VLDB 2026 Research / reviewers in the wild / expert
Kaizhi Wang
dblp:58/6232
· DBLP profile ↗
64ranked-venue papers
7as first author
5since 2021 · last 2024
—ORCID · conflict
Domains — the database's venue-derived domains; a paper can count in several
Applied, interdisciplinary, general and emerging computing · 60 · 5 first-author · 5 since 2021Graphics, computer vision, multimedia, augmented reality and games · 4 · 2 first-authorArtificial intelligence and machine learning · 1
| Year | Publication | Venue | Position |
|---|---|---|---|
| 2024 | Resolution Progressive Convolutional Neural Network for Fine-Grained SAR Ship RecognitionabstractThe advancement in Synthetic Aperture Radar (SAR) imaging quality, coupled with the integration of deep learning techniques, has propelled the research of fine-grained recognition tasks in SAR images. However, recognizing fine-grained ship categories in SAR images is challenging due to discriminative region localization and fine-grained feature learning. In this paper, we propose a resolution progressive convolutional neural network (RP-CNN) that automatically identifies discriminative regions and learns fine-grained features. The model gradually finds salient regions from input and enhances their resolution by localization proposal network (LPN) and attention proposal network (APN), resulting in more accurate recognition and classification. This approach achieves satisfactory results on the FUSAR-Ship dataset. Zian Tai, Chenguang Yang 0010, Kaizhi Wang |
IGARSS | 3 |
| 2024 | A Non-Reference SAR Image Quality Assessment Method Based on Average Blurred Edge Width in Salient AreaabstractThe traditional synthetic aperture radar (SAR) image quality assessment (IQA) indexes are mainly proposed based on the statistical characteristics of point and area targets. However, these indexes are not combined with the principle of SAR imaging focusing, so there are often failures. In order to overcome the shortcomings of traditional IQA indexes, based on SAR imaging principles, this paper analyzes the impact of defocusing caused by mismatched filter on imaging results, and proposes a non-reference SAR IQA index based on average blurred edge width (ABEW) in salient area. The effectiveness of this method has been validated by using SAR images of real scenes, and the results are highly consistent with the actual image quality. The novel algorithm provides a new idea and method for IQA of SAR. Chenguang Yang 0010, Zian Tai, Xiaoming Gu, Kaizhi Wang |
IGARSS | 4 |
| 2023 | Sensor-Based Motion Compensation Methods of Back Projection Algorithm in SARabstractSynthetic aperture radar (SAR) plays a crucial part in remote sensing applications. Back Projection (BP) algorithm is a representative SAR imaging algorithm. However, motion errors often worsen the imaging performance of BP. In this paper, we present four motion compensation methods of BP based on GPS (Global Positioning System) and IMU (Inertial Measurement Unit) data. First, we introduce the coordinate system involved in the four methods and the general formula of coordinate system rotation. Then the origin and steps of the four methods are described in detail and the relevant formulas are given. Finally, the actual airborne SAR data is used to verify the effectiveness of these methods. Jiajia Chen 0008, Kaizhi Wang |
IGARSS | 3 |
| 2023 | Design Platform Test and Airborne Implementation of FMCW SAR SystemabstractThe traditional SAR radar system is relatively complex, high cost, large volume and weight, and can not be installed on small and light aircraft and starchain platforms, which limits the large-scale application of SAR. The radar system design scheme adopts technologies such as FM continuous wave system, function and system integration, RF direct modulation, digital demodulation and chip design, which reduces the complexity of the system, reduces the volume, weight and power consumption of the system, and realizes a small size, light weight and low power consumption micro SAR system. The waveguide slot array antenna and the corresponding test platform are designed, and the imaging algorithm of FMCW SAR is improved. Through the flight test of the micro SAR system on a small aircraft platform, the test results verify the effectiveness and feasibility of the system. Dongcheng Yan, Enhua Zhang, Kaizhi Wang |
IGARSS | 4 |
| 2021 | Detection of Small Targets Based on Dual-Receive Channels RadarabstractWith the widespread application of unmanned aerial vehicles, higher requirements have been put forward for the detection of small targets moving at high speed. In this paper, we implement a millimeter wave Frequency Modulated Continuous Wave (FMCW) radar system with dual-receive channels to detect target motion parameters. In the radar system, a novel signal is designed to be composed of two FMCW signals whose instantaneous frequencies are symmetrical about carrier frequency, so as to get the estimation value of the targets' distance and radial velocity using doppler shift. Besides, signals of different periods are transmitted alternately to facilitate the removal of virtual targets. Furthermore, the height information of the target can be obtained through the interference of the signals received by the two channels. Based on the theory above, simulation results are provided to validate the effectiveness of the proposed approach and evaluate the performance of the radar system. Jinzhi Liu, Kaizhi Wang |
IGARSS | 4 |
| 2019 | A Finely Focusing Method of SAR Using Very Deep Neural NetworkabstractDoppler-parameter estimation is a basic auto-focusing method of SAR. However, as the stability of the platform decreases, the Doppler-parameter method cannot achieve high estimation accuracy, and thus leads to the degradation of image quality. In order to solve the problems, this paper proposed a model of SAR signal finely focusing based on Very Deep Neural Network. After roughly focused, SAR signal is sent to pre-trained network to get finely focused result. Experiments on simulated data and actual data shows that the image quality has been greatly improved, meanwhile, the PSLR and ISLR of the result are -14.5494dB and -13.8190dB, which indicates that this method is suitable for solving SAR signal finely focusing problem. Guangkai Qiao, Jingwei Dai, Kaizhi Wang, Yiran Jin |
IGARSS | 3 |
| 2018 | Increment Information Acquisition Technology for Remote SensingabstractIn this paper, increment information is defined as the change of a scene between two observations. The increment information would be limited and can be acquired as long as the observation interval is short enough. This paper proposes a novel technology to acquire increment information with the cooperation of two types of sensor. Our technology is implemented by a high time resolution but low spatial resolution sensor cooperated with a high spatial resolution but low time resolution sensor. And observation of high resolution both spatial and time will be yielded easily with the increment information acquired. The paper describes the main algorithm of this technology and validates the feasibility with series of simulation experiments. Then we have a deep analysis about our method's robustness. Zhiang Peng, Xingquan Zheng, Kaizhi Wang |
IGARSS | 4 |
