Backprojection Algorithm Research Articles

Multichannel Back Projection (MC-BP) Algorithm and Its Accelerated Form for HRWS SAR

Multichannel Back Projection (MC-BP) Algorithm and Its Accelerated Form for HRWS SAR

Filtered Backprojection Algorithms Enable Linear Scanning Computed Tomography High-Quality Reconstruction with Large Extended FOVs

Filtered Backprojection Algorithms Enable Linear Scanning Computed Tomography High-Quality Reconstruction with Large Extended FOVs

RAU-Net-Based Imaging Method for Spatial-Variant Correction and Denoising in Multiple-Input Multiple-Output Radar

The conventional back projection (BP) algorithm is an accurate time-domain algorithm widely used for multiple-input multiple-output (MIMO) radar imaging, owing to its independence of antenna array configuration. The time-delay curve correction back projection (TCC-BP) algorithm greatly reduces the computational complexity of BP but suffers from spatial-variant correction, sidelobe interference and background noise due to the use of coherent superposition of echo time-delay curves. In this article, a residual attention U-Net-based (RAU-Net) MIMO radar imaging method that adapts complex noisy scenarios with spatial variation and sidelobe interference is proposed. On the basis of the U-Net underlying structure, we develop the RAU-Net with two modules: a residual unit with identity mapping and a dual attention module to obtain resolution spatial-variant correction and denoising on real-world MIMO radar images. The network realizes MIMO radar imaging based on the TCC-BP algorithm and substantially reduces the total computational time of the BP algorithm on the basis of improving the imaging resolution and denoising capability. Extensive experiments on the simulated and measured data demonstrate that the proposed method outperforms both the traditional methods and learning-imaging methods in terms of spatial-variant correction, denoising and computational complexity.

Super-resolution terahertz synthetic aperture image reconstruction algorithm.

The resolution of terahertz images based on the near-field synthetic aperture radar (NSAR) imaging mode is low due to the narrow antenna beamwidth and the electromagnetic wave loss that was ignored by previous algorithms. We propose a super-resolution terahertz NSAR imaging algorithm. There are two algorithm steps: First, we use the forward mathematical model of the NSAR imaging system and the back-projection algorithm (BPA) to calculate the point spread function (PSF). The next step is to deconvolve the NSAR image reconstructed by BPA to enhance its lateral resolution. To evaluate the effectiveness of our proposed method, we conducted both simulations and experiments. The experiment results show that the proposed method achieves a resolution of 0.67λ, which is a significant improvement. Overall, the proposed method has great potential to enhance the resolution of THz images and advance the use of THz technology in various fields.

Tomographic reconstruction strategies for nondestructive testing with a commercial CT scanner

In this work, a framework was developed to access and process raw data from a commercial X-ray Computed Tomography (CT) scanner for research purposes. Our method requires vendor-provided binaries to convert the data to a readable format and also to remove the effect of proprietary beam hardening preprocessing. As a result, custom reconstruction techniques, including beam-hardening corrections algorithms, can be applied. Small region-of-interest CT imaging techniques and different backprojection algorithms were investigated to improve image quality (spatial resolution, noise) with an in-house iterative reconstruction algorithm. For a reconstruction matrix of 512 pixels × 512 pixels, processing times of approximately 2.5 s per slice were obtained using a set of 8 x GPUs. With this framework, high-quality images of high density samples (e.g., minerals) can be obtained with reduced truncation-induced blurring, free of artifacts stemming from the reconstruction process and reduced beam-hardening artifacts.

A Novel, Efficient Algorithm for Subsurface Radar Imaging below a Non-Planar Surface.

