Convolution Backprojection Research Articles

Improvement of the longitudinal phase space tomography at the J-PARC synchrotrons

The longitudinal phase space tomography, which reconstructs the phase space distribution from the one-dimensional bunch profiles, is used in various accelerators to measure longitudinal beam parameters. At the J-PARC, an implementation of the phase space tomography based on the Convolution Back Projection method (CBP) has been used to measure the momentum spread of the injected beam. The method assumes that the beam distribution rotates without significant deformation during the synchrotron oscillation. Because of the nonlinearity of synchrotron motion with sinusoidal RF voltage, the method can be used only in limited situations such as small amplitude synchrotron oscillation. Algebraic Reconstruction Techniques (ART) in conjunction with particle tracking, which is implemented in the CERN’s tomography code, allows accurate reconstructions even for nonlinear large amplitude synchrotron oscillations. We present the overview of the application of the CERN’s tomography code to the J-PARC synchrotrons. The results of benchmarking are also reported.

Inverse synthetic aperture lidar imaging and compensation in slant atmospheric turbulence with phase gradient algorithm compensation

To systematically study the influence of slant atmospheric turbulence on the inverse synthetic aperture lidar (ISAL) imaging, the atmospheric random phase screen with the modified von Kármán spectrum was numerically simulated via the fast Fourier transform spectral inversion method. Intensity phase distribution and brightness images of the Gaussian beam slant transmission were simulated under different turbulence intensities. Using the Kirchhoff approximation and convolution back-projection algorithm, ISAL images of rough surface (rough square and rough circular plates), rough graphics and rough body with different roughnesses under various turbulence intensities were obtained. The analyses showed that these ISAL images of rough targets can be resolved under weak turbulence but not under moderately strong turbulence. Aiming at the reduction of the resolution of the rough target ISAL images caused by atmospheric turbulence, the phase gradient autofocus (PGA) algorithm was used to improve image focusing and distinguish the shapes of rough targets.

Two-dimensional and pseudo three-dimensional visualisation of foreign objects in milk carton using ultrasonic tomography

This paper presents the development of two-dimensional and pseudo three-dimensional visualisation of foreign object in milk carton using ultrasonic tomography system. Mathematical modelling based on ultrasonic amplitude wave and correlation between ultrasonic projection distance and voltage sensor are elaborated in this paper. Physical hazard contaminants such as metal, plastic, wood and glass materials were placed in the milk. The forward problem and the inverse problem of image reconstruction technique have been discussed briefly. 2D images of the contaminants are reconstructed using Linear Back-Projection (LBP) and Convolution Back-Projection (CBP) with Hanning, Hamming and Ram-Lak filter. A median filter technique has been combined to the algorithms for filtering noise of reconstructed images. The results show that image reconstruction using CBP-Ram-Lak has significantly yield the best image reconstruction for most tested phantoms. The application of median filter with 20 × 20 matrix have obtained a better image quality as they achieved the best values of PSNR and SSIM compared to non-median filter with 13.2765 and 0.7318, respectively for pairs of metal A - glass B (phantom Y-2). Pseudo three-dimensional (3D) image reconstruction for the foreign object has been carried out to provide more sufficient monitoring process in milk cartons. The 3D images were constructed based on stacking the 2D slice images in z-axis. Thus, the exact location of the object in the milk carton can be exposed clearly from various viewing angles. The results indicate that the ultrasonic tomography imaging system promises to be a non-invasive tool in quality monitoring especially for the detection of foreign objects in milk carton.

Analysis of Error in Convolution Algorithm for Tomography in Discrete Spaces

In this paper simulation results of the error in computed tomography technique for discrete space is presented. In computerized tomography, due to ill posed and non-linear nature of reconstruction algorithms, the efficient algorithms are required for both medical and industry process. The error analysis for approximation algorithms of computerized tomography is necessary to check the efficiency of algorithm. The filter function for algorithm with some moments properties are already known. The use of same bandlimited filter with different number of rays in each projection data leads to different reconstruction and approximation nature of algorithm arises error in the implementation. The results of our theorem for different values are found to be compared with classic convolution back-projection algorithm.

Research on tomographic image reconstruction algorithms based on fixed-point rotation X-CT system

Aiming at the problem of parameter calibration and image reconstruction of typical two-dimensional CT system, this paper uses back projection, iradon function, Fourier transform, Lambert law, visualization and other methods to establish projection centroid model, convolution back projection model, TV constrained iterative filtering back projection model, and uses MATLAB, Solidworks, Lingo and other software to visualize data types, so as to achieve better results. Better to find X-CT system tomography reconstruction methods.

Experimental Research on Interferometric Inverse Synthetic Aperture Radar Imaging with Multi-Channel Terahertz Radar System.