| 2017 | Optical counterpart of SAR system and its applicationsabstractThis paper proposed a new concept of optical counterpart of radar system. Due to the difference between wavelength of microwave and light, we can build an optical counterpart of a radar system in reduced dimensions with optical components and light in place of microwave. The radar system is equivalent to its optical counterpart in physical principle. As for a C-band radar system, the wavelength is 5cm typically and 5 orders longer than 500nm green light. A scene of 10km for the C-band radar will be scaled to 0.1m for its optical counterpart. The optical counterpart of a radar system can simulate the backscattered signal in light-wave domain at a speed of light. Taking the advantage of reversibility of optical path, the optical counterpart can also be used to process the radar data and reconstruct the scene or target in spite of complex algorithms as long as the physical equivalence is kept well. Kaizhi Wang, Xingzhao Liu |
IGARSS | 1 |
| 2017 | Optimal cognitive radar transmit-receiver design for extended target with unknown target impulse responseabstractIn this paper, the problem of joint transmit waveform and receive filter design for cognitive radar (CR) is investigated. The problem is analyzed in signal-dependent interference, as well as additive channel noise for extended target with unknown target impulse response (TIR). An improved online waveform optimization design method is employed for target detection by maximizing the average signal to interference plus noise ratio (SINR) of the received echo on the premise of ensuring the TIR estimation precision. In the proposed method, the transmit waveform and receive filter are optimally determined at each step based on the observations in the previous steps. Simulation results demonstrate that CR with the proposed waveform achieve significantly higher rate of estimation accuracy and detection performance improvement compared to traditional radar system with fixed waveform, and offers more flexibility. Kaizhi Wang, Xingzhao Liu, Lei Liu 0023 |
IGARSS | 2 |
| 2017 | A flexible waveform optimization method for cognitive radarabstractIn this paper, the problem of adaptive waveform design for cognitive radar (CR) in signal-dependent interference, as well as additive channel noise is investigated. With constraints on waveform energy and bandwidth, a flexible waveform optimization method taking both detection and range resolution into account is proposed. Unlike existing optimal waveforms designed by a single design criterion, waveform designed by the proposed method can be updated according to the environment information fed back by receiver and radar performance demands simultaneously at each cycle of CR. Simulations are conducted to illustrate that CR with the proposed waveform performs better than traditional radar system with fixed waveform, and offers more practical and flexible. Kaizhi Wang, Xingzhao Liu, Lei Liu 0023 |
IGARSS | 2 |
| 2017 | Suppression of Azimuth Ambiguities of Strong Point-Like Targets for Multichannel SAR SystemsabstractMultichannel synthetic aperture radar (SAR) signal reconstruction methods can effectively suppress azimuth ambiguities and achieve high-resolution wide-swath imaging. However, due to the characteristics of the practical antenna patterns, there exist non-bandlimited Doppler spectra, which will result in residual azimuth ambiguities, especially for strong targets. This letter presents a novel method for the suppression of the azimuth ambiguities of the strong point-like targets. First, we find out the positions of the strong point-like targets from the multichannel reconstructed SAR image. Then, we locate the ambiguous range history of each strong point-like target. Finally, the ambiguous components in the range history are filtered out by an orthogonal projection method. Therefore, the spectra of the strong point-like targets will be converted into the bandlimited spectra, and then, the azimuth ambiguities can be effectively suppressed by the conventional multichannel SAR signal reconstruction methods. Theoretical analysis and experiments demonstrate the feasibility of the proposed methods. Xiaojiang Guo, Yesheng Gao, Kaizhi Wang, Xingzhao Liu |
IEEE Geosci. Remote. Sens. Lett. | 3 |
| 2016 | Transmitter leakage canceling for LFMCW SARabstractLinear frequency modulated (LFM) continuous wave (CW) synthetic aperture radar (SAR) is promising in airborne earth observation with compact, lightweight, cost-effective and high resolution advantages. For CW imaging radars, however, weak targets may be submerged by sidelobes of strong range interferences including transmitter leakage and nadir signal, especially when the slant range is far. This paper firstly discusses how to suppress transmitter leakage and nadir signal suppression for LFMCW SAR by choosing appropriate pulse repetition interval (PRI) and digital sampling frequency. Although the transmitter leakage could be weakened by an appropriate PRI and finite impulse response (FIR) filter, the residual leakage is so strong that its sidelobes will still submerge some weak targets. Then, a novel transmitter leakage canceling method based on orthogonal projection is derived, which could effectively reduce the sidelobe level of transmitter leakage. Theoretical analysis and experiments on a real unmanned LFMCW SAR system showed the efficiency of the proposed method. Xiaojiang Guo, Yesheng Gao, Kaizhi Wang, Xingzhao Liu, Qianrong Lu |
IGARSS | 3 |
| 2016 | A novel 3D imaging method based on orthogonal-track SARabstractA novel method of three-dimensional (3D) imaging based on orthogonal-track synthetic aperture radar (SAR), is proposed in this paper. In the scheme, the SAR sensor moves along two orthogonal tracks successively and two SAR images are obtained. Then we extract the spacial information from the two-dimensional (2D) SAR images to reconstruct the 3D distribution of scatterers in the common part. The orthogonal-track SAR obtains resolving ability in the normal direction of the azimuth-range plane by combining the information obtained along orthogonal tracks. Compared with conventional single-channel 2D SAR and interferometry SAR, the orthogonal-track SAR has distinct advantage in providing detailed and precise information about spatial distribution of the observed scene, and is capable of achieving real 3D resolution cell. Ji Guo, Kaizhi Wang, Xingzhao Liu |
IGARSS | 3 |
| 2016 | A optronic SAR processor with high-speed and high-precision phase modulationabstractSynthenic Aperture Radar (SAR) has an important role in the field of remote sensing. As optical SAR data processor has the outstanding advantage of high speed, it performs processing prospect in real-time SAR imaging field. Liquid crystal based spatial light modulators (SLMs) are widely used to make phase modulation in optical SAR processor. However, in some phase-sensing or real-time applications such as SAR imaging process, low phase precision of SLM may cause phase error and low data refresh rate of SLM may restrict processing speed. This paper proposes a new optical SAR data processor with high-speed and high-precision phase modulation. The core of this optical processor is a phase modulation module by using a digital micromirror device (DMD) which can achieve high-speed and high-precision phase modulation because of its high data refresh rate of 9500Hz and phase resolution of 0.002 rad. The principle of phase modulation with DMD and the structure of the new SAR optical processor are presented. The images processed by it are also presented. Lei Liu 0023, Yesheng Gao, Kaizhi Wang, Xingzhao Liu |
