Back Projection Imaging Algorithm Research Articles

An Accurate and Efficient BP Algorithm Based on Precise Slant Range Model and Rapid Range History Construction Method for GEO SAR

The Geosynchronous Satellite Synthetic Aperture Radar (GEO SAR) operates at a high orbital altitude, resulting in an extended imaging time and substantial variations in slant range. Additionally, the GEO SAR satellite orbit experiences a bending effect, and the target’s movement, caused by the Earth’s rotation, is influenced by the Earth’s curvature. The back-projection (BP) algorithm has been proven to be a highly effective technique for precise imaging with GEO SAR by processing these specific echo signals. However, this approach necessitates considerable computational resources. Existing BP algorithms, such as the fast BP algorithm, do not consider the “Stop-and-Go” error present in GEO SAR. Consequently, we developed a Precise Slant Range Model that considers the motion of both the satellite and targets. The model incorporates velocity and acceleration factors to accurately represent the signal transmission from transmission to reception. Additionally, we propose a Rapid Range History Construction Method to lessen the computational burden of generating the three-dimensional range history array. By utilizing the Precise Slant Range Model and the Rapid Range History Construction Method, and employing parallel processing through aperture segmentation, we propose an Accurate and Efficient BP imaging algorithm suitable for GEO SAR applications. To validate its effectiveness, simulations were conducted using the parameters of a GEO SAR system. The results indicated that the proposed algorithm enhances the imaging quality of GEO SAR, reduces the processing time, and achieves high-precision rapid imaging, thereby improving operational efficiency.

A Sub-Aperture Overlapping Imaging Method for Circular Synthetic Aperture Radar Carried by a Small Rotor Unmanned Aerial Vehicle.

Circular synthetic aperture radar (CSAR) can obtain higher image resolution and more target information using 360° observation of the target. Due to the anisotropy of target scattering characteristics in the actual scene, the sub-aperture imaging method is usually used for CSAR imaging. However, the uniformly divided overlapping sub-aperture CSAR imaging algorithm only considers phase compensation, ignoring the effect of target scattering characteristics on echo amplitude. In CSAR imaging scenarios carried by small rotor unmanned aerial vehicles (SRUAVs), the size of the observed scene cannot be ignored compared to the distance between the target and the antenna and the effect of the anisotropy of the target scattered energy on the echo amplitude should be considered. In this paper, a sub-aperture CSAR imaging method based on adaptive overlapping sub-aperture is proposed. First, the boundary points of the sub-aperture are determined by analyzing the correlation coefficient and the variation coefficient of the energy function. Next, the overlapping sub-aperture division schemes are automatically generated by screening and combining the boundary points. The sub-aperture images are then generated by a Back Projection (BP) algorithm. Finally, sub-aperture image registration and incoherent superposition are used to generate the final CSAR image. Verified by the CSAR field echo data, the proposed method can realize imaging of the original echo data without the Inertial Navigation System (INS) and Global Positioning System (GPS) observation data. Compared with the CSAR full-aperture BP imaging algorithm, the entropy of the image generated by the proposed method increased by 66.77%. Compared with the sub-aperture CSAR imaging algorithm, the entropy of the image generated by the proposed method was improved by 11.12%, retaining more details of the target, improving the target contour features, and enhancing the focusing effect.

Precursors for synthetic aperture radar

In this paper we study waveform design for synthetic-aperture radar (SAR) imaging through dispersive media. Under the assumptions of scalar wave propagation through a causal dielectric medium and single-scattering from an isotropic point scatterer, we use asymptotic analysis to derive the asymptotic approximation to the scattered electric field. From this asymptotic approximation, we define a sensing precursor that we propose for the transmit waveform for SAR imaging through dispersive material. We compare our sensing precursor with previously defined optimal waveforms (Varslot et al 2011 SIAM J. Appl. Math. 71 1780–800) in terms of both propagation and scattering capabilities, as well as imaging performance. With the filtered back-projection imaging algorithm that we use, we find that for high levels of signal-to-noise ratio (SNR), the optimal waveforms contain higher frequencies and thus produce better images. For low levels of SNR, the transmitted optimal waveforms and the sensing precursors are similar, thus giving comparable images.