The all solid-state terahertz (THz) radar has obvious miniaturized integration and high resolution imaging advantages compared with conventional microwave radar. In this paper, a 0.22 THz active frequency-modulated pulse radar system with one transmission channel and four receiving channels is presented, and interferometric inverse synthetic aperture radar (InISAR) imaging experiments, which can acquire altitude information of objects, are carried out. In order to acquire high-quality InISAR images, a calibration method is presented to solve the nonlinearity of wideband signal frequency and phase inconsistency of different receiving channels together. Furthermore, to deal with the phase wrapping in InISAR imaging of objects with large scale, a novel method based on the dominant scatterers to estimate the objects rotation rate is presented. Finally, to show more information of objects in the InISAR images, the imaging results with a large rotation angle by the convolutional back-projection algorithm are obtained. The imaging results verify the superior performance of the multi-channel THz radar system and the imaging processing method, which can provide support for further research on InISAR imaging in the THz band.

Image Reconstruction Enhancement Using Convolution Back Projection Method for Electrical Tomography Application

This paper presents an image enhancement technique using convolution back-projection (CBP) technique to overcome the blurry issue caused by linear back-projection (LBP) technique on tomographic images. The CBP technique is discussed and employed on four different types of stratified flow test profiles. The obtained image results are compared between LBP and CBP and further assessed using mutual structural similarity index (MSSIM). The enhancement technique has successfully scored MSSIM rating above 0.9 for all four test profiles whereby the rating is ranging from 0 (poor quality) to 1 (best quality).

Orbital-Angular-Momentum-Based ISAR Imaging at Terahertz Frequencies

The electromagnetic (EM) wave carrying orbital angular momentum (OAM) is usually named vortex EM wave, which has been found great potential to improve the target imaging performance. For conventional ISAR imaging, only 2-D target image can be obtained. In this paper, the OAM-based ISAR technique is developed to achieve 3-D target image with high resolution at terahertz frequencies. First, the imaging model is derived, and the point spread function is analyzed. Subsequently, two imaging algorithms, namely the FFT-based imaging method and the imaging method based on convolution backprojection and power spectrum density estimation, are proposed. Simulation results validate the effectiveness of the proposed methods and indicate that the high-resolution cross-range profile can still be obtained at terahertz frequencies with small rotational angle. This paper can provide a novel manner to realize 3-D imaging of universal targets with high resolution.

Ultrasonic tomography for detecting foreign objects in refrigerated milk cartons

This study presents an investigation of the detection of foreign objects in milk cartons using an ultrasonic tomography measurement system. Ultrasonic parameters such as acoustic impedance and wave amplitude were modelled and investigated using foreign materials of different densities such as metal, glass, wood and plastic. Linear back‐projection (LBP) and convolution back‐projection (CBP) algorithms with Hanning, Hamming and Ram‐Lak filters were implemented to reconstruct two‐dimensional cross‐sectional images of the milk and the foreign objects. The image quality assessment was conducted using the peak signal‐to‐noise ratio (PSNR) and structural similarity index (SSIM). The results revealed that the CBP‐Ram‐Lak filters managed to obtain the clearest and the sharpest reconstructed images as they achieved the best values of PSNR and SSIM (15.4537 and 0.8683, respectively) for a single glass material. It is envisaged that the ultrasonic tomography method can be very useful for monitoring the quality and safety of milk products, especially for detecting physical contaminants.

Research on Synthetic Aperture Radar Processing for the Spaceborne Sliding Spotlight Mode.

Gaofen-3 (GF-3) is China’ first C-band multi-polarization synthetic aperture radar (SAR) satellite, which also provides the sliding spotlight mode for the first time. Sliding-spotlight mode is a novel mode to realize imaging with not only high resolution, but also wide swath. Several key technologies for sliding spotlight mode in spaceborne SAR with high resolution are investigated in this paper, mainly including the imaging parameters, the methods of velocity estimation and ambiguity elimination, and the imaging algorithms. Based on the chosen Convolution BackProjection (CBP) and PFA (Polar Format Algorithm) imaging algorithms, a fast implementation method of CBP and a modified PFA method suitable for sliding spotlight mode are proposed, and the processing flows are derived in detail. Finally, the algorithms are validated by simulations and measured data.