IGARSS | 3 |
| 2016 | An automatic RCMC technique based on BFGS methodabstractHere automatic range cell migration correction (RCMC) is studied. Classic RCMC in Range-Doppler Algorithm (RDA) is realized by sinc interpolation so that exact instantaneous slant range distance between antenna phase center (APC) and scatterers is necessary. However, the later element above could not be satisfied especially in airborne SAR. Inspired by improved global method used for ISAR range alignment, we propose an automatic RCMC technique with Broyden-Fletcher-Goldfard-Shano(BFGS). This technique creates N variables (time shifts) to adjust range migration curve to make cost function minimum. Exact instantaneous slant range distance is not required while computation efficiency is a little lower than that of classic RCMC. Simulation validates this idea from the view of three isolate scatterers. It also proves that BFGS-RCMC has phase-keep property in azimuth direction. Qianrong Lu, Kaizhi Wang, Xingzhao Liu, Xiaojiang Guo |
IGARSS | 2 |
| 2016 | X-band mini SAR radar on eight-rotor mini-UAVabstractAn X-band Synthetic Aperture Radar (SAR), the mini-SAR, mounted on an eight-rotor Unmanned Aerial Vehicle (UAV), has been designed, built and tested at Shanghai Jiao Tong University, China. The main purpose of this work is to design a light-weight, cost-effective and easy-handy miniaturize SAR system with the ability to make repeated flights for an extended study. Real-time collected data can effectively test the validity of a newly proposed image algorithm. The system can apply in modeling and calculating the scattering characteristics of complex target such as tank which is vital in military reconnaissance. Recent tests have shown that the system is suitable for further experiments to validate the SAR system design via changing the parameter setting. This paper outlines design parameters and specifications for the mini-SAR, together with results from experimental data collection and test flights. Jiali Yan, Ji Guo, Qianrong Lu, Kaizhi Wang, Xingzhao Liu |
IGARSS | 4 |
| 2016 | Reconstruction of azimuth signal for multichannel HRWS SAR imaging based on periodic extensionabstractAlong a roughly chronological order, the azimuth signals undersampled from the multichannel synthetic aperture radar (SAR) for high-resolution wide-swath (HRWS) imaging correspond to recurrent nonuniform sampling. Only a finite-duration sequence of samples of the azimuth signal can be obtained in practical applications. A new recurrent nonuniform sampling scheme can be generated by extending these samples periodically across the boundaries provided that the azimuth signal is bandlimited. Thus, from the perspective of reconstructing recurrent nonuniform sampling, an innovative reconstruction algorithm for suppressing azimuth ambiguities of multichannel HRWS SAR is proposed, which is suitable to be implemented on digital computers. Furthermore, the presented algorithm acquires the filter weights without matrix inversion reducing tremendously the computational load. Linjian Zhang, Yesheng Gao, Kaizhi Wang, Xingzhao Liu |
IGARSS | 4 |
| 2016 | Waveform design based multi-target hypothesis testing under unknown clutter parametersabstractA method to solve multi-target classification problems with unknown clutter parameters is proposed in this paper. The unknown parameter is estimated and synthesized at each observation, and probability of each hypothesis is updated. Subsequently, the optimal waveform for the next illumination is designed based on NP criteria, and the final decision is made based on the sequential probability ratio testing. Simulated results are presented based on our method and show that the optimal waveform-based sequential testing can be decided through reduction of the average illumination number. Furthermore, results indicate a significant improvement over the non-optimal waveforms. Bingqi Zhu, Yesheng Gao, Hui Sheng, Kaizhi Wang, Xingzhao Liu |
IGARSS | 4 |
| 2016 | Optimal radar waveform design for moving targetabstractRadar performance improvement through waveform optimization has been an ongoing topic of research recent years. In this paper, we use the optimal waveform design method to deal with the moving target in the clutter and noise. Neyman-Pearson detector criterion is used to maximize the probability of target detection. The optimal waveform is then designed theoretically corresponding to the velocity of target and clutter/noise power spectrum density. Simple CW signals can produce maximum detectability based on different noise PSD situations. Simulated results are presented based on our method and improvement in image is approached. Finally, the conclusions are drawn based on our analysis and simulations. Bingqi Zhu, Hui Sheng, Yesheng Gao, Kaizhi Wang, Xingzhao Liu |
IGARSS | 4 |
| 2016 | Optronic High-Resolution SAR Processing With the Capability of Adaptive Phase Error CompensationabstractA system design of optronic high-resolution synthetic aperture radar (SAR) processing is proposed in this letter; it has the capability of adaptive phase error compensation. In our system design, SAR raw data are focused optically by phase correction in the two-dimensional frequency domain. The computations of SAR image formation are performed by spatial light modulators and lenses. With the propagation of the laser beam, the imaging results can be captured by the charge-coupled device. The phase error can be estimated from the imaging results, and adaptive phase error compensation is implemented in the optronic processing. Phase error compensation makes the optronic processing robust and flexible; it can be used for both the initial system calibration and the focus quality improvement. Finally, the experimental setup is demonstrated. The entropies of the images with and without phase error compensation are analyzed, which validates its performance on improving the focus quality. The real data results of an airborne SAR and RADARSAT are given. Yesheng Gao, Chaobo Lin, Kaizhi Wang, Xingzhao Liu |
IEEE Geosci. Remote. Sens. Lett. | 4 |
| 2016 | Improved Channel Error Calibration Algorithm for Azimuth Multichannel SAR SystemsabstractMultichannel synthetic aperture radar systems in azimuth can effectively suppress azimuth ambiguity and are promising in high-resolution wide-swath imaging. However, unavoidable channel errors will significantly degrade the performance of ambiguity suppression. Conventional subspace calibration methods usually estimate phase error via decomposing a Doppler-variant covariance matrix from one Doppler bin, and then average these errors estimated from several Doppler bins to improve the estimation accuracy, which will result in a large computational load. This letter presents an improved channel error calibration method, which works on the undersampled data of the individual azimuth channel. By a proposed matrix transformation method, the Doppler-variant covariance matrices will be transformed into a constant covariance matrix. Therefore, the improved calibration algorithm needs to estimate and decompose the new covariance matrix only once. The computation load could be greatly reduced. Moreover, the new covariance matrix can be estimated by training samples not only from range bins but also from Doppler bins, which will improve the estimation accuracy. Theoretical analysis and experiments based on simulations and measurements showed the high accuracy, efficiency, and robustness of the improved method, particularly in low signal-to-noise ratio. Xiaojiang Guo, Yesheng Gao, Kaizhi Wang, Xingzhao Liu |
