Backprojection Algorithm Research Articles

Machine learning‐driven microwave imaging for soil moisture estimation near leaky pipe

AbstractCharacterizing soil moisture around drip irrigation pipes is crucial for precise and optimized farming. Machine learning (ML) approaches are particularly suitable for this task as they can reduce uncertainties caused by soil conditions and the drip pipe positions, using features extracted from relevant datasets. This letter addresses local moisture detection in the vicinity of dripping pipes using a portable microwave imaging system. The employed ML approach is fed with two dimensional images generated using back projection as a radar‐based algorithm and the Born approximation as an inverse scattering method, based on spatio‐temporal (collected data at various positions over the soil surface and at different time points.) measurements at various frequencies. The study investigates the performance of K‐nearest neighbour (KNN) and convolutional neural networks (CNN) algorithms for moisture classification based on these imaging techniques. We also explore the potential of KNN and CNN for moisture estimation around the plant roots and in the presence of pebbles. In general, CNN outperforms KNN in moisture content detection from microwave data, especially after applying imaging algorithms. A combination of CNN as the ML approach and the back projection algorithm to provide training data, yielded accuracy more than other models for moisture content estimation. Also, the practical results demonstrate that our method can detect soil moisture with an estimation error of less than 10%.

Comparative Study of GPR Acquisition Methods for Shallow Buried Object Detection

This paper investigates the use of ground-penetrating radar (GPR) technology for detecting shallow buried objects, utilizing an air-coupled stepped frequency continuous wave (SFCW) radar system that operates within a 2 GHz bandwidth starting at 500 MHz. Different GPR data acquisition methods for air-coupled systems are compared, specifically down-looking, side-looking, and circular acquisition strategies, employing the back projection algorithm to provide focusing of the acquired GPR data. Experimental results showed that the GPR can penetrate up to 0.6 m below the surface in a down-looking mode. The developed radar and the back projection focusing algorithm were used to acquire data in the side-looking and circular mode, providing focused images with a resolution of 0.1 m and detecting subsurface objects up to 0.3 m below the surface. The proposed approach transforms B-scans of the GPR-based data into 2D images. The provided approach has significant potential for advancing shallow object detection capabilities by transforming hyperbola-based features into point-like features.

Radiation dose reduction and image quality in pediatric paranasal sinus CT: with automatic tube current modulation and iterative reconstruction technique.

Our objective is to evaluate radiation dose and image quality in pediatric paranasal sinus computed tomography (CT) with automatic tube current modulation (ATCM) and sinogram-affirmed iterative reconstruction algorithm (SAFIRE). CT scans from 80 patients were divided into two groups: Group A [80 kVp, pitch 1.5, 40 mAs, the filtered back projection (FBP) algorithm] and Group B (70 kVp, pitch 3, ATCM with reference at 40 mAs, SAFIRE strengths 1-5). We have evaluated image quality and radiation dose. Group B demonstrated significantly lower volume computed tomography dose index, dose-length product, and effective dose than Group A (0.13±0.03 vs. 1.57±0.01mGy, 2.27±0.82 vs. 19.88±2.01mGy·cm, and 0.0081±0.0017 vs. 0.079±0.013mSv, respectively; P<.001). Increasing SAFIRE strengths correlated with noise reduction and SNR enhancement. Group B's noise and SNRsoft at SAFIRE strength 5 were comparable with Group A. Images reconstructed with SAFIRE strength 5 in Group B exhibit comparable image quality with FBP in Group A.

Development of a proton CT imaging system using scintillator-based range detection.

