
Art. no. 62370K.
[10] U.S. Air Force, “The sensor data management system—SDMS,” Ac-cessed: Mar. 26, 2018. [Online]. Available: https://www.sdms.afrl.af.mil/ [11] V. T. Vu, R. Machado, M. I. Pettersson, P. Dammert, and H. Hellsten, “False alarm reduction in wavelength-resolution SAR change detection using adaptive noise canceler,” IEEE Trans. Geosci. Remote Sens., vol. 55, no. 1, pp. 591–599, Jan. 2017.
[12] V. T. Vu, M. I. Pettersson, N. R. Gomes, P. Dammert, and H. Hell-sten, “Wavelength-resolution SAR change detection with constant false alarm rate,” in Proc. IEEE Radar Conf., Seattle, WA, USA, May 2017, pp. 1504–1508.
[13] N. R. Gomes, M. I. Pettersson, V. T. Vu, P. Dammert, and H. Hellsten, “Likelihood ratio test for incoherent wavelength-resolution SAR change detection,” in Proc. CIE Int. Radar Conf., Guangzhou, China, Oct. 2016, pp. 420–423.
[14] M. Gong, J. Zhao, J. Liu, Q. Miao, and L. Jiao, “Change detection in synthetic aperture radar images based on deep neural networks,”
IEEE Trans. Neural Netw. Learn. Syst., vol. 27, no. 1, pp. 125–138,
Jan. 2016.
[15] L. Jia, M. Li, P. Zhang, and Y. Wu, “SAR image change detection based on correlation kernel and multistage extreme learning machine,” IEEE Trans.
Remote Sens., vol. 54, no. 10, pp. 5993–6006, Oct. 2016.
[16] S. Yang, Z. Liu, Q. Gao, Y. Gao, and Z. Feng, “Extreme self-paced learning machine for on-orbit SAR images change detection,” IEEE Access, vol. 7, pp. 116413–116423, 2019.
[17] F. Wang, Y. Wu, Q. Zhang, P. Zhang, M. Li, and Y. Lu, “Unsupervised change detection on SAR images using triplet Markov field model,” IEEE
Geosci. Remote Sens. Lett., vol. 10, no. 4, pp. 697–701, Jul. 2013.
[18] M. N. Sumaiya and R. S. S. Kumari, “Unsupervised change detection of flood affected areas in SAR images using Rayleigh-based Bayesian thresholding,” IEE Proc.-Radar Sonar Navig., vol. 12, no. 5, pp. 515–522, 2018.
[19] M. Preiss, D. A. Gray, and N. J. S. Stacy, “Detecting scene changes using synthetic aperture radar interferometry,” IEEE Trans. Geosci. Remote
Sens., vol. 44, no. 8, pp. 2041–2054, Aug. 2006.
[20] E. Rignot and R. Chellappa, “A Bayes classifier for change detection in synthetic aperture radar imagery,” in Proc. IEEE Int. Conf. Acoust., Speech,
Signal Process., San Francisco, CA, USA, 1992, pp. 25–28.
[21] H. Hellsten and R. Machado, “Bayesian change analysis for finding vehicle size targets in VHF foliage penetration SAR data,” in Proc. IEEE Radar
Conf., Johannesburg, South Africa, Oct. 2015, pp. 510–515.
[22] H. Hellsten, R. Machado, M. I. Pettersson, V. T. Vu, and P. Dammert, “Experimental results on change detection based on Bayes probability theorem,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., Milan, Italy, Jul. 2015, pp. 318–321.
[23] V. T. Vu, N. R. Gomes, M. I. Pettersson, P. Dammert, and H. Hellsten, “Bivariate Gamma distribution for wavelength-resolution SAR change detection,” IEEE Trans. Geosci. Remote Sens., vol. 57, no. 1, pp. 473–481, Jan. 2019.