IEEE Geosci. Remote. Sens. Lett. | 3 |
| 2015 | An automatic and programmable optical SAR data processorabstractSynthetic Aperture Radar now is widely used in remote imaging which have many kinds of system. But as SAR data become larger and larger, the traditional Digital Signal Processing processor can not afford the high speed and high resolution process in rated size and power. But our optical processor for SAR can finish the data process in high speed because it can perform the Fourier transformation at the speed of light with low power consumption. Besides, this system is automatic and programmable which can be realized by computer and spatial light modulator. Chaobo Lin, Huanglong Wang, Yesheng Gao, Kaizhi Wang, Xingzhao Liu |
IGARSS | 4 |
| 2015 | A novel SAR imaging processing method based on fractional fourier transformabstractThe fractional Fourier transform (FRFT) is a potent tool to analyze the chirp signal. Here a novel SAR imaging technique based on FRFT is studied. We apply FRFT to range compressed data instead of executing RCMC and Azimuth compression. By FRFT, we estimate (1) Doppler rate, (2) amplitude (3) azimuth beam center crossing time which means azimuth location of a point target in image in accurate way. The relative range locations of point targets can be also determined by the formulation of Doppler rate. Then SAR image can be reconstructed together with estimated amplitudes. The relationship between FRFT order and SAR resolution is also studied. Furthermore, we simulate this method from a multi-points view. Qianrong Lu, Kaizhi Wang, Xingzhao Liu |
IGARSS | 2 |
| 2015 | Azimuth wavefront modulation using plasma lens array for microwave staring imagingabstractMicrowave staring imaging scheme based on range pulse compression and azimuth wavefront modulation is a new radar scheme. Under the condition of no relative motion between radar and scene, the scheme can obtain radar images with high resolution in both range direction and azimuth direction. The paper presents this imaging technique by theoretical analysis and simulation. Microwave staring imaging structure is introduced firstly. Then, requirement of the azimuth wavefront modulation and target change detection is analyzed. Linjian Zhang, Yesheng Gao, Kaizhi Wang, Xingzhao Liu |
IGARSS | 4 |
| 2015 | SAR clutter suppression using recursive waveformsabstractIn this paper, we combine the waveform design method with the synthetic aperture algorithm to suppress clutter and generate clear microwave images of targets. The linear recursive model is introduced into the SAR operation principle and Kalman filter algorithm is used to estimate target and clutter responses in each azimuth direction based on their states before, which both are assumed to be Gaussian distributions. Optimal waveforms based on NP criteria are designed repeatedly and used as the transmitting signals. A clutter suppression filter is then designed and added to suppress the clutter response while maintaining most of the target response. The simulations show that our algorithm can significantly reduce the clutter response while targets are imaged. Bingqi Zhu, Hui Sheng, Yesheng Gao, Kaizhi Wang, Xingzhao Liu |
IGARSS | 4 |
| 2014 | Optronic processing of RCMC for real-time SAR image formationabstractOptronic processing is a promising way to real-time highresolution SAR image formation. Rang migration is inevitable in SAR imaging, especially in the case of highresolution SAR system, range cell migration correction (RCMC) is considered in nature. A solution of RCMC by using optronic processing is presented in this paper. In this optronic solution, most computation is undertaken by optical devices, while the data control is undertaken by electronic devices. The architecture of the experimental setup is presented, and the experimental results are given. Yesheng Gao, Kaizhi Wang, Xingzhao Liu |
IGARSS | 3 |
| 2014 | An automatic SAR-GMTI algorithm based on DPCAabstractAn automatic DPCA technique is presented for SAR Ground Moving Target Indication (GMTI). We note that there exists a shift and a phase difference between the images from two channels. Therefore, SAR-GMTI can be implemented in the following steps: Image registration, phase compensation, image subtraction, and CFAR detection. In our technique, these steps are carried out automatically, and thus no precise information is needed about the length of the baseline and the velocity of the platform. We utilize a set of real data to demonstrate the accuracy and the robustness of our algorithm. Yingjie Hou, Junfeng Wang 0001, Xingzhao Liu, Kaizhi Wang, Yesheng Gao |
IGARSS | 4 |
| 2014 | A tiling of multi-SLM is used in full resolution optical SAR data processorabstractSynthetic Aperture Radar (SAR) is a powerful tool for alltime and all-weather imaging. As the technology developed, the resolution of SAR image is required much higher, and the processing time is required shorter. Traditional DSP processor is difficult to process the high resolution complex SAR data of 3 meter and 1 meter, or even high. The optical processor performs the most promising capability, since the Fourier lens provide inherent parallel computing. In addition, it can perform the Fourier transformation at the speed of light. This paper proposes a tiling project to perform the full resolution SAR data imaging. Yiran Jin, Yesheng Gao, Kaizhi Wang, Xingzhao Liu, Chaobo Lin, Huanglong Wang |
IGARSS | 4 |
| 2014 | A novel concept of plane grid resolution for high-resolution SAR imaging systemsabstractSynthetic aperture radar (SAR) is an active microwave sensor which is able to produce high-resolution images with day and night capability. Traditionally, the image quality assessment of the SAR system is described by the response function of an isolated point target. However, some man-made targets which are placed together can not be distinguished clearly. As the point target has the characteristic of the isotropic scattering, the retrieval capability for target structure details and contours by using the point target assessment method cannot be assessed accurately in a practical scene. In this paper, a new image quality assessment method (especially for plane targets) is proposed to solve this problem. The definitions of the plane grid and the plane grid resolution are given to support. After giving the scene construction of the Test Field used for measuring the plane grid resolution (PGR), a corresponding algorithm is also proposed. Experiment results show that the proposed assessment method describes the SAR image quality for man-made targets more accurate than the traditional assessment method in a practical scene. Xin Lin 0002, Kaizhi Wang, Xingzhao Liu |
IGARSS | 3 |
