Correction of Ultra Wide-band Radio Frequency Interference in - URSI
32nd URSI GASS, Montreal, 19-26 August 2017
Correction of Ultra Wide-band Radio Frequency Interference in SAR Data Using Nonnegative Matrix Factorization Mingliang Tao*(1), Feng Zhou(2) (1) School of Electronics and Information, Northwestern Polytechnical University, 710072 Xi'an, China (2) National Laboratory of Radar Signal Processing, Xidian University, 710071 Xi'an, China
Abstract Radio frequency interference (RFI) is a major issue for synthetic aperture radar (SAR), and would affect the image quality and image interpretation. The majority of existing methods are applied on each azimuth echoes along range direction with the assumption that bandwidth of RFI is less than that of SAR. However, if SAR echoes are contaminated by ultra wide-band RFI, i.e., the bandwidth of RFI is relatively larger than the transmitted signal, traditional methods would fail due to large signal loss. In this paper, we discussed the characteristics of ultra wide-band RFI, and proposed a mitigation method using nonnegative matrix factorization along azimuth direction. The experimental results indicate the effectiveness of the proposed method.
bandwidth than that of the SAR system. Existing methods are not applicable to deal with this special type of RFI because of introducing large signal loss. Natsuaki et al. reported such RFI signatures in real measured PALSAR-2 data and utilized azimuth Doppler difference for suppression [7]. In this paper, we manage to mitigate the adverse impact introduced by the UWB RFI using nonnegative matrix factorization method. Its effectiveness is illustrated by the improvement of imaging quality.
2. Signal Model and Characteristics SAR system operates with the transmission of a sequence of short pulses while moving along a trajectory, and all returned signals containing reflectivity information are collected as the raw data. The received echo is a mixture of target echoes, noise, and interference [3]
1. Introduction With the ever-growing demand for radio spectrum use, many civilian and military electromagnetic services share and compete for the same frequency band, especially for the synthetic aperture radar (SAR) system with large bandwidth. The radio frequency interference (RFI) is referred to as the interfering signal originating from other radio sources, such as the wireless communication network, ground-based tracking radars, etc. RFI poses a hindrance to accurate remote sensing for both the passive and active instruments [1]-[2]. The presence of strong RFI would cause great distortions to the signal characteristics of the echo, such as the amplitude, phase, frequency, and polarization. It not only would increase the difficulty of image formation process, but also would present as hazelike artifacts in the SAR image [3]. Moreover, it will degrade the interpretation accuracy using incorrect imaging result, such as the target detection, information extraction, and parameters retrieval, etc. Therefore, it is of great importance to improve characterization of the RFI environment and seek an effective way to mitigate the adverse impacts on the SAR echoes. The sensitivity of a specific SAR to RFI is highly related with the specific characteristics of the RFI encountered. The majority of the existing literatures focus on the detection and removal of the RFI in the frequency domain or time-frequency domain along range direction [4]-[6]. However, ultra wide-band (UWB) RFI has not been considered in these literatures, i.e., it has a wider
X ( tˆ ) = S ( tˆ ) + W ( tˆ ) + I ( tˆ )
(1)
where X ( tˆ ) denotes the complex-valued radar pulse, S ( tˆ ) denotes the useful target echoes, W ( tˆ ) is the
additive noise and I ( tˆ ) is the RFI. tˆ denotes the fast time samples in range direction.
Generally, the intensity of RFI may be time varying with the azimuth time. Specifically, the UWB RFI can be modeled as a chirp-modulated signal or a sinusoidal modulated signal, and their mathematical expression are given by L
{
}
(2)
{
}
(3)
I CM ( tˆ ) = rect ( tˆ ) ⋅ Al ( tˆ ) ⋅ exp j ( 2π fl tˆ + πγ l tˆ 2 ) l =1 L
I SM ( tˆ ) = rect ( tˆ ) ⋅ Al ( tˆ ) ⋅ exp j ( 2π f l tˆ + πγ l tˆ 2 ) l =1
where rect ( ⋅) denotes the pulsed rectangular envelop. Al ,
fl , γ l , βl and φl is the amplitude, frequency, chirp rate, modulation factor of the l -th component, respectively. Possible source of the UWB RFI is the ground-based radiolocation radar system [2], [7]. In practical case, RFI may not be identical with the modeling. But these two special cases can be regarded as end members for characterizing the various UWB RFI signatures whose properties are a combination of them.