Video SAR Moving Target Shadow Detection Based on Intensity Information and Neighborhood Similarity

Video Synthetic Aperture Radar (SAR) has shown great potential in moving target detection and tracking. At present, most of the existing detection methods focus on the intensity information of the moving target shadow. According to the mechanism of shadow formation, some shadows of moving targets present low contrast, and their boundaries are blurred. Additionally, some objects with low reflectivity show similar features with them. These cause the performance of these methods to degrade. To solve this problem, this paper proposes a new moving target shadow detection method, which consists of background modeling and shadow detection based on intensity information and neighborhood similarity (BIIANS). Firstly, in order to improve the efficiency of image sequence generation, a fast method based on the Back-projection imaging algorithm (f-BP) is proposed. Secondly, due to the low-rank characteristics of stationary objects and the sparsity characteristics of moving target shadows presented in the image sequence, this paper introduces the low-rank sparse decomposition (LRSD) method to perform background modeling for obtaining better background (static objects) and foreground (moving targets) images. Because the shadows of moving targets appear in the same position in the original and the corresponding foreground images, the similarity between them is high and independent of their intensity. Therefore, using the BIIANS method can obtain better shadow detection results. Real W-band data are used to verify the proposed method. The experimental results reveal that the proposed method performs better than the classical methods in suppressing false alarms, missing alarms, and improving integrity.

Towards High-Resolution Imaging With Photonics-Based Time Division Multiplexing MIMO Radar

A photonics-based time division multiplexing (TDM) multiple-input and multiple-output (MIMO) radar is proposed to realize high-resolution imaging. In this MIMO radar, multiple transmitters generate time-domain orthogonal linearly frequency modulated (LFM) signals based on microwave photonic frequency octupling and optical TDM technique, and multiple receivers implement dechirping of the multi-channel radar echoes based on microwave photonic frequency mixing. The microwave photonic techniques make the system capable to generate and process broadband radar signals, and the TDM yields a high spectral efficiency, which allows a large bandwidth in each transmitter and receiver. Meanwhile, the TDM-MIMO ensures complete orthogonality between different channels and enables good flexibility in arranging more transmit and receive channels. Therefore, the proposed photonics-based TDM-MIMO radar can achieve both high range resolution and high angular resolution. In the experiment, a photonics-based 4 × 8 TDM-MIMO radar is established which has an operation bandwidth of 8 GHz in each transmit channel. The range resolution and angular resolution are estimated to be 1.9 cm and 1.1°, respectively. A broadband back projection (BP) imaging algorithm with both frequency and time-delay dependent phase compensation is proposed, based on which high resolution imaging of single and complex targets is achieved.

Parallel Optimisation and Implementation of a Real-Time Back Projection (BP) Algorithm for SAR Based on FPGA.

This study conducts an in-depth evaluation of imaging algorithms and software and hardware architectures to meet the capability requirements of real-time image acquisition systems, such as spaceborne and airborne synthetic aperture radar (SAR) systems. By analysing the principles and models of SAR imaging, this research creatively puts forward the fully parallel processing architecture for the back projection (BP) algorithm based on Field-Programmable Gate Array (FPGA). The processing time consumption has significant advantages compared with existing methods. This article describes the BP imaging algorithm, which stands out with its high processing accuracy and two-dimensional decoupling of distance and azimuth, and analyses the algorithmic flow, operation, and storage requirements. The algorithm is divided into five core operations: range pulse compression, upsampling, oblique distance calculation, data reading, and phase accumulation. The architecture and optimisation of the algorithm are presented, and the optimisation methods are described in detail from the perspective of algorithm flow, fixed-point operation, parallel processing, and distributed storage. Next, the maximum resource utilisation rate of the hardware platform in this study is found to be more than 80%, the system power consumption is 21.073 W, and the processing time efficiency is better than designs with other FPGA, DSP, GPU, and CPU. Finally, the correctness of the processing results is verified using actual data. The experimental results showed that 1.1 s were required to generate an image with a size of 900 × 900 pixels at a 200 MHz clock rate. This technology can solve the multi-mode, multi-resolution, and multi-geometry signal processing problems in an integrated manner, thus laying a foundation for the development of a new, high-performance, SAR system for real-time imaging processing.