| 2014 | Complex target-induced azimuth envelope reconstruction from SAR RAW dataabstractAn innovative algorithm to reconstruct complex target-induced azimuth envelope in synthetic aperture radar (SAR) system is proposed. Unlike the assumption in conventional SAR imaging algorithms, target's backscattering coefficient can hardly remain constant when synthetic aperture time is long enough. In order to fully understand the target feature, we extract both amplitude and phase information of target-induced azimuth envelope from SAR raw data. In this paper, we formulate range migration curve (RMC) with a parametric model and implement curve fitting to estimate these parameters. The input pixels of curve fitting process is extracted from range compression result of raw data. Applying the idea of random sample consensus (RANSAC), this algorithm classifies pixels according to the target's RMC they belongs to, and extracts target's feature information at the same time. Experimental results are conducted to validate this algorithm. Hui Sheng, Bingqi Zhu, Yesheng Gao, Kaizhi Wang, Xingzhao Liu |
IGARSS | 4 |
| 2014 | Radar staring imaging scheme and target change detection based on range pulse compression and azimuth wavefront modulationabstractMicrowave staring imaging scheme based on range pulse compression and azimuth wavefront modulation is a new radar scheme. Under the condition of no relative motion between radar and scene, the scheme can obtain radar images with high resolution in both range direction and azimuth direction. The paper presents this imaging technique by theoretical analysis and simulation. Microwave staring imaging scheme is introduced firstly. Then, imaging properties and target change detection is analyzed. Kaizhi Wang, Xingzhao Liu |
IGARSS | 4 |
| 2014 | Improved clutter suppression for SAR imaging based on optimal waveform design methodabstractIn this paper, we proposed a clutter suppression algorithm for SAR imaging due to different target power spectrum density (PSD) and clutter PSD in azimuth direction. The optimal waveform of the SAR system is designed according to the prior-knowledge of the target and clutter, an amplitude limiter set in frequency domain is used to suppress the clutter response and 2-dimentional pulse compression is then used to the SAR imaging. Simulated results are presented based on our method which is shown great improvement in target image over clutter image. Then conclusions are drawn based on our analysis and simulations. Bingqi Zhu, Hui Sheng, Yesheng Gao, Kaizhi Wang, Xingzhao Liu |
IGARSS | 4 |
| 2013 | A new MTF-based image quality assessment for high-resolution SAR SensorsabstractSynthetic aperture radar (SAR) is an active microwave sensor which is able to produce high-resolution images of the earth surface, with all-weather day and night capability. Conventionally, SAR image quality assessment is typically done by evaluating the signal of the corner reflectors which are positioned in the scenery, and a specialist is needed to extract some characteristic parameters (e.g. the 3-dB impulse response width, the PSLR and the ISLR) to assess the SAR image quality. But it is still an unsolved problem that whether the SAR image quality assessment based on current parameters can predict the reliable probabilities of target recognition from the high-resolution SAR images. For EO sensors (Electro Optical sensors), the image assessment is assessed by the evaluation of MTF (Modulation Transfer Function), with non-specialists. In this paper, a new concept for SAR image quality assessment is proposed to solve this problem. The definitions of spatial frequency and MTF are given to support the new concept. After giving the scene construction of a TEST Field used for measuring MTF, an MTF measuring algorithm is proposed. Experiment results show that the proposed assessment method can describe SAR image quality more accurately and effectively than traditional PSF assessment method. Xin Lin 0002, Kaizhi Wang, Xingzhao Liu |
IGARSS | 2 |
| 2013 | SAR simulation for large scenes by ray tracing technique based on GPUabstractThis paper uses ray tracing technique to simulate a complete imaging process of Synthetic Aperture Radar (SAR). The simulator can collect the raw data and generate accurate shadows of the object. The radiation pattern is defined by a spotlight to have more realistic imaging effect. Considering the high performance computing of modern graphics processing units (GPU), we transfer the ray tracing algorithm from CPU to GPU. Thus, the simulator can work on a large 3D scene with relatively high efficiency. Kaizhi Wang, Xingzhao Liu |
IGARSS | 2 |
| 2013 | Waveform design for target detection based on priori characteristicsabstractIn this paper we analyze the problem of waveform design for target detection in the presence of clutter and noise environment. We use the target priori characteristics to design the transmitted waveform. The waveform is designed by mutual information criterion. Firstly, we present the signal model and information theoretic approach to design waveform. Secondly, we discuss the waveform design is the one that maximizing mutual information between the target priori characteristics and the radar received signal. The results of simulation evaluate the efficiency of the proposed method to compare with the chirp signal. Jiliang Liu, Kaizhi Wang, Xingzhao Liu |
IGARSS | 2 |
| 2013 | Feature extraction of a generic SAR target using an improved data modelabstractHere feature extraction of a generic SAR target is studied. We apply a new data model to target feature extraction and improve SAR image quality. The data model we construct contains (1) envelope, (2) location of the target. The envelope shape can be controlled by four parameters, and location information is indicated by frequency pair in both range and cross-range. These parameters would be estimated by nonlinear least squares (NLS) and 1-D Cramer-Rao Bounds (CRB) for these parameters have also been analyzed. Numerical examples show this method can achieve CRB at high SNR and its computational complexity is acceptable. Qianrong Lu, Kaizhi Wang, Xingzhao Liu |
IGARSS | 2 |
| 2013 | A fast raw data simulator for the stripmap SAR based on CUDA via GPUabstractThis paper presents a novel and compressive SAR raw data simulator based on CUDA via GPU. The stripmap synthetic aperture radar(SAR) is introduced to model antenna illumination behavior. Compared with conventional raw data simulators, we no longer limit our research interests on a single point target's raw data simulation, but expend it to that of complex scene. In order to compensate the greatly increasing operational time with booming computational complexity, we optimize the process in two aspects. In the first, modern GPUs have the potential for highly parallel calculation, and it makes them much more efficient than CPUs in processing large blocks of data. Therefore, we implement the simulator on CUDA. The second method is to take advantage of symmetry in single raw data matrix based on stripmap mode SAR, and reduce 75 percent computational complexity. By these two effective methods, the simulator experiences an attractive operating time and enjoys high efficiency. Some simulation results prove the simulated raw data is acceptable in accuracy. Hui Sheng, Kaizhi Wang, Xingzhao Liu |
IGARSS | 2 |