However, it is shown that the UWB RFIs are concentrated into two narrow stripes in the range-time azimuthfrequency representation. This obviously result in less signal overlapping, and would further facilitate applying suppression techniques. 450 -40 Range Frequency (MHz)
In order to illustrate the characteristics of UWB RFI, we have simulated these two typical ones and injected them into a real measured radar echoes. Figure 1(a)-(c) compares the range spectrum without UWB RFI, with chirp modulated RFI and with sinusoidal modulated RFI, respectively. These two kinds of UWB RFI have distinct modulation behavior, but they both span a wide frequency bins. It is shown that the presence of RFI would alter the shape of the spectrum and bury the useful information.
Normalized Amplitude
1 0.8
250 200 150
20
100 50
0
2000 4000 Azimuth Time
6000
Figure 2. Range-frequency azimuth-time representation of SAR data with two simulated UWB RFIs.
0.2
0 Frequency (MHz)
600
50
500
Range Time
1 Normalized Amplitude
300
0
0.4
(a)
0.8 0.6
500
1000
400
1500
300
2000
200
2500
100
0.4
3000 -100
0.2 0 -50
0 Frequency (MHz)
50
(b)
0.8 0.6 0.4 0.2 0 -50
0 Frequency (MHz)
-50 0 50 Azimuth Frequency (Hz)
0
Figure 3. Range-time azimuth-frequency representation of SAR data with two simulated UWB RFIs.
3. Methodology
1 Normalized Amplitude
350
-20
40
0.6
0 -50
400
50
(c) Figure 1. Range spectrum (a) without UWB RFI, (b) with chirp modulated RFI, and (c) sinusoidal modulated RFI. Figure 2 and Figure 3 plots the raw data echoes by performing Fourier transform along range and azimuth direction respectively. Regardless of the modulation type, the UWB RFI has a wider bandwidth than the transmitted signal, and directly processes with existing range spectrum-based methods would lead to large signal loss.
Considering the distinct additive property in range-time azimuth-frequency representation, the key step is to extract out the latent factors representing the interference components. By enforcing the constraints of nonnegativity of the matrix factors, the nonnegative matrix factorization is a suitable separation technique to decompose the data matrix into different meaningful parts. It is essentially an optimization problem, which could be express as [8] 1 ( Xnm − [ WH ]nm ) argmin 2 n, m (4) W,H s.t. W ∈ N × K , H ∈ K × M ≥0 ≥0 where X is the nonnegative data matrix, W denotes the nonnegative basis matrix and H denotes the nonnegative activation matrix. Although this minimization problem is convex in W and H separately, it is not convex in both simultaneously. Due to the absence of strict convexity of the problem formulation, it is solved via alternating minimization schemes, such as the multiplicative update
algorithms, which based on updating one matrix factor at a time while keeping the other fixed [8].
S=
[ W] [H]
k ∈K S
:, k
40
1000
30
1500 2000
20
2500
10
k ,:
P
[W] [H] :, k
p =1 k ∈K S
Range Time
After obtaining the factor matrix and basis matrix, the components corresponding to interference could be extracted out. Then, the energy contribution of RFI could be filtered from the original raw data.
50 500
(5)
X
3000
k ,:
-50 0 50 Azimuth Frequency (Hz)
where K S represent the set of all component indices corresponding to useful signal. The division and multiplication of the rightmost expression is realized element-wise. Figure 4 shows the flowchart of the proposed scheme.
0
(b) Figure 5. Range-time azimuth-frequency representation of SAR data with simulated UWB RFI after RFI mitigation using proposed nonnegative matrix factorization-based method. Figure 6(a) shows the imaging results without RFI mitigation. It is shown that obvious artifacts are overlapped on the image, which buries the scene of interest, for example, the intersection of the river. Further interpretation such as ship detection would also fail. Figure 6(b)-(c) presents the imaging results after using the notch filtering and the proposed scheme respectively. It is shown that the artifacts are well eliminated and the image is well recovered.
Figure 4. Schematic of nonnegative matrix factorization.
In the following, experimental results of the simulated dataset are presented to show the validity of the proposed method. Meanwhile, the notch filtering method [7] is applied for comparison. Figure 5(a) shows the range-time azimuth-frequency representation after notch filtering. The excisions of UWB RFI are sacrificed with large portion of signal loss. Figure 5(b) presents the results after using the proposed scheme. It is shown that the proposed method is more capable of mitigating the RFI effect while retaining the useful information as much as possible.
