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

The back projection (BP) algorithm is highly effective in bistatic SAR imaging. But it is time-consuming for the large scene imaging. In this paper, we propose a GPU-based parallel BP algorithm, the range compression and back projection are implemented on the graphics processing unit (GPU) using CUDA language. We also present some optimum methods including memory optimization, phase accumulator reduction and imaging scene segmentation to implement fast and large scene imaging. Numerical experiments demonstrate that the GPU-based method can significantly improve the computational efficiency of the original BP algorithm, about 80 times faster, while the imaging scene size same as the CPU-based BP algorithm.

Due to the effects of the earth’s rotation and the satellite’s elliptical orbit, the Doppler centroid varies along the orbit in geosynchronous earth orbit synthetic aperture radar (GEO SAR). With an ultrahigh orbit height, the beam may illuminate outside the earth surface with a rotation angle large than 9 degrees. Therefore, the usual attitude steering methods to minimize the Doppler centroid in low earth orbit SAR (LEO SAR) may not be suitable for GEO SAR. In this paper, a novel steering strategy to maximize Nesigma0 for GEO SAR is proposed when the beam illuminates outside the earth surface. The new geometry and the gradient method are applied to demonstrate the method. The ability to stare imaging in geosynchronous orbit SAR is analyzed and verified by using the back projection (BP) algorithm to simulate the imaging principle. Nesigma0 under the new method improved 1dB comparing with the original image.

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.

This paper concerns the surface-tracing-based (STB) linear-array synthetic-aperture-radar (LASAR) 3-D imaging technique. The basic idea of this technique is to consider the 3-D SAR imaging problem as tracing a surface in the low height-resolution level. The STB 3-D imaging technique first initiates a low-resolution digital elevation map (DEM) using 3-D backprojection (BP) algorithm, predicts a higher resolution DEM from the known elevation using multivariate-interpolation technique, searches from the predicted elevation and obtains a higher resolution DEM, then repeats the prediction and searching recursively and obtains the fine-resolution DEM finally. By converting the 3-D LASAR imaging problem to a 2-D surface-tracing problem, the STB 3-D imaging technique can reduce the computational complexity by one order. The computational cost of STB 3-D imaging technique is analyzed, and we find out that the computational cost of STB 3-D LASAR imaging technique is determined by the surface prediction error and the fluctuation of ground. In particular, for normal distribution, when one of the earlier two factors is small, the computational cost is proportional to the other factor approximately. Finally, a new STB 3-D BP algorithm that implements the surface-prediction operation via multiresolution-approximation (MRA) technique (named as MRA 3-D BP algorithm) is presented. By operating the interpolation in frequency domain, the computational cost of MRA algorithm for sparse LASAR is near to that of RD algorithm for full-element LASAR.

In ground penetrating radar (GPR), back projection (BP) approach is a reliable method to image underground buried objects which unfortunately suffers from a high computational burden. In the BP algorithm, the refraction points have to be approximated to decrease the computational complexity. Another parameter that can improve both the accuracy and the speed of the algorithm is the antenna pattern. The 2-D algorithm is a convenient method which entails high artifacts. The proposed algorithm implemented in the 3-D domain is able to decrease the artifacts and is also a better discriminator. Meanwhile, it is possible to reconstruct a 2-D image with a better resolution in which artifacts have been suppressed. But scanning along both $\mathrm{x}$ and y-axes is needed. The computational burden of the 3-D algorithm has been reduced with the help of the antenna pattern. The 3-D scene is mapped to a 2-D scenario and the problem is changed to a 2-D algorithm problem.

In this article, a novel sinogram decimation fast back-projection (SD-FBP) algorithm for strip-map synthetic aperture radar (SAR) imaging is proposed. We first review the back-projection (BP) and the fast factorized BP (FFBP) algorithms, then analyze the cause of the FFBP imaging degradation theoretically based on the combination of SAR imaging and the sinogram concept of computed tomography, illustrating that the degradation is much more severe for strip-map mode. Based on the SAR sinogram, the SD-FBP algorithm is proposed to mitigate the FFBP degradation for strip-map SAR imaging. The complexity of the SD-FBP is analyzed and compared with that of the FFBP and the Cartesian factorized BP (CFBP). The superiority of the SD-FBP algorithm is validated using the simulation and real spaceborne strip-map SAR data, e.g., Sentinel-1, Gaofen-3, and LuTan-1. The results show that the SD-FBP can tackle the FFBP imaging degradation for strip-map SAR, and runs faster than the FFBP and the CFBP.

