Fast Backprojection Algorithm Research Articles

Transcranial thermoacoustic imaging based on the fast back-projection algorithm with nonuniform speed of sound layering

Thermoacoustic imaging (TAI) has the potential for detecting hemorrhagic stroke. However, in transcranial TAI, the speed of sound (SoS) between the skull and brain tissue varies significantly. Therefore, if the image reconstruction assumes a uniform SoS, accurately locating the hemorrhagic lesion becomes challenging. In this Letter, we propose a fast inhomogeneous layer back-projection (BP) method based on the basic boundary line with a statistical approach to reconstruct TA images for noninvasive and non-ionizing hemorrhage detection. To validate our proposed method, we conducted numerical simulations using real human skull data and two phantom transcranial TAI experiments. In the numerical simulation, the proposed method improves the structural similarity index measure from 0.034 879 for BP with uniform SoS to 0.624 44. The phantom experimental results demonstrate that the proposed method renders the targets in the reconstructed image more consistent with the real targets. In the case of considering a three-layer SoS distribution, the time reversal method requires 1 min and 37.391 s to reconstruct a 201 × 201 pixels TA image. Meanwhile, the proposed method accomplishes the same-sized TA image reconstruction in only 2.113 397 s. The simulation and experimental results indicate that the proposed method enhances TAI's ability for accurate and fast identification of cerebral hemorrhage.

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.

MuA-SAR Fast Imaging Based on UCFFBP Algorithm with Multi-Level Regional Attention Strategy

Multistatic airborne SAR (MuA-SAR) benefits from the ability to flexibly adjust the positions of multiple transmitters and receivers in space, which can shorten the synthetic aperture time to achieve the required resolution. To ensure both imaging efficiency and quality of different system spatial configurations and trajectories, the fast factorized back projection (FFBP) algorithm is proposed. However, if the FFBP algorithm based on polar coordinates is directly applied to the MuA-SAR system, the interpolation in the recursive fusion process will bring the problem of redundant calculations and error accumulation, leading to a sharp decrease in imaging efficiency and quality. In this paper, a unified Cartesian fast factorized back projection (UCFFBP) algorithm with a multi-level regional attention strategy is proposed for MuA-SAR fast imaging. First, a global Cartesian coordinate system (GCCS) is established. Through designing the rotation mapping matrix and phase compensation factor, data from different bistatic radar pairs can be processed coherently and efficiently. In addition, a multi-level regional attention strategy based on maximally stable extremal regions (MSER) is proposed. In the recursive fusion process, only the suspected target regions are paid more attention and segmented for coherent fusion at each fusion level, which further improves efficiency. The proposed UCFFBP algorithm ensures both the quality and efficiency of MuA-SAR imaging. Simulation experiments verified the effectiveness of the proposed algorithm.

The Adaptive Streaming SAR Back-Projection Algorithm Based on Half-Precision in GPU

The back-projection (BP) algorithm is completely accurate in the imaging principle, but the computational complexity is extremely high. The single-precision arithmetic used in the traditional graphics processing unit (GPU) acceleration scheme has low throughput and its usage of the video memory is large. An adaptive asynchronous streaming scheme for the BP algorithm based on half-precision is proposed in this study, and then it is extended to the fast back-projection (FBP) algorithm. In this scheme, the adaptive loss factors selection strategy ensures the dynamic range of data, the asynchronous streaming structure ensures the efficiency of large scene imaging, and the mixed-precision data processing ensures the imaging quality. The schemes proposed in this paper are compared with BP, FBP, and fast factorized back-projection (FFBP) algorithms of single-precision in GPU. The experimental results show that the two half-precision acceleration schemes in this paper reduce the video memory usage to 74% and 59% of the single-precision schemes with guaranteed image quality. The efficiency improvements of the proposed schemes are almost one and 0.5 times greater than that of the corresponding single-precision scheme, and the advantage can be more obvious when dealing with large computations.