Artifacts Suppression Using Correlation-Weighted Back Projection Imaging Algorithm for Chaotic GPR

A correlation weighted back projection (CWBP) imaging algorithm is proposed to suppress artifacts introduced by the classic back projection (BP) algorithm in the application of chaotic ground-penetrating radar (GPR). In the proposed CWBP algorithm, the backscattering response to each point in the imaging region is first reconstructed through the weighting, which is used to highlight the backscattering response of targets. Then the quadratic cross correlation is calculated to reduce the nontargets’ backscattering. The experimental results show that the artifacts are significantly suppressed. In addition, the ghosts generated by overlapped of multitargets artifacts in the classic BP are removed. Our results also show that the proposed CWBP can be applied for the stepped frequency continuous wave radar.

A Method for Signal Leakage Cancellation in Multistatic Subsurface SAR Imaging System

Multi-static subsurface synthetic aperture radar (SAR) is a promising tool capable of providing 3-D high resolution images of targets buried underground. The high detection capability of the system stems from the fact that the multi-static configuration allows for viewing the targets from many directions. However, a primal limiting factor for such configuration is the dominance of the direct and ground reflection signals over the scattered target signal hindering the system sensitivity. This letter presents a simple technique to overcome such drawback. By an appropriate utilization of SAR data, each adjacent sampling points are co-processed together as a two-element array in such a way as to have a null along the direction of the direct and ground reflection signals suppressing such signals and making the target signals more discernible. The technique is described in details and the potential problems arising from array processing are discussed. Additionally, a modified version of back projection imaging algorithm suitable for the array is provided. The performance of the proposed technique is assessed by simulation data of buried metallic spheres as well as measurement data for a buried metallic pipeline. Both simulation and measurements show a significant improvement in target detection and image quality.

Millimeter-level resolution through-the-wall radar imaging enabled by an optically injected semiconductor laser.

Millimeter-level resolution through-the-wall radar (TWR) imaging is demonstrated using a broadband nonlinear frequency-modulated (NLFM) signal that is generated by an optically injected semiconductor laser. The proposed system uses period-one dynamics of a semiconductor laser, together with an optical frequency downconversion technique to generate NLFM signals, which addresses the problem of traditional period-one oscillation not being able to generate broadband signals in the low-frequency region. In the experiment, an NLFM signal having a broad bandwidth of 18.5 GHz (1.5-20 GHz) is generated with a corresponding radar range resolution of 8.1 mm. Using this signal, TWR imaging is demonstrated, in which the use of the NLFM signal achieves good side-lobe suppression during pulse compression, and a modified back projection imaging algorithm with sub-aperture weighting is proposed to improve the imaging quality.

A 3-D SAR Imaging Method Based on Back Projection Algorithm

3D back projection (BP) algorithm is an imaging algorithm based on time domain echo data, which effectively solves the overlapping mask problem existing in 2D SAR. It can complete the imaging processing of echo signal under any geometry configuration, and has the advantages of high target focusing accuracy and high phase preservation. However, the high complexity and low efficiency of 3D BP imaging algorithm limit its application and development. In this paper, a 3d imaging method based on improved back projection algorithm is proposed. Aiming at the problem that existing imaging algorithms need 2D imaging first and then 3D imaging, an improved 3D BP algorithm is proposed to directly 3D imaging, which avoids 2d imaging processing. The proposed method simplifies the steps of the traditional 3D BP algorithm and improves the efficiency of the algorithm. The validity and effectiveness of the proposed method are verified by the 3d imaging results of simulated lattice targets.

Circular synthetic aperture acoustic imaging of spherical targets in cylindrical rod clutter

A model apparatus has been built to demonstrate acoustic imaging of several spherical targets in cylindrical clutter. Reflective ultrasonic tomography imaging was chosen because the medical community, using photo-acoustic tomography imaging, utilizes a similar back-projection imaging algorithm. The experiment involves suspending an ultrasonic transducer unit (resonant frequency 1.0 MHz) in an aquarium filled with water. The transducer (sender-receiver) generates a 5-cycle tone burst. The circular plane array transducer diameter is D = 1.27 cm. Its wavelength is 1.48 mm (using c = 1482 m/s). The target, located 15 cm from the source, consists of two 0.64 cm diameter metal spheres separated by 5 cm. A mechanical structure of thin perforated disks (10 cm diam) comprise a step-motor controlled rotational platform that supports the targets and slender stainless steel cylindrical vertical rods (2 mm diameter, 10 cm long) that serve as the clutter. Received echoes versus time (data sets) were measured at 10° rotation increments of the structure (from 0° to 360°) for back-projecting the 2-D image reflectance of the targets among the clutter (using Mathematica®). The original apparatus and supporting electronics were built by Madeline Bell for her USNA Capstone research (Fall 2020) involving scattering from cylindrical targets.