In classical radar imaging, such as in Earth remote sensing, electromagnetic waves are usually assumed to propagate in free space. However, in numerous applications, such as ground penetrating radar or non-destructive testing, this assumption no longer holds. When there is a multi-material background, the subsurface image reconstruction becomes considerably more complex. Imaging can be performed in the spatial domain or, equivalently, in the wavenumber domain (k-space). In subsurface imaging, to date, objects with a non-planar surface are commonly reconstructed in the spatial domain, by the Backprojection algorithm combined with ray tracing, which is computationally demanding. On the other hand, objects with a planar surface can be reconstructed more efficiently in k-space. However, many non-planar surfaces are partly planar. Therefore, in this paper, a novel concept is introduced that makes use of the efficient k-space-based reconstruction algorithms for partly planar scenarios, too. The proposed algorithm forms an image from superposing sub-images where as many image parts as possible are reconstructed in the wavenumber domain, and only as many as necessary are reconstructed in the spatial domain. For this, a segmentation scheme is developed to determine which parts of the image volume can be reconstructed in the wavenumber domain. The novel concept is verified by measurements, both from monostatic synthetic aperture radar data and multiple-input-multiple-output radar data. It is shown that the computational efficiency for imaging irregularly shaped geometries can be significantly augmented when applying the proposed concept.

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.

Comparison of Imaging Radar Configurations for Roadway Inspection and Characterization.

This paper investigates the performance of a wide variety of radar imaging modes, such as nadir-looking B-scan, or side-looking synthetic aperture radar tomographic acquisitions, performed in both back- and forward-scattering geometries, for the inspection and characterization of roadways. Nadir-looking B-scan corresponds to a low-complexity mode exploiting the direct return from the response, whereas side-looking configurations allow the utilization of angular and polarimetric diversity in order to analyze advanced features. The main objective of this paper is to evaluate the ability of each configuration, independently of aspects related to operational implementation, to discriminate and localize shallow underground defects in the wearing course of roadways, and to estimate key geophysical parameters, such as roughness and dielectric permittivity. Campaign measurements are conducted using short-range radar stepped-frequency continuous-waveform (SFCW) devices operated in the C and X bands, at the pavement fatigue carousel of Université Gustave Eiffel, over debonded areas with artificial defects. The results indicate the great potential of the newly proposed forward-scattering tomographic configuration for detecting slight defects and characterizing roadways. Case studies, performed in the presence of narrow horizontal heterogeneities which cannot be detected using classical B-scan, show that both the coherent integration along an aperture using the back-projection algorithm, and the exploitation of scattering mechanisms specific to the forward-looking bistatic geometry, allows anomalous echoes to be detected and further characterized, confirming the efficacy of radar imaging techniques in such applications.

Deep learning on photoacoustic tomography to remove image distortion due to inaccurate measurement of the scanning radius.

Photoacoustic tomography (PAT) is a non-invasive, non-ionizing hybrid imaging modality that holds great potential for various biomedical applications and the incorporation with deep learning (DL) methods has experienced notable advancements in recent times. In a typical 2D PAT setup, a single-element ultrasound detector (USD) is used to collect the PA signals by making a 360° full scan of the imaging region. The traditional backprojection (BP) algorithm has been widely used to reconstruct the PAT images from the acquired signals. Accurate determination of the scanning radius (SR) is required for proper image reconstruction. Even a slight deviation from its nominal value can lead to image distortion compromising the quality of the reconstruction. To address this challenge, two approaches have been developed and examined herein. The first framework includes a modified version of dense U-Net (DUNet) architecture. The second procedure involves a DL-based convolutional neural network (CNN) for image classification followed by a DUNet. The first protocol was trained with heterogeneous simulated images generated from three different phantoms to learn the relationship between the reconstructed and the corresponding ground truth (GT) images. In the case of the second scheme, the first stage was trained with the same heterogeneous dataset to classify the image type and the second stage was trained individually with the appropriate images. The performance of these architectures has been tested on both simulated and experimental images. The first method can sustain SR deviation up to approximately 6% for simulated images and 5% for experimental images and can accurately reproduce the GTs. The proposed DL-approach extends the limits further (approximately 7% and 8% for simulated and experimental images, respectively). Our results suggest that classification-based DL method does not need a precise assessment of SR for accurate PAT image formation.