An Efficient Backprojection Algorithm Based on Wavenumber-Domain Spectral Splicing for Monostatic and Bistatic SAR Configurations

This paper introduces a fast backprojection synthetic aperture radar (SAR) imaging algorithm based on wavenumber-domain spectral splicing. The traditional fast backprojection (FBP) algorithm establishes the polar coordinate system with the center of the sub-aperture as the origin. Therefore, the coordinates of the image obtained from each sub-aperture are different. Sub-aperture images must be projected to a uniform coordinate system before they can be coherently superimposed to form the final image, which requires a large amount of calculation. In order to deal with this problem, this paper proposes a novel imaging method, which uses the same polar coordinate system for each sub-aperture. The sub-aperture images are then spliced in the wavenumber-domain, and directly added after upsampling. This method avoids the projection from each sub-aperture to the uniform coordinate system, thus improving the imaging accuracy and efficiency. At the same time, the algorithm is suitable for various configurations, and can achieve good imaging results for bistatic forward-looking SAR and high-speed mobile platform. Finally, simulations are presented to demonstrate the effectiveness of the algorithm.

Theoretical Feasibility Analysis of Fast Back-Projection Algorithm for Moon-Based SAR in Time Domain

Nowadays, the Earth observation based on the Moon has attracted attention from many researchers and relevant departments. There also exists a considerable amount of interest in monitoring large-scale and long-term geoscience phenomena using the Moon-based SAR (MBS). However, the Earth’s observation from MBS has long transmission time, and the relative motion of MBS with its Earth ground target (EGT) is much different to the space-borne SAR, the above reasons indicate that the traditional stop-and-go model is no longer suitable for MBS in frequency domain imaging. Here a dual-path separate calculation method for single pulse is presented in this paper for a better match of a real scenario, and then the slant range is fitted to a high-order polynomial series. The MBS’s location, the synthetic aperture time and other factors have effects on length of the dual- path and fit bias. Without thoroughly investigated phase de-correlation processing in frequency domain, and to avoid computational costs in traditional back-projection (BP) algorithm, the paper first proposes a fast back-projection (FBP) algorithm in time domain for MBS, a platform that has long transmission time and long synthetic aperture time. In the FBP algorithm, the original method, that projected echo on all pixels in the imaging area, is changed to projected echo on a centerline instead. A suitable interpolation for points on the centerline is adopted to reduce the projected error; the synthetic aperture length and imaging area are also divided into subsections to reduce computation cost. The formula indicates that the range error could be control once the product of sub-imaging area’s length and sub-aperture’s length stay constant. Through the theoretical analysis, the detailed range difference mainly at apogee, perigee, ascending, and descending nodes indicate the necessity to separately calculate the dual-path for MBS’s single pulse transmission in Earth-Moon motion, with real ephemeris been adopted; then, the high-order polynomial fitting will better describe the motion trajectory. Lastly, the FBP algorithm proposed is simulated in a specific scenario under acceptable resolution, and the result shows its feasibility for image compression.

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.

Ground Cartesian Back-Projection Algorithm for High Squint Diving TOPS SAR Imaging

This article presents a fast back-projection (BP) algorithm based on subaperture (SA) image coherent combination in a downsampled Cartesian coordinate grid for high squint diving terrain observation by progressive scans (HSD-TOPS) synthetic aperture radar (SAR) ground plane imaging. A two-step spectrum compression (SC) method is proposed to coherently combine the aliasing SA images by exploiting the relationship between the wavenumber and the image frequency. The first-step SC is introduced to align the spectrum support region centers. The second-step SC effectively corrects the space-variant spectrum inclination. The proposed algorithm does not need interpolation in the process of image combination, which ensures the accuracy and the efficiency of the algorithm. Furthermore, the SC method is well-modified to suppress the sidelobes of the focused image. Simulation and measured data processing verify the effectiveness of the proposed method.

Fast Barycentric-Based Back Projection Algorithm for SAR Imaging

The paper presents a novel fast barycentric-based back projection (BP) algorithm for radar imaging using the synthetic aperture radar (SAR) technique. The innovation in the proposed method is in the determination of the reverse virtual synthetic aperture beam for each point of the observed radar scene and in classifying which portion of raw radar data must be considered to complete imaging processing. This approach allows the classical well-known BP algorithm to be significantly accelerated, which is one of the most computationally demanding methods in SAR imaging. The proposed barycentric-based BP method gives the opportunity to control the resolution of the processed image by changing the width of the calculated beam. Moreover, the described solution is still highly parallelizable such as the classical BP algorithm. The solution can be adapted to a real-time SAR system with modern high-end computational units such as graphical processor units (GPUs) that support parallel computing. In this paper, the BP algorithm is clearly described with its barycentric-based modification. The proposed method is compared with a classical BP algorithm based on the measurement of simulated and real data.