| 2013 | A novel high resolution optical SAR processor for satellite applicationsabstractOnboard SAR data imaging is increasingly important for many satellite applications. And optical SAR processor is one promising solution due to its extremely quick calculation speed, simple structure and strong radiation hardness. Recent relative researches done by researchers of National Optics Institute in Canada prove the feasibility of optical processor, but its resolution of 30 meter is relatively low. This paper proposes a novel high resolution optical SAR processor which is based on the Range Doppler Algorithm. The processor includes two main elements: the optical one-dimensional Fourier transformation element and the spatial light modulator (SLM). The usage of several SLMs gives wider parameter adjustment boundary and more flexibility to the processor. Penghao Zhao, Kaizhi Wang, Xingzhao Liu |
IGARSS | 2 |
| 2013 | Optimum waveform design and simulation with energy constraint for elastic targetsabstractIn this paper, we apply the optimum waveform design method to meet the application of elastic targets detection and aim at enhance the target detection rate. The target is assumed to be Gaussian elastic targets and the clutter is assumed to be a stationary Gaussian random process. The detection problem then is described using Neyman-Pearson Detector. The waveform design solutions for elastic targets are given theoretically, and numerical simulated results are presented based on different transmit energy and comparison results between optimum signal and LFM signal are shown. Finally, the conclusions are drawn based on our analysis and simulations. Bingqi Zhu, Kaizhi Wang, Xingzhao Liu |
IGARSS | 2 |
| 2013 | Superpixel-Based Classification With an Adaptive Number of Classes for Polarimetric SAR ImagesabstractPolarimetric synthetic aperture radar (PolSAR) image classification, an important technique in the remote sensing area, has been deeply studied for a couple of decades. In order to develop a robust automatic or semiautomatic classification system for PolSAR images, two important problems should be addressed: 1) incorporation of spatial relations between pixels; 2) estimation of the number of classes in the image. Therefore, in this paper, we present a novel superpixel-based classification framework with an adaptive number of classes for PolSAR images. The approach is mainly composed of three operations. First, the PolSAR image is partitioned into superpixels, which are local, coherent regions and preserve most of the characteristics necessary for image information extraction. Then, the number of classes and each class center within the data are estimated using the pairwise dissimilarity information between superpixels, followed by the final classification operation. The proposed framework takes the spatial relations between pixels into consideration and makes good use of the inherent statistical characteristics and contour information of PolSAR data. The framework is capable of improving the classification accuracy, making the results more understandable and easier for further analyses, and providing robust performance under various numbers of classes. The performance of the proposed classification framework on one synthetic and three real data sets is presented and analyzed; and the experimental results show that the framework provides a promising solution for unsupervised classification of PolSAR images. Bin Liu 0019, Kaizhi Wang, Xingzhao Liu, Wenxian Yu |
IEEE Trans. Geosci. Remote. Sens. | 4 |
| 2012 | Estimating target-induced azimuth envelope for SAR image formation and feature extractionabstractConventional SAR imaging algorithms form SAR image based on imaging geometries, the resulting image indicates the spatial location of illuminated targets with respect to radar platform. Scattering characteristics of targets are overlooked by these algorithms. We construct a model of received SAR signal in terms of (1) envelope, (2) phase, (3) duration, (4) arrival time, (5) frequency center and (6) chirp rate, and the envelope shape can be controlled by two parameters. Arrival time, frequency center and chirp rate indicate the spatial location and motion dynamics of the targets, while information of scattering characteristics can be analyzed from the other parameters. The parameters of the model are then estimated via atomic decomposition. In this paper, the impact of target-induced envelope on data focusing is analyzed, furthermore, target feature can be extracted from a signal-level point of view. Yesheng Gao, Kaizhi Wang, Xingzhao Liu |
IGARSS | 2 |
| 2012 | Optimum two-dimensional transmit-receiver designabstractIn this paper, a theory of two-dimensional transmit-receiver design is presented. Only deterministic targets and random clutters and noises are considered in this model, and we reach two-dimensional optimization based on maximization signal-to-interference-and-noise ratio(SINR). New result focuses on extending the previous one-dimensional waveform design to two-dimensional one, in order to satisfy some practical application like synthetic aperture radar(SAR). Both the theoretic derivation and simulation result proves that 2D radar imaging can gain high SINR with proper transmit-receiver design. Hui Sheng, Kaizhi Wang, Xingzhao Liu |
IGARSS | 2 |
| 2012 | A general 3D remote sensing data browser for fast application developmentabstractIt takes complex coding work to develop a remote sensing applications which needs to display various remote sensing data. To solve this problem, we propose a remote sensing information display platform of web-browser pattern. A 3D remote sensing browser is designed to parse kinds of information and display them in a 3D scene. The remote sensing information is organized as a page file according to a format we define in this paper. Finally, through a use case, we illustrate the convenience of developing remote sensing application on our platform. Jiaju Wei, Kaizhi Wang, Xingzhao Liu, Jiaqi Tang 0002 |
IGARSS | 2 |
| 2011 | Combinational matching method of amplitude-scale and time-shift for radar HRRP recognitionabstractRadar high-resolution range profiles (HRRPs) are very sensitive to amplitude-scale and time-shift, and their good recognition performance depends on precisely the matching methods of both sensitivities, thereby, the method to handle these sensitivities is a challenge in the field of Radar automatic targets recognition(RATR). However, most approaches available did not pay much attention to this problem. This paper proposes two algorithms to jointly matching the amplitude and time-shift for training and test phase, respectively, taking Automatic Gaussian Classifier (AGC) as an example. Experiments based on measured data show our algorithms have a remarkable larger average recognition rate than that of the regular method for AGC. Wenxian Yu, Xingzhao Liu, Kaizhi Wang |
IGARSS | 4 |
| 2011 | Graph-based ship extraction scheme for optical satellite imageabstractAutomatic detection and recognition of ship in satellite images is very important and has a wide array of applications. This paper concentrates on optical satellite sensor, which provides an important approach for ship monitoring. Graph-based fore/background segmentation scheme is used to extract ship candidant from optical satellite image chip after the detection step, from course to fine. Shadows on the ship are extracted in a CFAR scheme. Because all the parameters in the graph-based algorithms and CFAR are adaptively determined by the algorithms, no parameter tuning problem exists in our method. Experiments based on measured optical satellite images shows our method achieved good balance between computation speed and ship extraction accuracy. Wenxian Yu, Xingzhao Liu, Kaizhi Wang, Lin Gong, Wentao Lv |