The accuracy of proton therapy and preclinical proton irradiation experiments is susceptible to proton range uncertainties, which partly stem from the inaccurate conversion between CT numbers and relative stopping power (RSP). Proton computed tomography (PCT) can reduce these uncertainties by directly acquiring RSP maps. This study aims to develop a novel PCT imaging system based on scintillator-based proton range detection for accurate RSP reconstruction. The proposed PCT system consists of a pencil-beam brass collimator with a 1mm aperture, an object stage capable of translation and 360° rotation, a plastic scintillator for dose-to-light conversion, and a complementary metal oxide semiconductor (CMOS) camera for light distribution acquisition. A calibration procedure based on Monte Carlo (MC) simulation was implemented to convert the obtained light ranges into water equivalent ranges. The water equivalent path lengths (WEPLs) of the imaged object were determined by calculating the differences in proton ranges obtained with and without the object in the beam path. To validate the WEPL calculation, measurements of WEPLs for eight tissue-equivalent inserts were conducted. PCT imaging was performed on a custom-designed phantom and a mouse, utilizing both 60 and 360 projections. The filtered back projection (FBP) algorithm was employed to reconstruct the RSP from WEPLs. Image quality was assessed based on the reconstructed RSP maps and compared to reference and simulation-based reconstructions. The differences between the calibrated and reference ranges of 110-150 MeV proton beams were within 0.18mm. The WEPLs of eight tissue-equivalent inserts were measured with accuracies better than 1%. Phantom experiments exhibited good agreement with reference and simulation-based reconstructions, demonstrating average RSP errors of 1.26%, 1.38%, and 0.38% for images reconstructed with 60 projections, 60 projections after penalized weighted least-squares algorithm denoising, and 360 projections, respectively. Mouse experiments provided clear observations of mouse contours and major tissue types. MC simulation estimated an imaging dose of 3.44 cGy for decent RSP reconstruction. The proposed PCT imaging system enables RSP map acquisition with high accuracy and has the potential to improve dose calculation accuracy in proton therapy and preclinical proton irradiation experiments.

A single-layer compton camera for nuclear decommissioning: An improved back-projection algorithm

The decommissioning of nuclear facilities, a critical and hazardous process due to radiation exposure, necessitates the advancement of radiological measurement techniques concerning safety and efficiency. This study presents an optimized back-projection method, integrating a novel single-layer Compton camera and 3D camera setup with the Timepix3 readout chip to improve the precision and efficiency of gamma-ray source localization in decommissioning scenarios. Implementing ‘twin addition’ and ‘twin multiplication’ techniques addressed data ambiguities that arise from event selection in the Compton camera, enhancing the reliability of localization. Introducing a zoom function significantly improved computational efficiency, achieving 163 times faster computation times without sacrificing accuracy. Our method demonstrated enhanced precision with a median angular error of 1.41°, outperforming traditional methods and showing competitive advantages over state-of-the-art technologies, including the Caliste-HD detector. The feasibility of integrating this methodology onto mobile robotic platforms suggests a promising avenue to minimize human radiation exposure and optimize decommissioning tasks, ensuring safer and more effective nuclear facility decommissioning.

A direct comparison of multi-energy x-ray and proton CT for imaging and relative stopping power estimation of plastic and ex-vivo phantoms

Objective.Proton therapy administers a highly conformal dose to the tumour region, necessitating accurate prediction of the patient's 3D map of proton relative stopping power (RSP) compared to water. This remains challenging due to inaccuracies inherent in single-energy computed tomography (SECT) calibration. Recent advancements in spectral x-ray CT (xCT) and proton CT (pCT) have shown improved RSP estimation compared to traditional SECT methods. This study aims to provide the first comparison of the imaging and RSP estimation performance among dual-energy CT (DECT) and photon-counting CT (PCCT) scanners, and a pCT system prototype.Approach.Two phantoms were scanned with the three systems for their performance characterisation: a plastic phantom, filled with water and containing four plastic inserts and a wood insert, and a heterogeneous biological phantom, containing a formalin-stabilised bovine specimen. RSP maps were generated by converting CT numbers to RSP using a calibration based on low- and high-energy xCT images, while pCT utilised a distance-driven filtered back projection algorithm for RSP reconstruction. Spatial resolution, noise, and RSP accuracy were compared across the resulting images.Main results.All three systems exhibited similar spatial resolution of around 0.54 lp/mm for the plastic phantom. The PCCT images were less noisy than the DECT images at the same dose level. The lowest mean absolute percentage error (MAPE) of RSP,(0.28±0.07)%, was obtained with the pCT system, compared to MAPE values of(0.51±0.08)%and(0.80±0.08)%for the DECT- and PCCT-based methods, respectively. For the biological phantom, the xCT-based methods resulted in higher RSP values in most of the voxels compared to pCT.Significance.The pCT system yielded the most accurate estimation of RSP values for the plastic materials, and was thus used to benchmark the xCT calibration performance on the biological phantom. This study underlined the potential benefits and constraints of utilising such a novelex-vivophantom for inter-centre surveys in future.