[24] Y. Bian and B. Mercer, “SAR probability density function estimation using a generalized form of K-distribution,” IEEE Trans. Aerosp. Electron. Syst., vol. 51, no. 1, pp. 1136–1146, Apr. 2015.
[25] V. T. Vu, M. I. Pettersson, and N. R. Gomes, “Stability in SAR change detection results using bivariate Rayleigh distribution for statistical hy-pothesis test,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., Yokohama, Japan, Jul. 2019, pp. 37–40.
[26] M. K. Simon and M. S. Alouini, “A simple single integral representation of the bivariate Rayleigh distribution,” IEEE Commun. Lett., vol. 2, no. 5, pp. 128–130, May 1998.
[27] N. R. Gomes, P. Dammert, M. I. Pettersson, V. T. Vu, and H. Hellsten, “Comparison of the Rayleigh and K-distributions for application in inco-herent change detection,” IEEE Geosci. Remote Sens. Lett., vol. 16, no. 5, pp. 756–760, May 2019.
Dimas Irion Alves received the B.S degree in
electri-cal engineering from the Federal University of Santa Maria, Santa Maria, Brazil, in 2013, and the M.Sc. and Ph.D. degrees in electrical engineering from the Federal University of Santa Catarina, Florianpolis, Brazil, in 2015 and 2020, respectively.
From 2018 to 2019, he was a Visiting Ph.D. Re-searcher Fellow with the Blekinge Institute of Tech-nology, Karlskrona, Sweden. Since October 2015 he has been a Professor with the Federal University of Pampa, Alegrete, Brazil. His research interests include radars, SAR systems, image processing, and digital signal processing.
Bruna Gregory Palm received the B.Sc. degree in
statistics from the Federal University of Santa Maria, Santa Maria, Brazil, in 2014, and the D.Sc. degree in statistics from the Federal University of Pernambuco, Recife, Brazil, in 2020.
From February 2018 and January 2019, she was a Guest Ph.D. Researcher with the Blekinge Institute of Technology, Karlskrona, Sweden. She is currently a Research Fellow with the Department of Telecommu-nications, Aeronautics Institute of Technology, São José dos Campos, Brazil. Her main research interests include statistical computing, parametric inference, and statistical signal/image processing.
Hans Hellsten (Senior Member, IEEE) started his
radar career with the Swedish Defence Research Agency, subsequently becoming the Director of Re-search. Around 1990, he formulated and patented the basic principles for meter wave SAR imaging. In 1992, he and his colleagues’ work resulted in success-ful flights with VHF SAR, leading to worldwide in-terest. The continuing good results motivated signif-icant funding, allowing a second enhanced system— CARABAS II—to be built. Transferring to the radar industry in 2001, he was the main responsible for the Saab CARABAS III demonstrator radar system becoming operative around 2010. He is currently a Senior Radar Expert, Product Manager, and Principal Engineer with Saab Electronic Defence Systems, working to further enhance meter wave SAR. He also holds an Adjunct Professorship with Halmstad Technical University, Halmstad, Sweden. He is the inventor of about 30 patents and more than 50 scientific and technical publications, including a recently published book on meter wave SAR technology.
Viet Thuy Vu (Senior Member, IEEE) was born in
Hanoi, Vietnam. He received the Diploma degree in electronics from the Hanoi University of Technol-ogy, Hanoi, Vietnam, in 1999, the M.Sc. degree in communication engineering from the University of Duisburg-Essen, Duisburg, Germany, in 2004, and the Licentiate and the Doctoral degrees in applied signal processing from the Blekinge Institute of Technol-ogy (BTH), Karlskrona, Sweden, in 2009 and 2011, respectively.
Currently he is an Associate Professor at BTH. His research interests include mono- and bistatic-SAR signal processing, applica-tions of SAR in change detection, moving target detection and terahertz 3D imaging, and radio occultation.