IGARSS | 4 |
| 2011 | Towards a framework of algorithm management for remote sensing image analysisabstractThis work is devoted to the proposal of the algorithm management framework for remote sensing image analysis. A hierarchical framework of algorithm management is first introduced. Then we establish an algorithm description model and corresponding reasoning mechanism based on the quotient space problem solving theory and graph theory. With this model the developers can avoid wasteful duplicate algorithm development and complicated parameter adjustment during the algorithm development process for remote sensing image. The effect and efficiency of the framework has been proved through our preliminary experiment results. Yongke Ding, Kaizhi Wang, Wenxian Yu, Xingzhao Liu |
IGARSS | 2 |
| 2011 | Atomic decomposition-based SAR imaging techniqueabstractThe conventional SAR imaging algorithms are developed based on specified imaging geometry models, and these algorithms become more complex considering finer resolution or more complicated geometry. The quality of the product is measured by resolution, PSLR and ISLR, etc. without regard to its application. This paper proposes a signal-model-based imaging scheme. Independent of imaging geometry, the new scheme focuses the backscattered echoes by estimating the signal parameters. Furthermore, two realizations of the scheme are presented. This scheme will also have great potential for target feature extraction and image interpretation. Yesheng Gao, Kaizhi Wang, Xingzhao Liu, Wenxian Yu |
IGARSS | 2 |
| 2011 | A number-of-classes-adaptive unsupervised classification framework for SAR imagesabstractIn this paper, we present a number-of-classes-adaptive unsupervised classification framework for synthetic aperture radar (SAR) images. The framework aims at the provision of robust classification for SAR images even if the number of classes existing in the scene is unknown. It mainly consists of estimation of the number of classes, extraction of each class center, classification of image patches, and integration of spatial relations between patches. The experiment on a TerraSAR-X SAR image shows that the proposed framework presents a promising performance for SAR image classification. Bin Liu 0019, Kaizhi Wang, Xingzhao Liu, Wenxian Yu |
IGARSS | 3 |
| 2011 | Scene interpretation for SAR images using supervised topic modelsabstractIn this paper, we present a scene interpretation framework for Synthetic Aperture Radar (SAR) images, using keywords of the image contents provided by users. The framework consists of incorporation of prior knowledge with SAR iMage Annotation Tool (SARMAT), representation of SAR images, and prediction of scene labels based on the supervised Latent Dirichlet Allocation (sLDA) model. The experiment on a TerraSAR-X SAR image shows that the proposed framework provides a promising performance for SAR image scene interpretation. Bin Liu 0019, Kaizhi Wang, Xingzhao Liu, Wenxian Yu |
IGARSS | 3 |
| 2011 | Concurrent SAR images denoising and segmentation based on a novel model of wavelet coefficientsabstractA novel segmentation algorithm for Synthetic Aperture Radar (SAR) images is presented in this paper to improve performance. First, we design a model of wavelet coefficients based on the relativities of the coefficients at different scales to sup press noise. Furthermore, we employ a weight-variant graph cuts-based approach to extract objects from complex back ground. Finally, we compare our proposed algorithms with several segmentation measures on synthetic and real SAR images and the experimental results demonstrate that the pro posed strategies have better performances in speckle suppression and image segmentation compared with other methods. Wentao Lv, Wenxian Yu, Qiuze Yu, Kaizhi Wang |
IGARSS | 5 |
| 2011 | Supper resolution radar imaging: A virtual array concept approachabstractA virtual array concept is proposed to get supper-resolution in synthetic aperture radar imagery. Two kinds of virtual arrays called virtual frequency array and virtual azimuth array are constructed, combining with phased array signal processing methods, to bring out better imaging performance than traditional range-Doppler and reciprocal spectrum algorithms used in previous literatures. Gaohuan Lv, Kaizhi Wang, Xingzhao Liu, Wenxian Yu |
IGARSS | 2 |
| 2011 | A Foreground/Background Separation Framework for Interpreting Polarimetric SAR ImagesabstractIn this letter, we present a novel foreground/background separation (FBS) framework for interpreting polarimetric synthetic aperture radar (PolSAR) images. The FBS framework takes the spatial relations between pixels into consideration and incorporates the advantages of pairwise dissimilarity-based grouping schemes. The FBS method can separate specific targets and objects from the background, which is essential in an interpretation system. Multiple FBS operations can be integrated to interpret PolSAR images, flexibly fusing various inherent features of PolSAR data. Several PolSAR data sets are used to verify the proposed approach. Bin Liu 0019, Kaizhi Wang, Xingzhao Liu, Wenxian Yu |
IEEE Geosci. Remote. Sens. Lett. | 3 |
| 2010 | Reciprocal spectrum algorithm for radar imaging with frequency sampling waveformabstractA radar imaging algorithm named reciprocal spectrum algorithm (RSA) is proposed in this paper to get higher resolution in azimuth direction with frequency sampling waveform. Theoretical analysis and simulation results show that the algorithm can give better performance than the tradition range Doppler algorithm (RDA) at the cost of peak value reduction at the object points in radar image. Gaohuan Lv, Kaizhi Wang, Xingzhao Liu, Wenxian Yu, Guozhong Chen, Junli Chen |
IGARSS | 2 |
| 2010 | Progressive SAR imaging techniqueabstractA progressive SAR imaging technique is proposed as a novel SAR raw data processing scheme in this paper. Different from the classic SAR imaging algorithms which focus the SAR raw data as a whole regardless of the backscattering signal, the novel scheme discriminate the backscattering signal and choose the proper ones to be focused progressively according to some application context while the others will be discarded. The new scheme makes the SAR imaging algorithm not only focus the energy back to the scattering points but also form an image more suitable for some special applications. In this paper, a realization of the scheme present via Atomic Decomposition (AD)[1]–[3]. AD helps estimate the parameters of backscattered signal of a scattering point and detach it from the raw data. With the parameters, the backscattering-signal can be reconstructed and focused. Targets or scatter-points in the scene will be imaged progressively in a sequence of their energy due to the greedy natural of matching pursuit employed during AD. Therefore, the contents in the final SAR image can be controlled by an energy threshold. Besides the interested targets can be extracted easily from the background clutter and this may be helpful for the SAR image understanding Kaizhi Wang, Xingzhao Liu, Wenxian Yu, Junli Chen, Guozhong Chen |
