GPU-based parallel back projection algorithm for the translational variant BiSAR imaging

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.

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.

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.

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.

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.

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.

Photoacoustic tomography (PAT) offers structural and functional imaging of living biological tissue with highly sensitive optical absorption contrast and excellent spatial resolution comparable to medical ultrasound (US) imaging. We report the development of a fully integrated PAT and US dual-modality imaging system, which performs signal scanning, image reconstruction and display for both photoacoustic (PA) and US imaging all in a truly real-time manner. The backprojection (BP) algorithm for PA image reconstruction is optimized to reduce the computational cost and facilitate parallel computation on a state of the art graphics processing unit (GPU) card. For the first time, PAT and US imaging of the same object can be conducted simultaneously and continuously, at a real time frame rate, presently limited by the laser repetition rate of 10 Hz. Noninvasive PAT and US imaging of human peripheral joints in vivo were achieved, demonstrating the satisfactory image quality realized with this system. Another experiment, simultaneous PAT and US imaging of contrast agent flowing through an artificial vessel was conducted to verify the performance of this system for imaging fast biological events. The GPU based image reconstruction software code for this dual-modality system is open source and available for download from http://sourceforge.net/projects/pat realtime .

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.

SAR processing can be applied to ice sounder data to improve along-track resolution and clutter suppression. This paper presents a time-domain back-projection technique for SAR focusing of ice sounder data. With this technique, variations in flight track and ice surface slope can be accurately accommodated at the expense of computation time. The back-projection algorithm can be easily parallelized however, and can advantageously be implemented on a graphics processing unit (GPU). Results from using the back-projection algorithm on POLARIS ice sounder data from North Greenland shows that the quality of data is improved by the processing, and the performance of the GPU implementation allows for very fast focusing.

Although the back-projection algorithm(BPA) is the best method for image reconstruction of air-borne synthetic-aperture radar(SAR), it requires a long processing time. In this study, a real-time processing method of BPA was proposed to reconstruct the image of a compact drone-borne SAR in real time. To achieve this, the raw data of the SAR was acquired by a test flight with SAR based on frequency-modulated continuous wave(FMCW) radar. The performance of the BPA was confirmed by using raw data and a modified BPA processing kernel based on graphics processing unit(GPU) technology. The results confirmed the possibility of real-time image reconstruction of SAR.

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.

In this paper, a novel method for the detection of external insulation defects based on the ultrawideband impulse radar is proposed. The circular synthetic aperture radar method was adopted to collect reflected signals in this paper, since the detected object often has a symmetric shape (e.g., insulators, bushings, etc.). The mean suppression method is adopted to filter out the clutters of reflected waveforms from different directions, and thus the reflected signals of defects can be amplified. Then, the defect images are extracted from the processed reflected signals with the back projection algorithm. Moreover, since the example objects studied here are of multi-layer circular structure with different dielectrics for each layer, the accurate wave-propagation time should be calibrated before the calculation of back projection amplitudes. Thus, the multi-layer model is established to figure out the refraction path, while the propagation time is compensated based on the wave speeds of different dielectrics. The non-destructive detection capacity of the proposed UWB detection method is verified by the simulation first, and then the practical detection effectiveness is verified by the comparison experiment of an intact insulator and a defective one. The experimental results indicate that the measured length of the internal crack as an extension of the observed surface cavity is about 30 mm, and the severest defect point is only 4.2 mm away from the latter, which means the defect locating is of high accuracy. The investigation results demonstrate that, due to the good penetrability and imaging resolution, the impulse radar exhibits good potential in the online detection of both surface and internal defects of the external insulation equipment.

One of the most important applications of optoacoustics is the visualization of oxygenation, hemoglobin concentration, and monitoring. The paper presents the results of processing an acoustic signal obtained as a result of thermoelastic expansion under the influence of an ND: YAG laser with a duration of 84 ns on an aqueous solution using a modified back projection algorithm based on a combined wavelet for high-frequency optoacoustic tomography. The results show that the above wavelet-based back projection algorithm effectively improves the resolution and contrast of reconstruction images under conditions of strong background noise. It is shown that the method can be used in optoacoustic signal reconstruction to obtain images of biological tissues. The paper presents a modified reverse projection algorithm based on a combined wavelet for high-frequency optoacoustic tomography. The given wavelet-based back projection algorithm will improve the resolution and contrast images during reconstruction under strong background noise. The aqueous solution was irradiated with nanosecond laser pulses, and acoustic waves were formed in the result of thermoelastic expansion of the irradiated volume. The model liquid was exposed to a laser with a constant intensity. The results of the experimentally obtained and restored acoustic signals formed as a result of ND: YAG laser exposure were presented with an optoacoustic effect in an aqueous solution. Signal processing was performed using the reverse projection algorithm. A method for processing the acoustic signal based on the reverse filtering method is proposed, which showed that the modified algorithm can significantly improve the quality of the reconstructed 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.

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