Mats I. Pettersson received the M.Sc. degree in
engineering physics, the Licentiate degree in radio and space science, and the Ph.D. degree in signal processing from the Chalmers University of Technol-ogy, Gothenburg, Sweden, in 1993, 1995, and 2000, respectively.
For some years, he was with Mobile Communica-tion Research, Ericsson, and for ten years, he was with Swedish Defence Research Agency (FOI). At FOI, he focused on ultrawide band low-frequency SAR systems. Since 2005, he has been with the Blekinge Institute of Technology, Karlskrona, Sweden, where he is currently a Full Professor. His research is related to remote sensing and his main interests include SAR processing, space-time adaptive processing, high-resolution SAR change detection, automotive radar, radio occultation, and computer vision.
Renato Machado (Member, IEEE) received the B.S.
degree in electrical engineering from the São Paulo State University, Ilha Solteira, Brazil, in 2001, and the M.Sc. and Ph.D. degrees in electrical engineering from the Federal University of Santa Catarina, Flori-anópolis, Brazil, in 2004 and 2008, respectively.
He was a Visiting Ph.D. Researcher with the De-partment of Electrical Engineering, Arizona State University, Tempe, AZ, USA, from August 2006 to June 2007. He was with the Research and Devel-opment Department, Nokia Institute of Technology, Brasília, Brazil, in 2007 and 2008. Between 2009 and 2017, he has served as a Professor with the Department of Electronics and Computing, Federal University of Santa Maria, Santa Maria, Brazil. From December 2011 to October 2013, he was the Director of the Santa Maria Space Science Laboratory— LACESM/CRS/INPE, Santa Maria, Brazil. Between November 2013 and March 2015, he spent his sabbatical license, as a Visiting Researcher Fellow, with the Blekinge Institute of Technology, Karlskrona, Sweden, working in partnership with Saab Electronic Defence Systems, SAAB AB. Since December 2017, he has been a Professor with the Department of Telecommunications, Aeronautics Institute of Technology (ITA), São José dos Campos, Brazil, and with the Graduate Program in Electronics and Computer Engineering, ITA. His research interests include SAR image processing, wireless communications, digital signal processing, and radar signal processing.
Dr. Machado is a member of the IEEE Geoscience and Remote Sensing Society, IEEE Aerospace and Electronic Systems Society, and the Brazilian Telecommunications and Signal Processing Society.
Bartolomeu F. Uchôa-Filho (Senior Member, IEEE)
was born in Recife, Brazil, in 1965. He received the B.S. degree from the Federal University of Per-nambuco (UFPE), Recife, Brazil, in 1989, the M.Sc. degree from the State University of Campinas (UNI-CAMP), Campinas, Brazil, in 1992, and the Ph.D. de-gree from the University of Notre Dame, Notre Dame, Indiana, U.S.A., in 1996, all in electrical engineering. He has held Postdoctoral/Visiting Scholar posi-tions with UNICAMP from 1977 to 1999, The Uni-versity of Sydney, Camperdown, NSW, Australia, from 2009 to 2010, Centrale-Suplec, and CNAM, both in France, in 2016. His research interests include coding and information theory, with applications to digital communications systems.
Patrik Dammert (Senior Member, IEEE) received
the M.Sc. degree in electrical engineering and the Ph.D. degree in the field of applications of spaceborne SAR interferometry from the Chalmers University of Technology, Gothenburg, Sweden, in 1993 and 1999, respectively.
He joined Saab, Gothenburg, Sweden, in 2000. At Saab, he has been responsible for the development of high-performance SAR systems for airborne radars, spanning from VHF-band to X-band systems (with flat plate antennas and with AESA antennas). He has also been the Project Manager and Associate Doctoral Student Supervisor for research projects with Saab in collaborations with the Chalmers University of Technology and Blekinge Institute of Technology. His research interests include high-resolution radar and SAR systems, radar modeling, algorithms and signal processing, autofocus, and target detection in heavy-tailed radar clutter.