Range
4 Experimental Results
Azimuth
(a)
50 40
1000
30
1500 2000
20
2500
10
3000 -100
-50 0 50 Azimuth Frequency (Hz)
(a)
Range
Range Time
500
0
Azimuth
(b)
5. Acknowledgements
Range
This work is supported by Postdoctoral Innovation Talent Support Program under grant BX201700199. This work was supported in part by the National Natural Science Foundation of China under Grant U1430123, 61201283, 61471284 and 61522114, 61601372 and 61601373; it was also supported by the Foundation for the Author of National Excellent Doctoral Dissertation of PR China under Grant 201448, and by the Young Scientist Award of Shaanxi Province under Grants 2015KJXX-19 and 2016KJXX-82. Thanks NASA/JPL for providing the UAVSAR dataset for free downloading.
Azimuth
(c) Figure 6. Imaging results (a) without RFI mitigation, (b) using notch filtering, and (c) after using proposed method. To provide a quantitative evaluation, a metric termed processing gain (PG) is introduced. The PG measures the performance gain of signal-to-noise ratio (SNR) that the suppression method can achieve over the original RFIcontaminated data in the raw data domain or image domain, which is calculated as [3] PG = 20 log10
RMS ( x )
RMS ( xˆ − x )
where RMS ( x ) = x
2
− 20 log10
RMS ( x )
RMS ( y − x )
(6)
N . N is the number of samples.
TABLE I compares the PG metric in both the raw data domain and image domain for notch filtering and the proposed method. It is shown that the proposed method has a better improvement of SNR both in the raw data domain and image domain. TABLE I Performance Evaluation
Method Raw Data Image
Notch Filtering [7] 1.27 dB 1.18 dB
Proposed Method 1.44 dB 1.36 dB
5. Conclusion In this paper, we analyzed the characteristics of UWB RFI, and proposed a mitigation method which utilizes nonnegative matrix factorization along azimuth direction. UWB RFI is difficult to deal along range direction as traditional methods do, and would generally introduce large signal loss. By representing the data in range-time azimuth-frequency domain, the nonnegative matrix factorization is utilized to extract the latent factors representing the interference components. Further, the energy contribution of RFI is excised from the original raw data. This work is a complementary recognition about UWB RFI, and could fill a priori information gap for charactering the complex RFI environment.
6. References 1. S. Misra, and P. Matthaeis, “Passive remote sensing and radio frequency interference (RFI): an overview of spectrum allocations and RFI management algorithms,” IEEE Geosci. Remote Sens. Mag., 2, 2, June 2014, pp. 6873, doi: 10.1109/MGRS.2014.2320879. 2. National Academies of Sciences, Engineering, and Medicine. A Strategy for Active Remote Sensing Amid Increased Demand for Radio Spectrum. Washington, DC: National Academies Press, 2015. doi: 10.17226/21729. 3. L. H. Nguyen, and T. D. Tran, “Efficient and robust RFI extraction via sparse recovery,” IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 9, 6, Jun. 2016, pp. 2104-2117. doi: 10.1109/JSTARS.2016.2528884. 4. F. J. Meyer, J. B. Nicoll, and A. P. Doulgeris, “Correction and characterization of radio frequency interference signatures in L-band synthetic aperture radar data,” IEEE Trans. Geosci. Remote Sens., 51, 10, Oct. 2013, pp. 4961-4972. doi: 10.1109/TGRS.2013.2252469. 5. Z. Yang, W. Du, Z. Liu, and G. Liao, “WBI suppression for SAR using iterative adaptive method,” IEEE J. Sel. Topics Appl. Earth Observ., 9, 3, Mar. 2016, pp. 1008-1014. doi: 10.1109/JSTARS.2015.2470107. 6. M. Tao, F. Zhou, and Z. Zhang, “Wideband interference mitigation in high-resolution airborne synthetic aperture radar data,” IEEE Trans. Geosci. Remote Sens., 54, 1, Jan. 2016, pp. 74-87. doi: 10.1109/TGRS.2015.2450754. 7. R. Natsuaki, M. Watanabe, T. Motohka, and S. Suzuki, “RFI detection and removal in range-time azimuth-frequency domain,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., Jul. 2016, pp. 313–316. doi: 10.1109/IGARSS.2016.7729074. 8. A. Cichocki, R. Zdunek, A. H. Phan, S. Amari. Nonnegative Matrix and Tensor Factorizations. UK: John Wiley & Sons, 2015.