A modified capacitance tomography image reconstruction approach based on iterative shrinkage-thresholding algorithm combined with deep networks

Abstract Due to the ‘soft-field’ effect and the challenges posed by ill-posed and ill-conditioned inverse problems, it is difficult to obtain high quality images from an electrical capacitance tomography (ECT) system. To achieve both high-quality images and fast imaging speed with limited measurement data, an image reconstruction algorithm, which was initially proposed for compressive sensing, is adapted for ECT image reconstruction to optimize the ill-posed nature of its inverse problem. The proposed algorithm leverages deep learning networks inspired by the iterative shrinkage-thresholding algorithm (ISTA), thereby creating a model that is both mathematically interpretable and endowed with trainable parameters. Building upon this foundation, the conventional Landweber iteration is integrated with the ISTA-Net to refine the optimization process for ECT image reconstruction. In order to propose an effective model adapting to the actual multiphase flow characteristics and complex flow pattern changes, the training and test process is driven by a comprehensive dataset generated from dynamic simulations, rather than artificial samples of multiphase distributions. This numerical methodology simulates the dynamic measurement process of a virtual ECT sensor by coupling the gas–liquid two-phase flow field and the ECT electrostatic field. The results of the testing phase indicate that the proposed algorithm outperforms traditional ECT image reconstruction methods. Compared with the linear back projection algorithm, the average image error and gas fraction error have been reduced by 20.44% and 16.74%, respectively, while maintaining a computational speed comparable to that of the Landweber iteration. The accuracy of the new algorithm in reconstructing the two-phase interface and estimating the gas fraction has been validated by static experimental tests, showing its potential for practical application in online gas–liquid two-phase flow measurement scenarios.

Optimised electrical resistance tomography performance for coarse-particle suspensions with a settled bed

Electrical Resistance Tomography (ERT) offers a non-intrusive method to visualise the dynamic distribution of internal solids in suspension flows. While ERT can produce good qualitative images, quantitative analysis faces challenges due to low spatial resolution, sensitivity to electric noise, and the ill-posed nature of the inverse problem. This study aims to enhance ERT's performance for coarse-particle suspensions by considering system configuration, injection current, background conductivity and reconstruction techniques. Validation is performed on both static and dynamic suspensions with physically sensible flow scenarios. To ensure high-quality ERT data acquisition, the background conductivity must allow a range of injection current while maintaining a favourable signal-to-noise ratio. A more conductive carrier is needed for effective current injection in densely packed beds or larger-scale pipes. Reconstruction based on current and voltage measurements following Ohm's law is essential. The commonly adopted Linear Back Projection (LBP) algorithm in a commercial ERT system exhibits limited information in the bed-occupied area, leading to underestimations of integrated concentration. ERT predictions of chord-averaged concentration profiles in a dynamic suspension display similar trends as those from the one-dimensional Eskin model. When compared to experimental measurements, ERT results generally underestimate the integrated concentration by approximately 15 % v/v in a dynamic suspension.

Accurate extraction method of multi-laser stripes for stereo-vision based handheld scanners in complex circumstances

A technique for extracting multiline lasers is proposed for handheld scanner. First, a robust matching method for multi-lasers is presented in this work to distinguish every laser stripe in the left and right images by using back-projection algorithm. Then, an improved DBSCAN (Density-Based Spatial Clustering of Applications with Noise) clustering method is promoted to detect noise in the laser images caused by complex scenarios. This approach is focused on the features of the laser stripes in the images, such as normal vectors, stripe width and gray values. These parameters are used as the criteria to find the noise in the images. After the calibration results of stereo-vision and laser-matching results are combined, the 3D information of the noise parts in the laser stripes are recovered accurately. Finally, a subpixel interpolation method based on Shepard interpolation is used to achieve the precise subpixel centerline extraction of laser stripes. And the experiments further valide the effectiveness of the proposed method.

Rare-earth dopant distribution measurement of optical fibers based on filtered back projection

We present a nondestructive measurement based on filtered back projection (FBP) for the distribution of rare-earth dopant in optical fibers. Based on the approach, a measurement system is established, where the single-mode pumped laser illuminates the fiber under test from the side, generating multi-wavelength fluorescence through photoluminescence (PL). The distribution of rare-earth doped particles is proportional to the distribution of fluorescence intensity. The projection images are collected by the CCD camera at 90° relative to the excitation arm. According to the computed tomography (CT), the rotation of the optical fiber enables the experimental measurements of intensity information extracted from multi-angle projections. The rare-earth dopant distribution of the fiber is reconstructed by the improved filtered back projection algorithm, which improves the quality of the reconstructed result by incorporating total variation (TV) algorithm. To evaluate the proposed approach, rare-earth dopant distribution is compared with results measured by EPMA, exhibiting a correlation coefficient above 0.99, and the relationship between the dopant distribution and the refractive index is analyzed. Measurements on doped particle distributions at various wavelengths are conducted, and the fluorescence spectrum are constructed to further analyze the fluorescence characteristics of rare earth doped fiber. Measurement of RE dopant distribution will be useful for quality evaluation and optimization of partial active optical fibers.