Three-dimensional BP Imaging Algorithm using MIMO System

Multiple-input multiple-output (MIMO) radar is a radar system that simultaneously uses multiple transmitting antennas and receiving antennas to transmit and receive diversity waveforms for centralized processing. The MIMO system avoids the mechanical transmission structure in traditional RCS measurement and has high data acquisition efficiency, making it possible for three-dimensional (3D) imaging with large data volume requirements. Compared with the traditional two-dimensional (2D) radar image, the target 3D radar image can provide the spatial three-dimensional position of the scattering center of the complex target and its scattering intensity information, making the RCS measurement data more complete. The 3D imaging technology based on the MIMO system uses a portable MIMO array to quickly acquire data, and then uses the back-projection (BP) imaging algorithm to perform 3D imaging. This method obtains data quickly with simple hardware conditions, which has the characteristics of low cost and high efficiency. This paper derives a 3D BP imaging algorithm using MIMO system. And the applicability and correctness are verified by simulation experiments on PSF and multiple point targets.

A 3-D Novel Fast Back-Projection Imaging Algorithm for Stratified Media Based on Near-Field Monostatic and Bistatic SAR

A fast back-projection (FBP) imaging algorithm is proposed to generate 3-D uniformly balanced images of an object embedded in a layered structure based on a combined near-field monostatic and bistatic synthetic aperture radar (SAR) system. The spectral layered Green's function is used in the FBP algorithm. Like conventional real-time imaging algorithms, the complexity of the imaging function is reduced via the stationary phase method, and the fast Fourier transform is implemented to accelerate the computation. Unlike conventional real-time imaging algorithms, the singularity problem associated with Green's function and antenna pattern is solved in this proposed algorithm by using a point spread function (PSF). For a real-time imaging system, besides fast image generation, an efficient data acquisition is needed. A combined monostatic and bistatic SAR configuration is used here to decrease the data collection time. The performance of this proposed FBP method is demonstrated by measurements of a stratified environment.

Photonic-assisted high-resolution incoherent back projection synthetic aperture radar imaging

We demonstrate the photonic-assisted high-resolution synthetic aperture radar imaging applying broadband photonic signal generation and a modified incoherent back projection (BP) imaging algorithm. The radar transmits linear frequency modulated (LFM) signals generated by period-one oscillation in an optically injected semiconductor laser. Since the signal bandwidth is greatly enlarged compared with traditional electric radars, a significantly improved imaging resolution can be achieved. Besides, we use a modified incoherent BP imaging algorithm with self-amplitude weighting and multiplicative tomography weighting, to further increase the imaging resolution and to suppress the undesired high-energy artifacts and background interferences. An experiment is carried out. Based on the established radar with a signal bandwidth as large as 12 GHz, high-resolution and clear images of different scenes are successfully constructed, through which the advantages of the proposed scheme over traditional BP imaging system can be soundly verified. The demonstrated scheme provides a good solution to enhance the performance of the incoherent BP imaging algorithm and simultaneously overcome the radar bandwidth limitation. It would find applications where high-resolution radar imaging is needed.

Demonstration of 3-D Security Imaging at 24 GHz With a 1-D Sparse MIMO Array

A 3-D security imaging experiment at 24 GHz is demonstrated with a 1-D sparse multi-input multi-output (MIMO) array. The MIMO array is an 8 transmission/16 reception arc array to achieve real-aperture imaging along the vertical dimension. It is time-switching multiplexed with a low-cost frequency modulated continuous wave transceiver working at 22-26 GHz. A calibration procedure is proposed to calibrate the channel imbalance across the MIMO array. The experiment is conducted on humans moving on a cart, where we take advantage of the linear motion of humans to form inverse synthetic aperture along the horizontal dimension. To track the motion of humans, a 3-D depth camera is used as an auxiliary sensor to capture the rough position of the target to aid synthetic aperture radar imaging. The back-projection imaging algorithm is implemented on a graphics processing unit for quasi-real-time operations. Finally, experiments are conducted with a real human with concealed objects and a preliminary automatic object detection algorithm based on convolutional neural networks is developed and evaluated on real data.