Correction of Ultra Wide-band Radio Frequency Interference in SAR Data Using Nonnegative Matrix Factorization Mingliang Tao*(1), Feng Zhou(2) (1) School of Electronics and Information, Northwestern Polytechnical University, 710072 Xi'an, China (2) National Laboratory of Radar Signal Processing, Xidian University, 710071 Xi'an, China
Abstract Radio frequency interference (RFI) is a major issue for synthetic aperture radar (SAR), and would affect the image quality and image interpretation. The majority of existing methods are applied on each azimuth echoes along range direction with the assumption that bandwidth of RFI is less than that of SAR. However, if SAR echoes are contaminated by ultra wide-band RFI, i.e., the bandwidth of RFI is relatively larger than the transmitted signal, traditional methods would fail due to large signal loss. In this paper, we discussed the characteristics of ultra wide-band RFI, and proposed a mitigation method using nonnegative matrix factorization along azimuth direction. The experimental results indicate the effectiveness of the proposed method.
bandwidth than that of the SAR system. Existing methods are not applicable to deal with this special type of RFI because of introducing large signal loss. Natsuaki et al. reported such RFI signatures in real measured PALSAR-2 data and utilized azimuth Doppler difference for suppression [7]. In this paper, we manage to mitigate the adverse impact introduced by the UWB RFI using nonnegative matrix factorization method. Its effectiveness is illustrated by the improvement of imaging quality.
2. Signal Model and Characteristics SAR system operates with the transmission of a sequence of short pulses while moving along a trajectory, and all returned signals containing reflectivity information are collected as the raw data. The received echo is a mixture of target echoes, noise, and interference [3]
1. Introduction With the ever-growing demand for radio spectrum use, many civilian and military electromagnetic services share and compete for the same frequency band, especially for the synthetic aperture radar (SAR) system with large bandwidth. The radio frequency interference (RFI) is referred to as the interfering signal originating from other radio sources, such as the wireless communication network, ground-based tracking radars, etc. RFI poses a hindrance to accurate remote sensing for both the passive and active instruments [1]-[2]. The presence of strong RFI would cause great distortions to the signal characteristics of the echo, such as the amplitude, phase, frequency, and polarization. It not only would increase the difficulty of image formation process, but also would present as hazelike artifacts in the SAR image [3]. Moreover, it will degrade the interpretation accuracy using incorrect imaging result, such as the target detection, information extraction, and parameters retrieval, etc. Therefore, it is of great importance to improve characterization of the RFI environment and seek an effective way to mitigate the adverse impacts on the SAR echoes. The sensitivity of a specific SAR to RFI is highly related with the specific characteristics of the RFI encountered. The majority of the existing literatures focus on the detection and removal of the RFI in the frequency domain or time-frequency domain along range direction [4]-[6]. However, ultra wide-band (UWB) RFI has not been considered in these literatures, i.e., it has a wider
X ( tˆ ) = S ( tˆ ) + W ( tˆ ) + I ( tˆ )
(1)
where X ( tˆ ) denotes the complex-valued radar pulse, S ( tˆ ) denotes the useful target echoes, W ( tˆ ) is the
additive noise and I ( tˆ ) is the RFI. tˆ denotes the fast time samples in range direction.
Generally, the intensity of RFI may be time varying with the azimuth time. Specifically, the UWB RFI can be modeled as a chirp-modulated signal or a sinusoidal modulated signal, and their mathematical expression are given by L
{
}
(2)
{
}
(3)
I CM ( tˆ ) = rect ( tˆ ) ⋅ Al ( tˆ ) ⋅ exp j ( 2π fl tˆ + πγ l tˆ 2 ) l =1 L
I SM ( tˆ ) = rect ( tˆ ) ⋅ Al ( tˆ ) ⋅ exp j ( 2π f l tˆ + πγ l tˆ 2 ) l =1
where rect ( ⋅) denotes the pulsed rectangular envelop. Al ,
fl , γ l , βl and φl is the amplitude, frequency, chirp rate, modulation factor of the l -th component, respectively. Possible source of the UWB RFI is the ground-based radiolocation radar system [2], [7]. In practical case, RFI may not be identical with the modeling. But these two special cases can be regarded as end members for characterizing the various UWB RFI signatures whose properties are a combination of them.