A Fast Back-Projection Approach to Diffraction Tomography for Near-Field Microwave Imaging

A novel fast back-projection (FBP) approach is presented as a more robust alternative to conventional diffraction tomography (DT) for near-field three-dimensional (3-D) microwave imaging. Like DT, the FBP algorithm utilizes the spectral Green's function and stationary phase solution in the forward model, enabling the implementation of the fast Fourier transform to achieve real-time image generation with the same efficiency as DT. However, if the Green's function or the antenna gain pattern has any nulls within the imaging volume, the DT can have singularities that give rise to unbalanced images. The FBP not only naturally avoids the singularity problem and obtains balanced images through the point spread function, but is also much less sensitive to noise due to the matched-filter property of back-projection. 3-D simulations and measurement of a monostatic near-field free-space imaging scenario are presented to demonstrate the efficiency of the proposed FBP method in comparison with DT, and the improved uniformity and noise resistance of the image.

The Efficient High‐Resolution SAR Reconstruction Imaging Algorithms for Three‐Dimensional Electrically Large‐Scale Targets in Clutter

AbstractIn recent years, significant effort of both the scientific and industrial community is invested in research and development of multifrequency, multipolarization, and high‐resolution synthetic aperture radar (SAR) systems. One of the key issues is to realize efficient methods for imaging, reconstruction, and target detection of three‐dimensional (3‐D) electrically large‐scale objects. In this paper, an advanced multiple‐input multiple‐output (MIMO) SAR based on high‐resolution imaging algorithm was developed. Specifically, a reasonable sea surface model to quantify the influence of physical parameters in clutter was yielded as well. The SAR simulation system includes the following: (i) refined geometric‐electromagnetic modeling by Gmsh, (ii) a dynamic sea surface model, (iii) single‐input multiple‐output (SIMO) radar imaging formation by employing a fast backprojection algorithm, (iv) design of MIMO antenna arrays to achieve a good trade‐off between the main beam width and the side lobe level, (v) 3‐D SAR imaging algorithm on the basis of optimized physical optics for electromagnetic scattering computation, and (vi) hardware acceleration technique using graphics processing unit. Finally, numerical experiments indicate that 3‐D visualization of sphere, and examples of fighter aircraft and aircraft carrier are generated within 200 s, further proving correctness and effectiveness of the developed 3‐D MIMO SAR imaging algorithm.

An Extended Fast Factorized Back Projection Algorithm for Missile-Borne Bistatic Forward-Looking SAR Imaging

In this paper, an extended fast factorized back projection (FFBP) algorithm is proposed to focus the missile-borne bistatic forward-looking synthetic aperture radar (BFSAR) data. It is also based on the subaperture processing technique to reduce the computational burden, but represents the subimages on the elliptical polar coordinates referenced to the tracks of both transmitter and receiver. First, the imaging geometry and signal model of the missile-borne BFSAR are established. Then, considering the special configuration of the missile-borne BFSAR, a novel elliptical polar coordinate system whose origin is determined by the positions of both transmitter and receiver is established. The subaperture processing approach based on this coordinate system is presented. Successively, based on the range error analysis, the sampling requirements of the elliptical polar subimages are derived to provide a tradeoff between the imaging quality and efficiency. Finally, the computational burden of the proposed algorithm is discussed, and the speed-up factor of the proposed algorithm with respect to the direct back projection algorithm is derived. The experimental results with simulated data prove the validity and feasibility of the proposed algorithm.