Back-projection imaging algorithm of random noise frequency modulation continuous wave SAR

The combination of random noise frequency-modulation continuous wave technology and synthetic aperture radar (SAR) promises a cost-effective, low probability of intercept and high electromagnetic compatibility. This paper analyses the time-domain restricting algorithms for random noise frequency modulation continuous wave (RNFMCW) SAR. Two versions of the back-projection algorithm are proposed. At first, the radar antenna continuous motion in a pulse repetition period of RNFMCW SAR is analysed. Then the phase term which is caused by the continuous motion is described by a approximate expression with Taylor expansion. Meanwhile, both the start-stop approximate back-projection algorithm and the modified back-projection algorithm are proposed. In the end, with the help of numerical simulation, the limitations of the start-stop approximation back-projection algorithm and the validity of the modified back-projection algorithms are illustrated.

Back-projection imaging algorithm of random noise frequency modulation continuous wave SAR

The combination of random noise frequency-modulation continuous wave technology and synthetic aperture radar (SAR) promises a cost-effective, low probability of intercept and high electromagnetic compatibility. This paper analyses the time-domain restricting algorithms for random noise frequency modulation continuous wave (RNFMCW) SAR. Two versions of the back-projection algorithm are proposed. At first, the radar antenna continuous motion in a pulse repetition period of RNFMCW SAR is analysed. Then the phase term which is caused by the continuous motion is described by a approximate expression with Taylor expansion. Meanwhile, both the start-stop approximate back-projection algorithm and the modified back-projection algorithm are proposed. In the end, with the help of numerical simulation, the limitations of the start-stop approximation back-projection algorithm and the validity of the modified back-projection algorithms are illustrated.

Improved Clutter Removal by Robust Principal Component Analysis for Chaos Through-Wall Imaging Radar

Chaos through-wall imaging radar has attracted wide attention due to its inherent low probability of detection/interception, strong anti-jamming, and high resolution. However, the target response is usually overwhelmed by strong clutter. This paper proposes an imaging-then-decomposition method based on two-stage robust principal component analysis (RPCA) to remove the clutter and recover the target image. The proposed method firstly focuses the energy of the preprocessing data by the back-projection imaging algorithm; then, it performs matrix decomposition on the full and the sparse component of the focused data, in succession, by the RPCA algorithm. Simulation and experimental results show that the proposed method can suppress the clutter dramatically and indicate human targets distinctly. Compared with the traditional methods, it has effectiveness and superiority in improving the signal-to-clutter ratio.

Prior design for tomographic volume fraction estimation in pneumatic conveying systems from capacitive data

Pneumatic conveying systems have become a standard technique for the transport of bulk materials such as powdery or granulates. The spatial dependence of the material density and the stream velocity in such transport systems require a volumetric measurement principle for flow measurement. In this paper we analyse the capability to estimate the volume fraction from capacitive sensing data using electrical capacitance tomography (ECT). In particular, we investigate the capability of back-projection type imaging algorithms. The ill-posed nature of the imaging problem of ECT require the incorporation of prior knowledge in the design of the estimator. We analyse the different flow profiles in pneumatic conveying in order to generate specific sample-based prior information to improve the estimation performance and robustness. We discuss the construction of different linear image reconstruction algorithms and present a framework, which allows a detailed statistical analysis of the estimator performance. Simulation studies show the estimation behaviour of different algorithms with respect to the incorporated prior information. We demonstrate, that the incorporation of specific prior knowledge leads to an improved estimator behaviour; for example, reduced variance and unbiased estimates. We implemented laboratory experiments in order to analyse the presented approach for the application in real pneumatic conveying processes. We demonstrate the improved robust estimation behaviour by means of comparative reconstruction results obtained with different algorithms and priors. Furthermore, the uncertainty of the estimated volume fraction is analysed in steady state conveying processes. Hereby, it is demonstrated, that appropriate prior information improves the estimation performance also for measurements coming from real pneumatic conveying processes, making ECT a suitable tool for the volume fraction estimation in such transport systems.

Corner target positioning with unknown walls' positions

Here we consider a corner target positioning problem under the condition of unknown walls' positions using time-division multiple-input-multiple-output (MIMO) radar. Firstly, we propose an estimation algorithm for the walls' positions using the Back-Projection (BP) imaging algorithm. Then, after obtaining the BP image of target, we extract the focus regions produced by different multipaths. Finally, we obtain the position of the target based on the extracted walls' positions and the focus regions. Simulations and experiments results validate the proposed algorithm.