IGARSS | 1 |
| 2009 | Antenna Pointing Measurement for Spaceborne SAR based on Sign-MLCC AlgorithmabstractDual-antenna single-pass synthetic aperture radar interferometry needs alignment of both antenna beams to achieve the best interferometric performance. Meanwhile, geosynchronous synthetic aperture radar, potentially used for global earthquake prediction and many other attractive applications, also requires antenna pointing control system to steer the radar antenna to illuminate desired territory, otherwise, even slight deviation from ideally boresight direction can cause a great variation of footprint position, because of the large slant range from the radar to mapped area. In principle, it is possible to measure antenna pointing information directly; however, measurement uncertainties will limit the accuracy. Thus it is feasible to resort to received radar data to measure the antenna pointing. This paper concentrates on the antenna pointing measurement using onboard Doppler centroid estimator, and furthermore, to drive pitch and yaw angles to steer the antenna pointing. In order to realize real-time onboard processing, a novel Doppler centroid estimation algorithm, called sign-MLCC, is presented here, utilizing the phase information of the received signal and the arcsine law by analyzing the sign alone, then evaluation of the algorithm is discussed. Finally, simulations are shown to prove the validity and reliability of the proposed method. Yesheng Gao, Kaizhi Wang, Xingzhao Liu, Wenxian Yu |
IGARSS (4) | 2 |
| 2009 | A GPU based Time-domain Raw Signal Simulator for Interferometric SARabstractA novel GPU based time-domain raw signal simulator for InSAR is proposed in this paper to exploit the parallel computation of GPU using CUDA language. This simulator combines the advantages of both time-domain and frequency-domain InSAR simulator, i.e., it considers the baseline oscillation and real orbit, and it is also very efficient. Experimental results show the effectiveness of the simulator in varieties of conditions. Kaizhi Wang, Xingzhao Liu, Wenxian Yu |
IGARSS (5) | 2 |
| 2009 | A Model-Spectrum-Based Flattening Algorithm for Airborne Single-Pass SAR InterferometryabstractAn effective method is proposed to remove the flat-Earth phase (i.e., flattening) in airborne single-pass interferometric synthetic aperture radar (InSAR) imaging. Two conventional flattening methods, namely, the orbit-equation algorithm and the fringe-frequency algorithm, are used for comparison. The orbit-equation algorithm is theoretically accurate, but the orbit ephemeris that it requires is maybe inaccurate or even unknown. The fringe-frequency algorithm is effective in spaceborne InSAR flattening, but in airborne cases, a phase trend will remain in the residual interferogram with this method. To overcome these limitations, this letter presents a novel flattening algorithm by combining the two conventional methods for airborne single-pass InSAR flattening. By exploiting a reasonable model of the flat-Earth phase and the spectrum information of the practical interferogram, the proposed algorithm is able to flatten the interferogram accurately without knowledge of the airplane trajectory (except for the airplane height). Finally, some experimental results demonstrate the effectiveness of the proposed flattening algorithm. Kaizhi Wang, Xingzhao Liu |
IEEE Geosci. Remote. Sens. Lett. | 2 |
| 2008 | A new DEM reconstruction method based on an accurate flattening algorithm in interferometric SARabstractThis paper presents a new approach to reconstruct digital elevation model (DEM) without compensating the flat earth phase back to the unwrapped interferometry in the Interferometric Synthetic Aperture Radar (InSAR). The new approach is based on an accurate flattening algorithm called model-spectrum algorithm which combines the advantages of classic algorithms. The experimental results show that the new algorithm has a better performance than the conventional ones. Based on this novel algorithm, DEM reconstruction can be implemented by a quasi-linear scaling after phase unwrapping. There is no need to add the flat earth phase back to the flattened interferogram, which avoids complex geometrical conversion as what is done in the conventional algorithms. Kaizhi Wang, Xingzhao Liu |
ICASSP | 2 |
| 2007 | Quartic-Phase Algorithm for Highly Squinted SAR Data ProcessingabstractIn this letter, an algorithm based on a quartic-phase model is discussed for processing highly squinted synthetic aperture radar (SAR) data from a large range swath. In the algorithm, a precise quartic-phase model is adopted to describe a range-dependent property of the SAR signal; a constant factor and a secondary scaling process are introduced to make the algorithm easy to be utilized compared with traditional nonlinear chirp scaling algorithms. The novel algorithm can process SAR data under a squint angle above 50deg and achieve a focus depth over 60 km Kaizhi Wang, Xingzhao Liu |
IEEE Geosci. Remote. Sens. Lett. | 1 |
| 2006 | A Quartic Algorithm For Squint Sar ImagingabstractIn this paper some improvements of Non-linear Chirp Scaling (NCS) approach are proposed and a modified algorithm based on the NCS is described. The improvements include three main aspects. A quartic polynomial model is adopted to represent SAR signal in Range-Doppler domain and 2-D frequency domain to improve precision. A constant scaling factor is employed to replace the reference frequency in the NCS, which makes NCS more flexible. A second chirp scaling operation is added to the end of the NCS so as to remove scaling effect on range direction of SAR image. Those improvements make NCS applicable to process highly squinted SAR data from a large range swath at a fine resolution. Kaizhi Wang, Xingzhao Liu |
ICASSP (4) | 1 |
| 2005 | Squint mode SAR imaging with range-walk removalabstractA new point of view is proposed to correct range migration and focus highly squinted SAR data. The procedure of range-migration correction is done not only in the range-Doppler (R-D) domain and the 2D frequency domain as usual, but also in the time domain. A modified chirp scaling (CS) algorithm is described, based on the new point. A quantitative analysis and simulations show that the new algorithm can process SAR data with a squint angle as large as 70/spl deg/ and a range swath of 50 km or wider. Kaizhi Wang, Xingzhao Liu |
ICASSP (4) | 1 |
| 2005 | Auto-combination of sub-band for spotlight SAR imaging
Kaizhi Wang, Xingzhao Liu |
IGARSS | 1 |
| 2004 | Squint-spotlight SAR imaging by subband combination and rage-walk removalabstractA new algorithm for spotlight SAR imaging under squint mode is proposed in this paper. The structure of the algorithm is rather simple and can be divided into two parts: the sub-aperture imaging with range-walk removal and sub-band combination, which are relatively independent Kaizhi Wang, Xingzhao Liu |
IGARSS | 1 |
| 2004 | Data pruning approach to unit selection for inventory generation of concatenative embeddable Chinese TTS systems
Zhenli Yu, Kaizhi Wang, Yiqing Zu, Dongjian Yue, Guilin Chen |
INTERSPEECH | 2 |