In order to solve the problems that the existing high squint missile-borne synthetic aperture radar( SAR) algorithm can not deal with too high squint angle,and that the calculated amount of traditional back-projection( BP) imaging algorithm is too large,as well as that the current fast BP algorithm can not process the echo data in parallel,an improved approximate forward looking missile-borne SAR back-projection imaging algorithm which can process echo data in parallel was proposed. According to geometrical relationship of approximate forward looking missile-borne SAR,an echo signal model was established. And the imaging area was divided to equidistance strip in range along the distance direction. The image was split when merging sub aperture,and the splitting and merging did not stop until the accuracy of image met the requirements.Next the raw echo data was back projected to each strip for coherent integration,and then the missile-borne SAR image was obtained. If these strips were processed for imaging in parallel,the imaging speed would be further improved. Finally,results of simulation echo data and real echo data validate that the improved algorithm can deal with approximate forward looking scene with 86° squint angle,and it can greatly improve the computation speed compared with that of traditional BP algorithm. Moreover,the computation speed is faster than that of other improved BP algorithms by processing those strips in parallel.

Circular SAR (CSAR) has the ability of 3-D imaging due to its special curve trajectory. Single-pass CSAR can theoretically obtain the resolution of the sub-wavelength level on the distance-azimuth plane, but its resolution at the elevation direction is very low. At the same time, CSAR 3-D imaging with Back Projection(BP) has high algorithm complexity and low imaging efficiency. A coherent 3-D imaging method for multi-circular SAR based on an improved 3-D back projection algorithm is proposed. For the problem of high time complexity of the imaging algorithm, an improved 3-D BP algorithm for CSAR based on constructing geometric interpolation kernel is proposed. 3-D interpolation operations are transformed into 1-D interpolation operations and distance vector searching operations. The final imaging result is obtained by coherently accumulating the improved 3-D BP results of multi-circular SAR. The proposed method solves effectively the problem of low elevation resolution of single-pass CSAR, improves 3-D imaging details, and reduces greatly the time of CSAR 3-D imaging simultaneously. The simulated 3-D imaging results of the conical target and GOTCHA data set from the US Air Force Laboratory verify the effectiveness of the proposed method.

VideoSAR is a land-imaging mode where the synthetic aperture radar (SAR) is operated in a spotlight configuration for an extended period of time. A sequence of images is continuously formed to a common Cartesian grid, while the radar is either flying towards, by or circling a target area. In general, VideoSAR imaging maintains antenna illumination on a target regardless of changes in squint angle, within theoretical and practical limitations. The video-like nature is a result of the imagery being produced using overlapped synthetic apertures such that the output frame rate can be commensurate with that of a video system. Enhanced exploitation of this product typically requires that the imagery be phase preserving, and that the data acquisition geometries be highly controlled for generation of secondary products such as coherence images (coherence maps) for change detection. One of the most accurate image formation algorithms for the formation of phase preserved imagery is the back-projection algorithm. Though computationally intensive, its attraction lies in its simplicity, the fact that the relative location of each pixel in the output imagery is precisely known and the complex imagery is phase preserved. The backprojection algorithm is presented in terms of its application to VideoSAR imaging. Mathematical decomposition techniques for improving the computational efficiency of the algorithm are reviewed. The application of change detection between pairs of VideoSAR images and `stacks' of VideoSAR images where the benefits of trading off spatial image filtering and temporal image filtering by averaging coherence in slow-time is also examined. Finally, computer topologies applicable to back projection are outlined from the perspectives of both the signal processing architecture and advances in massively parallel computing.