A Fast Inverse Synthetic Aperture Radar Imaging Scheme Combining GPU-Accelerated Shooting and Bouncing Ray and Back Projection Algorithm under Wide Bandwidths and Angles

A Fast Inverse Synthetic Aperture Radar Imaging Scheme Combining GPU-Accelerated Shooting and Bouncing Ray and Back Projection Algorithm under Wide Bandwidths and Angles

A novel BP algorithm‐based UWB MIMO ground‐penetrating imaging system

AbstractUltra‐wideband (UWB) multiple input multiple output (MIMO) radar has been widely used in detection systems due to its advantages, such as low cost and high data acquisition capability. The detection system is applied in various ground‐penetrating applications, including mine detection and earthquake rescue. In this paper, a novel UWB MIMO radar system based on step‐frequency continuous wave is designed for underground target detection. To improve the penetration depth and high‐range resolution, a new miniature Vivaldi antenna with a bandwidth of 1–3 GHz is designed and integrated into the ground‐penetrating imaging system. Furthermore, a multiscale weighted time‐domain back projection (BP) algorithm is proposed to suppress artifacts and reduce the computational complexity of the BP algorithm. The designed system is tested by detecting stationary targets. The experimental results agree well with the simulation. The reconstructed images show that the designed MIMO radar system can successfully image underground targets.

Geometric artifacts correction of equiangular fan-beam industrial CT system

To address the issue of geometric artifacts in equiangular fan-beam industrial computed tomography (CT) systems, this paper proposes a projection sinogram-based method for correcting these artifacts. Firstly, we discuss the formation mechanism of geometric artifacts in equiangular fan-beam industrial CT system when there is geometric deviation. Secondly, we establish a geometric model that incorporates these deviations and mathematically describe the projected position curve of a point within the plane. Subsequently, we use a needle gauge as a surrogate for the point, and fit the curve in the projection sinusoidal graph obtained from scanning the needle gauge to calibrate the geometric deviations. Finally, we introduce the calibrated geometric deviations into the filtered back projection (FBP) algorithm to achieve more accurate reconstructed images. The proposed method precisely calibrates geometrical deviations in the equiangular fan-beam industrial computed tomography (CT) system and effectively eliminates geometric artifacts in the reconstructed CT images, this is demonstrated by simulation and practical experiment. This method has also been successfully applied in engineering practice.

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.

DdeNet: A dual-domain end-to-end network combining Pale-Transformer and Laplacian convolution for sparse view CT reconstruction

Sparse view (SV) computed tomography (CT) is a clinical diagnostic technique aimed at reducing radiation dose to the human body from X-rays. However, SVCT reconstructed using conventional filtered back-projection (FBP) algorithms will produce severe streak artifacts. In recent years, convolutional neural networks (CNNs) have demonstrated considerable success in addressing the inverse problem of SVCT reconstruction. However, the local convolutional operations of CNNs ignores long-range dependencies of contextual feature information, thereby limiting their capability in feature extraction. To address this limitation, we propose a dual-domain end-to-end network (DdeNet) combining Pale-Transformer and Laplacian convolution for SVCT reconstruction. Initially, in the projection domain, a UNet is employed to restore the interpolated sinogram. Subsequently, in the image domain, we introduce Pale-Transformer and Laplacian convolution to design a dual-stream feature fusion network for finely restoring the CT images reconstructed by FBP. The dual-stream feature fusion network comprises an image restoration network (IRN) module and an edge enhancement network (EEN) module. The depthwise separable convolution based modified pale-shaped self-attention mechanism in Pale-Transformer captures global feature information of the CT image in the IRN, while the Laplacian convolution and multi-scale convolution block with a squeeze and excitation mechanism in the EEN further extract and restore edge feature information of the CT image. Finally, the feature information output from IRN and EEN is fused along the channel dimension and then convolved to obtain the final reconstructed CT image. Experimental results demonstrate that DdeNet exhibits superior generalization and reconstruction performance compared to the previous CNN or Transformer-based reconstruction methods.