The Influence of Reconstruction Kernel on Bone Mineral and Strength Estimates Using Quantitative Computed Tomography and Finite Element Analysis

Quantitative computed tomography has been posed as an alternative imaging modality to investigate osteoporosis. We examined the influence of computed tomography convolution back-projection reconstruction kernels on the analysis of bone quantity and estimated mechanical properties in the proximal femur. Eighteen computed tomography scans of the proximal femur were reconstructed using both a standard smoothing reconstruction kernel and a bone-sharpening reconstruction kernel. Following phantom-based density calibration, we calculated typical bone quantity outcomes of integral volumetric bone mineral density, bone volume, and bone mineral content. Additionally, we performed finite element analysis in a standard sideways fall on the hip loading configuration. Significant differences for all outcome measures, except integral bone volume, were observed between the 2 reconstruction kernels. Volumetric bone mineral density measured using images reconstructed by the standard kernel was significantly lower (6.7%, p < 0.001) when compared with images reconstructed using the bone-sharpening kernel. Furthermore, the whole-bone stiffness and the failure load measured in images reconstructed by the standard kernel were significantly lower (16.5%, p < 0.001, and 18.2%, p < 0.001, respectively) when compared with the image reconstructed by the bone-sharpening kernel. These data suggest that for future quantitative computed tomography studies, a standardized reconstruction kernel will maximize reproducibility, independent of the use of a quantitative calibration phantom.

Single-Plane Dual-Modality Tomography for Multiphase Flow Imaging by Integrating Electrical Capacitance and Ultrasonic Sensors

This paper presents an experimental study of a single-plane dual-modality tomography (DMT) system integrating electrical capacitance tomography (ECT) and ultrasonic tomography (UT) for water–oil–gas three-phase flow imaging. The soft-field (ECT) and hard-field (UT) systems measure different physical parameters, making them both a fine combination in complementing each system’s limitations. The DMT system consists of 16 units of customized ECT sensors and 16 units of UT transducers, which are composited on a single-plane arrangement to perform concurrent measurement. A finite-element method is used to model and study its feasibility and performance before engaging with the actual hardware. The DMT system is carried out on a vertical test column and horizontal stratified flow to obtain sensor data from each modality by inspection of separate tomographic image using linear back-projection (LBP) image reconstruction algorithm and convolution back projection with Gaussian filtering (CBPF). A fuzzy logic pixel fusion method is used for image fusion process. To evaluate the reconstructed images, the mean structural similarity index (MSSIM) method and the mutual information method ( $M_{F})$ are employed on both the LBP and CBPF image results. The analysis and assessments proved that the CBPF method has successfully improvised the image results and thus has better MSSIM rating and $M_{F}$ over the LBP method with an enhancement up to 12.55% and 8.92%, respectively.

Efficient Terahertz Wide-Angle NUFFT-Based Inverse Synthetic Aperture Imaging Considering Spherical Wavefront.

An efficient wide-angle inverse synthetic aperture imaging method considering the spherical wavefront effects and suitable for the terahertz band is presented. Firstly, the echo signal model under spherical wave assumption is established, and the detailed wavefront curvature compensation method accelerated by 1D fast Fourier transform (FFT) is discussed. Then, to speed up the reconstruction procedure, the fast Gaussian gridding (FGG)-based nonuniform FFT (NUFFT) is employed to focus the image. Finally, proof-of-principle experiments are carried out and the results are compared with the ones obtained by the convolution back-projection (CBP) algorithm. The results demonstrate the effectiveness and the efficiency of the presented method. This imaging method can be directly used in the field of nondestructive detection and can also be used to provide a solution for the calculation of the far-field RCSs (Radar Cross Section) of targets in the terahertz regime.

Inverse problems-based maximum likelihood estimation of ground reflectivity for selected regions of interest from stripmap SAR data

In this paper, we derive a comprehensive forward model for the data collected by stripmap synthetic aperture radar (SAR) that is linear in the ground reflectivity parameters. It is also shown that if the noise model is additive, then the forward model fits into the linear statistical model framework, and the ground reflectivity parameters can be estimated by statistical methods. We derive the maximum likelihood (ML) estimates for the ground reflectivity parameters in the case of additive white Gaussian noise. Furthermore, we show that obtaining the ML estimates of the ground reflectivity requires two steps. The first step amounts to a cross-correlation of the data with a model of the data acquisition parameters, and it is shown that this step has essentially the same processing as the so-called convolution back-projection algorithm. The second step is a complete system inversion that is capable of mitigating the sidelobes of the spatially variant impulse responses remaining after the correlation processing. We also state the Cramer-Rao lower bound (CRLB) for the ML ground reflectivity estimates.We show that the CRLB is linked to the SAR system parameters, the flight path of the SAR sensor, and the image reconstruction grid.We demonstrate the ML image formation and the CRLB bound for synthetically generated data.