Real Time Measurement of Multiphase Flow Velocity using Electrical Capacitance Tomography

Accurate and real-time measurement of fluid flow velocity is crucial in various industrial processes, especially when dealing with multiple phase fluids. Traditional flow measurement methods often struggle to accurately quantify the velocity of complex multiphase flows within pipes. This challenge necessitates the exploration of innovative techniques capable of providing reliable measurements. This paper proposes the utilization of Electrical Capacitance Tomography (ECT) as a promising approach for measuring the velocity of multiple phase fluids in pipes. The ECT technique involves the non-intrusive imaging of the electrical capacitance distribution within the pipe. By utilizing an array of electrodes placed around the pipe circumference, the capacitance distribution can be reconstructed, offering insight into the fluid flow patterns. By analyzing the temporal changes in the capacitance distribution, the velocity of different phases within the pipe can be estimated. To achieve accurate velocity measurements, an ECT system needs to account for the complexities introduced by multiphase flows. Various image reconstruction algorithms, such as linear back-projection and iterative algorithms like Gauss-Newton and Levenberg-Marquardt, are employed to reconstruct the capacitance distribution. Additionally, advanced signal processing techniques, such as cross-correlation analysis and time-difference methods, are used to extract velocity information from the reconstructed images. This paper presents an experimental investigation of measuring the velocity of multiple-phase fluids in pipes using the ECT technique. The study aims to address the challenges associated with different flow regimes, fluid properties, and pipe geometries by exploring advancements in electrode design, system calibration, and data processing techniques to enhance the accuracy and robustness of ECT-based velocity measurements.

Back projection deep unrolling network for handwritten text image super resolution

Current super-resolution (SR) methods have demonstrated exceptional advancements in the domain of natural image processing. Nevertheless, these approaches do not fully address the open issues of edge blurring and distortion. In order to address the aforementioned challenges, we propose a novel deep unrolling model, coined back projection deep unrolling network (BPDUN), for super-resolution of handwritten text images leveraging the Algorithm Unrolling paradigm. We design the network model of BPDUN by unfolding and truncating the traditional iterative back projection algorithm (IBPA). We unroll IBPA into a cascade operation of three building blocks (deep denoising module, low-frequency reconstruction module, and residual projection module). BPDUN inherits the interpretability of the iterative optimization algorithm and is also designed to make the reconstructed text image more realistic and natural. Moreover, we propose a new benchmark dataset to address challenging SR problems of handwritten text image (HDT300). Extensive experiments show that BPDUN obtains an enhanced balance between the performance (quantified by PSNR and SSIM) and the cost (as measured by network parameters). Notably, BPDUN sets new benchmarks on the HDT300 dataset, surpassing previous state-of-the-art approaches by achieving up to 0.2 dB gains in PSNR.

Novel reconstruction method of angle-limited backprojection (ALBP) for low-dose dental panoramic X-ray imaging

Panoramic radiography is a popular two-dimensional X-ray imaging modality in dentistry. It produces a single image of the overall facial view, including the maxillary and mandibular arches and supporting structures. Panoramic images are typically reconstructed using the shift-and-add (SAA) algorithm, in which only structures within a certain image layer are in focus, and others are out of focus on the panoramic image. As the clinical use of panoramic radiography has grown rapidly, radiologists are continuously seeking ways to reduce the radiation dose to patients. This study proposes a novel panoramic reconstruction method called the angle-limited backprojection (ALBP) algorithm for low-dose panoramic X-ray imaging. In ALBP, X-rays that meet the angular criterion established in this study are selected from the measured panoramic projection data and then backprojected onto the spherical voxels placed along the dental arch, as in a typical computed tomography reconstruction. The angular criterion selects X-rays that pass through a given spherical voxel and simultaneously have directional vectors within a prespecified angular range concerning the directional vector at the corresponding source position. To validate the efficacy of the proposed reconstruction method, we conducted a numerical simulation and experiment and investigated the image characteristics. Panoramic images were reconstructed using the SAA and ALBP algorithms with full and half (i.e., half radiation dose) panoramic projections, and their image quality was quantitatively evaluated using the intensity profile and universal quality index (UQI). The image quality of the ALBP with half projections was similar to that of the SAA with full projections, indicating the efficacy of the proposed method. Accordingly, our results demonstrated the potential for radiation dose reduction in panoramic X-ray imaging.