However, it is shown that the UWB RFIs are concentrated into two narrow stripes in the range-time azimuthfrequency representation. This obviously result in less signal overlapping, and would further facilitate applying suppression techniques. 450 -40 Range Frequency (MHz)
In order to illustrate the characteristics of UWB RFI, we have simulated these two typical ones and injected them into a real measured radar echoes. Figure 1(a)-(c) compares the range spectrum without UWB RFI, with chirp modulated RFI and with sinusoidal modulated RFI, respectively. These two kinds of UWB RFI have distinct modulation behavior, but they both span a wide frequency bins. It is shown that the presence of RFI would alter the shape of the spectrum and bury the useful information.
Normalized Amplitude
1 0.8
250 200 150
20
100 50
0
2000 4000 Azimuth Time
6000
Figure 2. Range-frequency azimuth-time representation of SAR data with two simulated UWB RFIs.
0.2
0 Frequency (MHz)
600
50
500
Range Time
1 Normalized Amplitude
300
0
0.4
(a)
0.8 0.6
500
1000
400
1500
300
2000
200
2500
100
0.4
3000 -100
0.2 0 -50
0 Frequency (MHz)
50
(b)
0.8 0.6 0.4 0.2 0 -50
0 Frequency (MHz)
-50 0 50 Azimuth Frequency (Hz)
0
Figure 3. Range-time azimuth-frequency representation of SAR data with two simulated UWB RFIs.
3. Methodology
1 Normalized Amplitude
350
-20
40
0.6
0 -50
400
50
(c) Figure 1. Range spectrum (a) without UWB RFI, (b) with chirp modulated RFI, and (c) sinusoidal modulated RFI. Figure 2 and Figure 3 plots the raw data echoes by performing Fourier transform along range and azimuth direction respectively. Regardless of the modulation type, the UWB RFI has a wider bandwidth than the transmitted signal, and directly processes with existing range spectrum-based methods would lead to large signal loss.
Considering the distinct additive property in range-time azimuth-frequency representation, the key step is to extract out the latent factors representing the interference components. By enforcing the constraints of nonnegativity of the matrix factors, the nonnegative matrix factorization is a suitable separation technique to decompose the data matrix into different meaningful parts. It is essentially an optimization problem, which could be express as [8] 1 ( Xnm − [ WH ]nm ) argmin 2 n, m (4) W,H s.t. W ∈ N × K , H ∈ K × M ≥0 ≥0 where X is the nonnegative data matrix, W denotes the nonnegative basis matrix and H denotes the nonnegative activation matrix. Although this minimization problem is convex in W and H separately, it is not convex in both simultaneously. Due to the absence of strict convexity of the problem formulation, it is solved via alternating minimization schemes, such as the multiplicative update
algorithms, which based on updating one matrix factor at a time while keeping the other fixed [8].
S=
[ W] [H]
k ∈K S
:, k
40
1000
30
1500 2000
20
2500
10
k ,:
P
[W] [H] :, k
p =1 k ∈K S
Range Time
After obtaining the factor matrix and basis matrix, the components corresponding to interference could be extracted out. Then, the energy contribution of RFI could be filtered from the original raw data.
50 500
(5)
X
3000
k ,:
-50 0 50 Azimuth Frequency (Hz)
where K S represent the set of all component indices corresponding to useful signal. The division and multiplication of the rightmost expression is realized element-wise. Figure 4 shows the flowchart of the proposed scheme.
0
(b) Figure 5. Range-time azimuth-frequency representation of SAR data with simulated UWB RFI after RFI mitigation using proposed nonnegative matrix factorization-based method. Figure 6(a) shows the imaging results without RFI mitigation. It is shown that obvious artifacts are overlapped on the image, which buries the scene of interest, for example, the intersection of the river. Further interpretation such as ship detection would also fail. Figure 6(b)-(c) presents the imaging results after using the notch filtering and the proposed scheme respectively. It is shown that the artifacts are well eliminated and the image is well recovered.
Figure 4. Schematic of nonnegative matrix factorization.
In the following, experimental results of the simulated dataset are presented to show the validity of the proposed method. Meanwhile, the notch filtering method [7] is applied for comparison. Figure 5(a) shows the range-time azimuth-frequency representation after notch filtering. The excisions of UWB RFI are sacrificed with large portion of signal loss. Figure 5(b) presents the results after using the proposed scheme. It is shown that the proposed method is more capable of mitigating the RFI effect while retaining the useful information as much as possible.