The back-projection algorithm is the most common method for the reconstruction of circular-scanning-based photoacoustic tomography (CSPAT) due to its simplicity, computational efficiency, and robustness. It usually can be implemented in two models: one for ideal point detector, and the other for planar transducer with infinite element size. However, because most transducers in CSPAT are planar with a finite size, the off-center targets will be blurred in the tangential direction with these two reconstruction models. Here in this paper, we put forward a new model of the back projection algorithm for the reconstruction of CSPAT with finite size planar transducer, in which the acoustic spatial temporal response of the employed finite size transducer is approximated with a virtual detector placed at an optimized distance behind the transducer, and the optimized distance is determined by a phase square difference minimization scheme. Notably, this proposed method can also be suitable for reconstruction with the ideal point detector and infinite planar detector, and thus is a generalized form of the back-projection algorithm. Compared with the two conventional models of the back-projection method and the modified back-projection method, the proposed method in this work can significantly improve the tangential resolution of off-center targets, thus improving the reconstructed image quality. These findings are validated with both simulations and experiments. We propose a generalized model of the back projection algorithm to restore the elongated tangential resolution in CSPAT in case of a planar transducer of finite size, which can also be applicable for point and large-size planar transducers. This proposed method may also guide the design of CSPAT scanning configurations for potential applications such as human breast imaging for cancer detection.

In this paper, considering the relative motion between satellite and earth during signal propagation time, the accurate analysis method for propagation slant range is presented in geosynchronous SAR. Furthermore, the difference between accurate analysis method and `Stop-and-Go' assumption is analytically obtained. Meanwhile based on the derived accurate slant range model, it is found that the corresponding range migration correction and azimuth reference function must consider the high order term, and therefore the modified SPECAN algorithm is proposed. The simulation results verify the correctness of `Stop-and-Go' assumption error derivation and SPECAN algorithm modification.

Highly squint synthetic aperture radar (SAR) increases the flexibility and aspect-information of observation but poses several challenges to frequency-domain algorithms. The back-projection (BP) algorithm is recognized to produce the best results for highly squint mode but at high computational expense. Several fast BP algorithms have been developed to enhance the efficiency of the BP integral. The Cartesian factorized BP (CFBP) algorithm has been proposed to improve the performance. However, CFBP is ineffective in the highly squint case because its range model (RM) is imprecise. In this letter, we propose a modified CFBP (MCFBP) algorithm for highly squint spotlight SAR imaging. We employ a transformed Cartesian coordinate system to treat the transceiver mode as approximately side-looking mode. According to the transformed coordinate system, we propose a modified RM (MRM) to reduce the range error. Based on the MRM, we derive modified image spectrum compression steps and the Nyquist sampling rate of the subaperture image. MCFBP inherits CFBP's accuracy and efficiency advantages. Results of simulations and experiments performed by the X-band airborne SAR system with a maximum bandwidth of 1.2 GHz validate the improved performance of the proposed algorithm relative to BP and fast factorized BP.

This study presents a fast backprojection algorithm (FBPA) for bistatic forward-looking spotlight synthetic aperture radar (BFSSAR) imaging. It represents the subimages on the polar grids to reduce the computational burden. First, the backprojection algorithm for the BFSSAR imaging is introduced. Then, FBPA for the BFSSAR imaging based on the subaperture processing is provided, and the sampling requirements for the polar grids of subimages are derived from the bandwidth angle. Simulation results are shown to demonstrate its validity.

Circular synthetic aperture radar (CSAR) has a 360° observation capability on the central observation scenario. A typical way to process CSAR imaging is to cut data into small sub-apertures because most targets are only coherent at a very small observation angle. There are many sub-aperture imaging methods after development in recent years. The back-projection algorithm is widely used because it is simple and can be applied to an arbitrary trajectory. Because of the limitation of the Nyquist sampling frequency and influence of the antenna sidelobe, azimuth ambiguity is a phenomenon that may occur in the radar imaging process. The existing researches typically choose the back-projection (BP) imaging area according to the SAR platform flight path and the antenna beam width. The limitation of the CSAR imaging area and its azimuth ambiguity region are rarely analyzed theoretically. This paper focus on the sub-aperture imaging of CSAR, based on the BP algorithm, which derives the relationship of azimuth ambiguity with CSAR parameters such as the pause repeat frequency (PRF), slant range angle, velocity of radar platform, etc. This paper proposes an equation for the calculation of the azimuth ambiguity region and analyzes the limitations, which provides theoretical support for CSAR parameter design, imaging area selection, and azimuth ambiguity analysis.

Faster tomographic fan-beam back-projection using Cartesian axes pre-projection