FSSBP: Fast Spatial–Spectral Back Projection Based on Pan-Sharpening Iterative Optimization

Pan-sharpening is an important means to improve the spatial resolution of multispectral (MS) images. Although a large number of pan-sharpening methods have been developed, improving the spatial resolution of MS while effectively maintaining its spectral information has not been well solved so far, and it has also been taken as a criterion to measure whether the sharpened product can meet the practical needs. The back-projection (BP) method iteratively injects spectral information backwards into the sharpened results in a post-processing manner, which can effectively improve the generally unsatisfied spectral consistency problem in pan-sharpening methods. Although BP has received some attention in recent years in pan-sharpening research, the existing related work is basically limited to the direct utilization of the BP process and lacks a more in-depth intrinsic integration with pan-sharpening. In this paper, we analyze the current problems of improving the spectral consistency based on BP in pan-sharpening, and the main innovative works carried out on this basis include the following: (1) We introduce the spatial consistency condition and propose the spatial–spectral BP (SSBP) method, which takes into account both spatial and spectral consistency conditions, to improve the spectral quality while effectively solving the problem of spatial distortion in the results. (2) The proposed SSBP method is analyzed theoretically, and the convergence condition of SSBP and a more relaxed convergence condition for a specific BP type, degradation transpose BP, are given and proved theoretically. (3) Fast computation of BP and SSBP is investigated, and non-iterative fast BP (FBP) and fast SSBP algorithms (FSSBP) methods are given in a closed-form solution with significant improvement in computational efficiency. Experimental comparisons with combinations formed by seven different BP-related post-processing methods and up to 18 typical base methods show that the proposed methods are generally applicable to the optimization of the spatial–spectral quality of various sharpening methods. The fast method improves the computational speed by at least 27.5 times compared to the iterative version while maintaining the evaluation metrics well.

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.

An Efficient Spectrum Reconstruction Algorithm for Non-Uniformly Sampled Signals and Its Application in Terahertz SAR

An efficient spectrum reconstruction algorithm based on the Tikhonov regularization for terahertz (THz) synthetic aperture radar (SAR) azimuth non-uniform sampling is proposed in this article. The high bandwidth, high azimuth resolution, and high frame rate characteristics of THz SAR contribute to its wide application prospects in both military and civilian remote sensing fields. However, the higher azimuth sampling rate also leads to the more severe non-uniform sampling issues of THz SAR. Traditional methods based on the hardware adjustment of pulse repetition frequency (PRF) and simple interpolation for azimuth resampling struggle to meet the higher imaging quality requirements. The back projection algorithm (BPA) can accurately focus non-uniformly sampled data but requires significant computational resources. The algorithm proposed in this paper, which can reconstruct the wavenumber spectrum of SAR azimuth non-uniformly sampled signals, transforms the spectrum reconstruction problem into a linear equation system and solves it using Tikhonov regularization, thereby exhibiting higher computational efficiency compared to BPA. Furthermore, the proposed algorithm is derived from precise theoretical formulations and controls the solution error by utilizing a regularization parameter, leading to a superior imaging quality compared to the azimuth resampling algorithm. In this paper, an accurate spectrum reconstruction formula of non-uniform sampling signals with a finite length is derived, the influence of noise error on the solution is analyzed, and the THz SAR azimuth non-uniform sampling signals are processed from the wavenumber domain. Finally, simulation and experimental results verify the effectiveness of the proposed algorithm.