R-L-MS-L Filter Function for CT Image Reconstruction

In X-ray computer tomography (CT), convolution back projection is a fundamental algorithm for CT image reconstruction. As filtering plays an important part in convolution back projection, the choice of filter has a direct impact upon the quality of reconstructed images. Aim at improving reconstructed image quality, a new mixed filter based on the idea of “first weighted average then linear mixing” is designed in this article, denoted by R-L-MS-L. Here, R-L filter is relied on to guarantee the spatial resolution of reconstructed image and S-L filter is processed via 3-point weighted averaging to improve the density resolution, thus enhancing the overall reconstruction quality. Gaussian noise of different coefficients is added to the projection data to contrast the noise performance of the new and traditional mixed filters. The simulation and experiment results show that the new filter is better in anti-noise performance and produces reconstructed images with notably improved quality.

Design of a portable optical emission tomography system for microwave induced compact plasma for visible to near-infrared emission lines.

A new non-invasive diagnostic system is developed for Microwave Induced Plasma (MIP) to reconstruct tomographic images of a 2D emission profile. A compact MIP system has wide application in industry as well as research application such as thrusters for space propulsion, high current ion beams, and creation of negative ions for heating of fusion plasma. Emission profile depends on two crucial parameters, namely, the electron temperature and density (over the entire spatial extent) of the plasma system. Emission tomography provides basic understanding of plasmas and it is very useful to monitor internal structure of plasma phenomena without disturbing its actual processes. This paper presents development of a compact, modular, and versatile Optical Emission Tomography (OET) tool for a cylindrical, magnetically confined MIP system. It has eight slit-hole cameras and each consisting of a complementary metal-oxide-semiconductor linear image sensor for light detection. The optical noise is reduced by using aspheric lens and interference band-pass filters in each camera. The entire cylindrical plasma can be scanned with automated sliding ring mechanism arranged in fan-beam data collection geometry. The design of the camera includes a unique possibility to incorporate different filters to get the particular wavelength light from the plasma. This OET system includes selected band-pass filters for particular argon emission 750 nm, 772 nm, and 811 nm lines and hydrogen emission H(α) (656 nm) and H(β) (486 nm) lines. Convolution back projection algorithm is used to obtain the tomographic images of plasma emission line. The paper mainly focuses on (a) design of OET system in detail and (b) study of emission profile for 750 nm argon emission lines to validate the system design.

Convolution backprojection algorithm for tomographic image reconstruction with contourlet transform

In the present script, the problem of recovering tomographic images from projection data using the multiresolution approximation of contourlet transform, is considered. This algorithm has similarity with main convolution backprojection but it defines local information in different directions. In this algorithm, error arises due to the approximation of the density function has also been estimated.

Sparse Bayesian learning in ISAR tomography imaging

Inverse synthetic aperture radar (ISAR) imaging can be regarded as a narrow-band version of the computer aided tomography (CT). The traditional CT imaging algorithms for ISAR, including the polar format algorithm (PFA) and the convolution back projection algorithm (CBP), usually suffer from the problem of the high sidelobe and the low resolution. The ISAR tomography image reconstruction within a sparse Bayesian framework is concerned. Firstly, the sparse ISAR tomography imaging model is established in light of the CT imaging theory. Then, by using the compressed sensing (CS) principle, a high resolution ISAR image can be achieved with limited number of pulses. Since the performance of existing CS-based ISAR imaging algorithms is sensitive to the user parameter, this makes the existing algorithms inconvenient to be used in practice. It is well known that the Bayesian formalism of recover algorithm named sparse Bayesian learning (SBL) acts as an effective tool in regression and classification, which uses an efficient expectation maximization procedure to estimate the necessary parameters, and retains a preferable property of the l0-norm diversity measure. Motivated by that, a fully automated ISAR tomography imaging algorithm based on SBL is proposed. Experimental results based on simulated and electromagnetic (EM) data illustrate the effectiveness and the superiority of the proposed algorithm over the existing algorithms.

Error estimation of discrete convolution back projection for discrete Radon transform

In computerised tomography, an image must be recovered from its sampled projections in the form of Radon transform. In this work, we propose a method for recovering the image from convolution backprojection algorithm for discrete Radon transform. This method is easy to implement with some arithmetic operations without interpolation. The implementation of method is reported on sample images. The total error estimation in this algorithm, owing to approximation of the function is also reported.

Image Reconstruction Methods for Ultrasonic Transmission Mode Tomography in Bubbly Flow Regime

Image reconstruction from projections plays an important role in monitoring flow regimes by ultrasonic transmission mode tomography (UTMT) system. Fast and more accurate methods are necessary in case of on-line process e.g. bubbly flow regimes. In this work, analytical image reconstruction methods such as linear back projection (LBP), filter back projection (FBP) and convolution back projection (CBP) in bubbly flow regime is investigated and found that CBP is superior to other methods. Furthermore, different filters were applied to CBP to investigate the image quality improvement. Among different types of filters for CBP method, Ram-lack outperforms the others for UTMT. The peak signal to noise ratio (PSNR) of reconstructed images in this particular experiment was improved using Ram-lack in noiseless data.