PHOTOGRAMMETRIC PROCESSING OF PLANETARY LINEAR PUSHBROOM IMAGES BASED ON APPROXIMATE ORTHOPHOTOS

Abstract. It is still a great challenging task to efficiently produce planetary mapping products from orbital remote sensing images. There are many disadvantages in photogrammetric processing of planetary stereo images, such as lacking ground control information and informative features. Among which, image matching is the most difficult job in planetary photogrammetry. This paper designs a photogrammetric processing framework for planetary remote sensing images based on approximate orthophotos. Both tie points extraction for bundle adjustment and dense image matching for generating digital terrain model (DTM) are performed on approximate orthophotos. Since most of planetary remote sensing images are acquired by linear scanner cameras, we mainly deal with linear pushbroom images. In order to improve the computational efficiency of orthophotos generation and coordinates transformation, a fast back-projection algorithm of linear pushbroom images is introduced. Moreover, an iteratively refined DTM and orthophotos scheme was adopted in the DTM generation process, which is helpful to reduce search space of image matching and improve matching accuracy of conjugate points. With the advantages of approximate orthophotos, the matching results of planetary remote sensing images can be greatly improved. We tested the proposed approach with Mars Express (MEX) High Resolution Stereo Camera (HRSC) and Lunar Reconnaissance Orbiter (LRO) Narrow Angle Camera (NAC) images. The preliminary experimental results demonstrate the feasibility of the proposed approach.

Fast Time-domain Imaging Method for Bistatic Circular SAR

Fast time-domain algorithm (FTDA) for the one-stationary bistatic circular synthetic aperture radar (OS-BCSAR) imaging is presented. In this paper, the subimage is represented in the slant-range plane instead of ground plane. FTDA includes the fast backprojection algorithm (FBPA) with the subaperture and elliptical polar grid processing and the FBPA with the subaperture and polar grid processing. Experimental results are given to prove its validity.

Precise Aperture-Dependent Motion Compensation with Frequency Domain Fast Back-Projection Algorithm.

Precise azimuth-variant motion compensation (MOCO) is an essential and difficult task for high-resolution synthetic aperture radar (SAR) imagery. In conventional post-filtering approaches, residual azimuth-variant motion errors are generally compensated through a set of spatial post-filters, where the coarse-focused image is segmented into overlapped blocks concerning the azimuth-dependent residual errors. However, image domain post-filtering approaches, such as precise topography- and aperture-dependent motion compensation algorithm (PTA), have difficulty of robustness in declining, when strong motion errors are involved in the coarse-focused image. In this case, in order to capture the complete motion blurring function within each image block, both the block size and the overlapped part need necessary extension leading to degeneration of efficiency and robustness inevitably. Herein, a frequency domain fast back-projection algorithm (FDFBPA) is introduced to deal with strong azimuth-variant motion errors. FDFBPA disposes of the azimuth-variant motion errors based on a precise azimuth spectrum expression in the azimuth wavenumber domain. First, a wavenumber domain sub-aperture processing strategy is introduced to accelerate computation. After that, the azimuth wavenumber spectrum is partitioned into a set of wavenumber blocks, and each block is formed into a sub-aperture coarse resolution image via the back-projection integral. Then, the sub-aperture images are straightforwardly fused together in azimuth wavenumber domain to obtain a full resolution image. Moreover, chirp-Z transform (CZT) is also introduced to implement the sub-aperture back-projection integral, increasing the efficiency of the algorithm. By disusing the image domain post-filtering strategy, robustness of the proposed algorithm is improved. Both simulation and real-measured data experiments demonstrate the effectiveness and superiority of the proposal.

Computer simulation of synthetic aperture sonar or radar for classroom demonstration: Part II

In our presentation, a Mathematica® simulation of Synthetic Aperture Acoustic Radar will demonstrate how point-like targets placed on a smooth surface can be imaged from a collection of acoustic echoes. The transmitter and receiver are collocated and modeled as a single element that stops along a linear track at collection points and hops to the next location (stop and hop approximation). The transmitter on the hypothetical apparatus will transmit a linear frequency modulated LFM chirp pulse that reflect off the targets and are recorded as echoes by the receiver at discrete locations along the track. A matched filter correlation process will perform a pulse compression of the LFM chirp. A series of still frames from the animated simulation will be displayed. These frames show the echoes arriving at different times from the targets in conjunction with a receiver wave recorder screen. The time correlation backprojection algorithm is motivated when pulse compressed arrivals are displayed (at various track locations) including the echo arrival of a hypothetical point target adjusted in the x,y plane on or near one of the actual point targets. [See Yegulap, “Fast backprojection algorithm for SAR,“ in Proc. 1999 IEEE Radar Conf., Waltham, MA, April 20–22, 1999, 60–65].