Synthetic Photoconductive Antenna Array for Terahertz 3-D Imaging and Spectroscopy

We propose a 3D imaging and spectroscopy approach in the terahertz (THz) domain based on the synthetic aperture (SA) imaging technique achieved using a time domain spectroscopy system (TDS). The proposed system enables the imaging and spectroscopy of an object in a stationary position in transmission configuration. We demonstrate the reconstruction of 3D amplitude images with a sub-millimeter resolution of a multi-material object from 0.6 to 1 THz using the back-projection algorithm. The reconstructed data is further used to characterize the optical properties of the substrates forming the object by calculating the refractive index and the absorption coefficient of its constituents in the reconstruction frequency band. We demonstrate the use of the SA not only for imaging, but also for material characterization. Consequently, we are able to reconstruct 2D high-resolution spectral maps of the real refractive index at different THz frequencies of the imaged object.

A highly accurate quantum optimization algorithm for CT image reconstruction based on sinogram patterns

Computed tomography (CT) has been developed as a nondestructive technique for observing minute internal images in samples. It has been difficult to obtain photorealistic (clean or clear) CT images due to various unwanted artifacts generated during the CT scanning process, along with the limitations of back-projection algorithms. Recently, an iterative optimization algorithm has been developed that uses an entire sinogram to reduce errors caused by artifacts. In this paper, we introduce a new quantum algorithm for reconstructing CT images. This algorithm can be used with any type of light source as long as the projection is defined. Assuming an experimental sinogram produced by a Radon transform, to find the CT image of this sinogram, we express the CT image as a combination of qubits. After acquiring the Radon transform of the undetermined CT image, we combine the actual sinogram and the optimized qubits. The global energy optimization value used here can determine the value of qubits through a gate model quantum computer or quantum annealer. In particular, the new algorithm can also be used for cone-beam CT image reconstruction and for medical imaging.

Void fraction measurement of gas–liquid two-phase flow based on compressed sensing theory and capacitively coupled electrical resistance tomography system

Capacitively coupled electrical resistance tomography (CCERT) is an innovative technique for electrical resistance tomography based on capacitively coupled contactless conductivity detection (C4D). Despite its potential, there are only a few studies on image reconstruction algorithms for CCERT. To address this, a CCERT measurement system is developed, and the compressed sensing (CS) theory is applied to the inverse problem imaging of CCERT to improve the image reconstruction quality and speed. Firstly, a mathematical CCERT image reconstruction model is constructed under CS theory and three algorithms under CS theory are employed to solve the convex optimization problem of the reconstruction model. Then a thresholding operation is applied to obtain the post-processed image and compared it with the classical linear back projection and Landweber algorithms. The simulation results demonstrate that the Barzilai–Borwein gradient projection for sparse reconstruction (GPSR-BB) algorithm yields more satisfactory imaging results than the other four algorithms. Additionally, three sensitivity matrix optimization methods for GPSR-BB algorithm are compared and find that the new method of screening the rows of the sensitivity matrix to zero is more effective than the other two common optimization methods in terms of reconstructed image quality. Finally, the static experiments of void fraction measurement are conducted using the developed CCERT system. The results indicated that the absolute error of void fraction measurement by GPSR-BB algorithm was less than 6.59% in the range of void fraction from 0.90% to 66.29%.

First Experimental Demonstration of the Use of a Novel Planar Segmented HPGe Detector for Gamma Emission Tomography of Mockup Fuel Rods

Postirradiation examination of nuclear fuel is routinely performed to characterize the important properties of current and future fuel. Gamma emission tomography is a proven noninvasive technique for this purpose. Among various measurement elements of the technique, a gamma-ray detector is an important element whose spectroscopic abilities and detection efficiency affect the overall results. Finding a combination of high detection efficiency and excellent energy resolution in a single detector is often a challenge. We have designed a novel planar segmented high-purity germanium detector that offers simultaneous measurement in six lines of sight with excellent energy resolution. The simultaneous detection ability enables faster data acquisition in a tomographic measurement, which may facilitate achieving higher spatial resolution. In this work, we have demonstrated the first use of the detector by performing a full tomographic measurement of mockup fuel rods. Two methods of detector data analysis were used to make spectra, and the images (tomograms) were reconstructed using the filtered back projection algorithm. The reconstructed images validate the successful use of the detector for tomographic measurement. The use of the detector for real fuel measurement is being planned and will be performed in the near future.