Range
4 Experimental Results
Azimuth
(a)
50 40
1000
30
1500 2000
20
2500
10
3000 -100
-50 0 50 Azimuth Frequency (Hz)
(a)
Range
Range Time
500
0
Azimuth
(b)
5. Acknowledgements
Range
This work is supported by Postdoctoral Innovation Talent Support Program under grant BX201700199. This work was supported in part by the National Natural Science Foundation of China under Grant U1430123, 61201283, 61471284 and 61522114, 61601372 and 61601373; it was also supported by the Foundation for the Author of National Excellent Doctoral Dissertation of PR China under Grant 201448, and by the Young Scientist Award of Shaanxi Province under Grants 2015KJXX-19 and 2016KJXX-82. Thanks NASA/JPL for providing the UAVSAR dataset for free downloading.
Azimuth
(c) Figure 6. Imaging results (a) without RFI mitigation, (b) using notch filtering, and (c) after using proposed method. To provide a quantitative evaluation, a metric termed processing gain (PG) is introduced. The PG measures the performance gain of signal-to-noise ratio (SNR) that the suppression method can achieve over the original RFIcontaminated data in the raw data domain or image domain, which is calculated as [3] PG = 20 log10
RMS ( x )
RMS ( xˆ − x )
where RMS ( x ) = x
2
− 20 log10
RMS ( x )
RMS ( y − x )
(6)
N . N is the number of samples.
TABLE I compares the PG metric in both the raw data domain and image domain for notch filtering and the proposed method. It is shown that the proposed method has a better improvement of SNR both in the raw data domain and image domain. TABLE I Performance Evaluation
Method Raw Data Image
Notch Filtering [7] 1.27 dB 1.18 dB
Proposed Method 1.44 dB 1.36 dB
5. Conclusion In this paper, we analyzed the characteristics of UWB RFI, and proposed a mitigation method which utilizes nonnegative matrix factorization along azimuth direction. UWB RFI is difficult to deal along range direction as traditional methods do, and would generally introduce large signal loss. By representing the data in range-time azimuth-frequency domain, the nonnegative matrix factorization is utilized to extract the latent factors representing the interference components. Further, the energy contribution of RFI is excised from the original raw data. This work is a complementary recognition about UWB RFI, and could fill a priori information gap for charactering the complex RFI environment.
6. References 1. S. Misra, and P. Matthaeis, “Passive remote sensing and radio frequency interference (RFI): an overview of spectrum allocations and RFI management algorithms,” IEEE Geosci. Remote Sens. Mag., 2, 2, June 2014, pp. 6873, doi: 10.1109/MGRS.2014.2320879. 2. National Academies of Sciences, Engineering, and Medicine. A Strategy for Active Remote Sensing Amid Increased Demand for Radio Spectrum. Washington, DC: National Academies Press, 2015. doi: 10.17226/21729. 3. L. H. Nguyen, and T. D. Tran, “Efficient and robust RFI extraction via sparse recovery,” IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 9, 6, Jun. 2016, pp. 2104-2117. doi: 10.1109/JSTARS.2016.2528884. 4. F. J. Meyer, J. B. Nicoll, and A. P. Doulgeris, “Correction and characterization of radio frequency interference signatures in L-band synthetic aperture radar data,” IEEE Trans. Geosci. Remote Sens., 51, 10, Oct. 2013, pp. 4961-4972. doi: 10.1109/TGRS.2013.2252469. 5. Z. Yang, W. Du, Z. Liu, and G. Liao, “WBI suppression for SAR using iterative adaptive method,” IEEE J. Sel. Topics Appl. Earth Observ., 9, 3, Mar. 2016, pp. 1008-1014. doi: 10.1109/JSTARS.2015.2470107. 6. M. Tao, F. Zhou, and Z. Zhang, “Wideband interference mitigation in high-resolution airborne synthetic aperture radar data,” IEEE Trans. Geosci. Remote Sens., 54, 1, Jan. 2016, pp. 74-87. doi: 10.1109/TGRS.2015.2450754. 7. R. Natsuaki, M. Watanabe, T. Motohka, and S. Suzuki, “RFI detection and removal in range-time azimuth-frequency domain,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., Jul. 2016, pp. 313–316. doi: 10.1109/IGARSS.2016.7729074. 8. A. Cichocki, R. Zdunek, A. H. Phan, S. Amari. Nonnegative Matrix and Tensor Factorizations. UK: John Wiley & Sons, 2015.