Computer simulation of synthetic apertures radar for classroom demonstration

Synthetic Aperture Radar (SAR) has many civilian and military applications as a high resolution imaging system. A Mathematica® simulation of Synthetic Aperture Acoustic Radar will demonstrate how two-dimensional point targets on a ground plane can be imaged from a collection of acoustic echoes. A transmitter and receiver will be modeled as a one point element that stops along a linear track at collection points and hops to the next location (stop and hop approximation). The transmitter on the hypothetical apparatus will transmit acoustic signals that reflect off the targets as echoes to be collected by the receiver at each location of the track. A matched filter correlation process will complete pulse compression of the LFM (linear frequency modulated) chirp. The image reflectance of the point targets will be constructed using a time correlation/backprojection algorithm developed by Yegulap [“Fast Backprojection Algorithm for Synthetic Aperture Radar,” In Proceedings 1999 IEEE Radar Conference, Waltham, MA, April 20-22, 1999, 60-65]. Image resolution may be improved by increasing chirp bandwidth.

Precision Imaging of Frequency Stepped SAR with Frequency Domain Extracted HRRP and Fast Factorized Back Projection Algorithm

Novel frequency domain extracted method (FDEM) to obtain high range resolution profile (HRRP) for frequency stepped synthetic aperture radar (SAR) is proposed in this paper, and the mathematical principle and formulas of this new HRRP obtaining idea combined with classical fast Fourier transform (FFT), chirp z transform (CZT), and single point Fourier transform (SPFT) are deduced, analyzed, and compared in detail. Based on the HRRP data, precision imaging processing is completed using a data block partition based fast factorized back projection algorithm. Imaging validations are executed and all results proved that the FDEM has a great capability of antijamming. It is more effective than conventional time domain IFFT method (TDM) and shows a great promise in frequency stepped radar imaging and applications.

Application of fast factorized back-projection algorithm for high-resolution highly squinted airborne SAR imaging

In squinted synthetic aperture radar (SAR) imaging, the range-azimuth coupling requires precise range cell migration correction (RCMC). Moreover, for high-resolution airborne SAR, motion compensation (MOCO) becomes complicated as the squint angle increases, thereby degrading the performance of Doppler-domain imaging algorithms. On the other hand, time-domain back-projection (BP) SAR imaging approaches are considered as optimal solutions to performing precise image focusing and MOCO. Among current BP algorithms, the fast factorized back-projection (FFBP) algorithm is one of the most essential representatives that achieve high-resolution images in an efficient manner. In this paper, the principle and applications of the FFBP algorithm are investigated through the derivation of the azimuth impulse response function (AIRF) of the resulting image. The phenomenon of spectrum displacement induced by motion errors in the BP image is presented and analyzed. Based on rigorous mathematical derivations, a modified FFBP algorithm is proposed to facilitate a seamless integration with motion compensation and accurate imagery of high-resolution highly squinted airborne SAR. Real data results confirm the effectiveness of the proposed approaches.

Processing video-SAR data with the fast backprojection method

Video synthetic aperture radar (video-SAR) is a land-imaging mode where a sequence of images is continuously formed when the radar platform either flies by or circles the scene. In this paper, the fast backprojection (FBP) algorithm is introduced for video-SAR image formation. It avoids unnecessary duplication of processing for the overlapping parts between consecutive video frames and achieves O(N2 log N) complexity through a recursive procedure. To reduce the processing complexity in video-SAR system, the scene is partitioned into the general region (GR) and the region of interest (ROI). In different regions, different aperture lengths are used. The proposed method allows a direct trade between processing speed and focused quality for the GR, meanwhile reserving particular details in the ROI. The effectiveness is validated both for a simulated scene and for X-band SAR measurements from the Gotcha data set.