Ultra-wideband Imaging of Breast Tumors Based on Global Back Projection Algorithm

Abstract Tumor imaging in medicine requires consideration of human safety, image quality clarity, and cost of imaging. Ultra-wideband (UWB) technology employs large bandwidth channels that enable high-speed data transmission. This determines that it can provide high-quality images quickly while still being a harmless imaging method. Therefore, it is essential to construct a UWB microwave detection tumor system. The creation of a vector network analyzer (VNA) based microwave imaging system in this work. To adapt to breast imaging, this paper improved the imaging algorithm of global back projection (GBP) based on the classical back projection algorithm. To verify the system’s feasibility, this paper performed UWB detection experiments using a breast tumor model. By comparing the simulation results, the final imaging results show that the UWB imaging system can detect tumors located at two different locations in the model and that high-quality images can be obtained in the near field using the GBP algorithm. This paper provides a reliable and low-cost method for medical diagnosis.

ISAR Imaging for Drone Detection Based on Backprojection Algorithm Using Millimeter-Wave Fast Chirp Modulation MIMO Radar

ISAR Imaging for Drone Detection Based on Backprojection Algorithm Using Millimeter-Wave Fast Chirp Modulation MIMO Radar

Reconstruction of Tomographic Size Using a Filtered Back Projection Algorithm

Due to their widespread use, image processors are among the most essential computer processors. FBP technique is one of the most widely used tomographic reconstruction methods. Images from a computed tomography (CT) scanner with 512x512 pixels of raw data for parallel beam projections are the metadata to which this approach is applied. This work is divided into three parts. Several projections are created from an input test picture termed Shepp-Logan phantom in the first section, utilizing radon transformation. The picture is rebuilt from the projection of a parallel beam in the second section to minimize reconstruction time. Finally, the proposed system filters the projections using the Ram Lak filter and the Hann window in the third section to refine the picture and then recombine the projections to generate the reconstructed image. The reconstruction procedure is performed on CT images using a filtered back-projection algorithm in this article for image optimization and then projection recombination to generate the rebuilt picture. Since CT can accurately depict anatomical elements like bones and organs and may pick slides in any orientation, it is frequently used in biological applications and diagnostics. It also offers a great spatial resolution and soft tissue contrast. We develop, create, and run computer programs when we work with MATLAB. After projecting the 2D image onto a CT scanner, a very good result in reconstructing the image is received.

Reconstruction of Tomographic Size Using a Filtered Back Projection Algorithm

Due to their widespread use, image processors are among the most essential computer processors. FBP technique is one of the most widely used tomographic reconstruction methods. Images from a computed tomography (CT) scanner with 512x512 pixels of raw data for parallel beam projections are the metadata to which this approach is applied. This work is divided into three parts. Several projections are created from an input test picture termed Shepp-Logan phantom in the first section, utilizing radon transformation. The picture is rebuilt from the projection of a parallel beam in the second section to minimize reconstruction time. Finally, the proposed system filters the projections using the Ram Lak filter and the Hann window in the third section to refine the picture and then recombine the projections to generate the reconstructed image. The reconstruction procedure is performed on CT images using a filtered back-projection algorithm in this article for image optimization and then projection recombination to generate the rebuilt picture. Since CT can accurately depict anatomical elements like bones and organs and may pick slides in any orientation, it is frequently used in biological applications and diagnostics. It also offers a great spatial resolution and soft tissue contrast. We develop, create, and run computer programs when we work with MATLAB. After projecting the 2D image onto a CT scanner, a very good result in reconstructing the image is received.

IMAGING OF BUBBLY FLOW USING ULTRASOUND

Flow measurement is a vital ‎issue in instrumentation and has been applied in the various industries. The characteristics of a single phase regime has been extensively researched. On the other hand obtaining the characteristics of a multi-component flow is more complex and traditional equipment do not provide ‎reliable results. As such, tomography utilizing non-invasive ‎transducers is getting attention in the industries because it does not invade the flow. Ultrasonic tomography is among the methods which is suitable for flow containing bubbles. In this project, 16 ultrasonic transducers are placed around a flow pipe. Five different phantoms representing solid flow are placed in the pipe. The flow is imaged using the linear back projection algorithm. The results show that the system was able to image the phantoms which are placed at different locations.