Convolution Backprojection Algorithm Research Articles

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.

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.

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.

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.

HF Radar Signal Processing Based on Tomographic Imaging and CS Technique

This study presents the application of a spotlight-mode synthetic aperture radar (SAR) imaging technique to the problem of high probablity target detection in high frequency (HF) radar system, attempting to improve its spatial resolution. The effects of finite aperture on resolution, sampling constraints and reconstruction over a complete angular range of 360 degrees are discussed. A Convolution Back Projection (CBP) algorithm has been applied to image reconstruction. In order to solve the range limitation of aspect angle with one radar-carrying platform, we collect data over a larger azimuthal range by making multi-aspect observations. Each straight line is a sub aperture over which we can perform the CBP algorithm. When we demand higher resolution for stationary target, it will cause blur with longer data acquisition time. Thus the application of the traditional imaging algorithm is limited. Compressed Sensing (CS) has recently attracted much interest as it can reduce the number of samples without compromising the imaging quality. Within this motivation, we discuss the applicability of CS and present the application constraint for HF radar system.

Characterization of multiphase flow in bubble columns using KT-1 signature and fractal dimension

This work presents the analysis of phase fraction distribution in bubble column reactor using KT-1 signature and fractal dimension. The experiment was carried out using X-ray CT scanner at Leibniz University Hannover. Convolution back projection algorithm is used to obtain the cross-sectional attenuation coefficient distribution. Individual phase distributions of the three phases (air, water and PVC), across the column cross-section, have been obtained using dual energy X-ray tomography. This paper reports measurement of phase fraction distribution at a cross-section level located at 3.2m from the inlet. The effect of variation of PVC concentration on phase fraction distribution of air and PVC has been investigated. Analysis of reconstructed phase fraction using KT-1 signature and fractal dimension reveals interesting information regarding the flow regime transition and mixing phenomenon in the bubble column.

Mart Algorithms for Circular and Helical Cone-Beam Tomography

The present work is concerned with the evaluation of the performance and the efficient implementation of multiplicative algebraic reconstruction technique (MART) to reconstruct three-dimensional (3D) objects for two different source/detector trajectories. Three types of MART algorithms are tested on a numerical phantom (Defrise), and they are implemented on a 3D X-ray system of Vikram Sarabhai Space Centre (VSSC). Circular and helical cone-beam trajectories are used. The results are compared with convolution backprojection (CBP) algorithm for each trajectory. It is found that iterative algorithms perform better than their counterpart, the transform-based CBP algorithm, whenever tomography systems are ill-conditioned due to limited views and/or noisy projection data.

GPGPU Accelerated Fast Convolution Back-Projection for Radar Image Reconstruction

This paper describes a parallel fast convolution back-projection algorithm design for radar image reconstruction. State-of-the-art general purpose graphic processing units (GPGPU) were utilized to accelerate the processing. The implementation achieves much better performance than conventional processing systems, with a speedup of more than 890 times on NVIDIA Tesla C1060 supercomputing cards compared to an Intel P4 2.4 GHz CPU. 256×256 pixel images could be reconstructed within 6.3 s, which makes real-time imaging possible. Six platforms were tested and compared. The results show that the GPGPU super-computing system has great potential for radar image processing.

Tomographic KT-1 signature of phase-fraction distributions in multiphase bubble columns

Characterization of multiphase bubble column flow conditions is performed via the KT-1 signature route of computerized tomography (CT). Cross-sectional images of the bubble column are used for this study. These images were obtained non-invasively by the dual energy X-ray CT developed at Leibniz University Hannover. The solid phase is polyvinyl chloride (PVC) granules, the liquid phase is water and the gaseous phase is air. A convolution back-projection algorithm is used for tomographic reconstruction. Quantification of CT images (obtained for various combinations of liquid velocity, gas velocity and solid concentration of bubble column) is performed using CT fundamentals. The use of KT-1 as a tool for further analysis (of physical phenomenon from CT images) is demonstrated giving a very good insight into bubble column physics.

Rotational motion estimation for ISAR via triangle pose difference on two range-Doppler images

Rotational motion estimation is essential for inverse synthetic aperture radar (ISAR) imaging and understanding. For an object rotating with a constant acceleration, a closed-form solution is proposed to jointly estimate the initial rotating velocity (IRV) and the rotating acceleration (RA) by exploiting the pose difference of a triangle on two range-Doppler (RD) images. Then, the RA can be compensated with interpolation processing and an equivalent uniformly rotating object may be obtained. After that, the estimated IRV can be used to re-scale the RD image into the homogeneous range-cross range domain, or to provide more satisfactory imaging result via elaborated algorithms such as polar format algorithm or convolution back-projection algorithm. Finally, experimental results with both simulated and real airplane data are provided to demonstrate the effectiveness of the proposed method.

High-resolution computed tomography of refractive index distribution by transillumination low-coherence interferometry

We present a method to image refractive index distribution within a sample across 8 mm dimension with high spatial resolution by a transmission low-coherence interferometer. The relative strong forward-scattering light is collected, from which the parallel projections of refractive indices within the sample are obtained. A convolution backprojection algorithm is used to transform the projection data set recorded at sufficient angular views into the spatial distribution of refractive indices within the sample. We experimentally demonstrate this method by imaging a phantom. We show that this method can achieve a precision of 0.01 in determining the refractive index and a spatial resolution of 40 microm.

Landweber iterative methods for angle-limited image reconstruction

We introduce a general iterative scheme for angle-limited image reconstruction based on Landwe- ber's method. We derive a representation formula for this scheme and consequently establish its convergence conditions. Our results suggest certain relaxation strategies for an accelerated convergence for angle-limited im- age reconstruction in L2-norm comparing with alternative projection methods. The convolution-backprojection algorithm is given for this iterative process.

An iterative algorithm for angle-limited three-dimensional image reconstruction

We establish an improved GP iterative algorithm for the extrapolation of band-limited function to fully 3-dimensional image reconstruction by the convolution-backprojection algorithm. Numerical experiments demonstrate that the image resolving power of IGP algorithm is better than that of the original GP algorithm for noisy data.

An improved algorithm for beam-hardening corrections in experimental X-ray tomography

This paper is a follow-up of an earlier work dealing with beam-hardening (BH) correction for simulated X-ray tomography. Here, the projection data (obtained experimentally) is used directly for the initial step. Convolution back projection algorithm has been used to reconstruct the cross-section of the specimen from the BH corrected projection data. Removal of the cupping artifact is targeted. In addition, error analysis is applied for the removal of inherent error. Tests are conducted for simulated data and this modified algorithm is then applied for experimental data. Results are compared from the points of view of the nearness of the corrected polychromatic projection data to the desired monochromatic projection data. Visual quality of the reconstructions is also taken into account. Experimental results are quite encouraging for future applications.

Rotating polar-coordinate ART applied in industrial CT image reconstruction

With incomplete or noisy projections, algebraic reconstruction technique (ART) algorithms can get better image qualities than convolution back-projection (CBP) algorithm. But, it's too slow to meet the practical industrial requirements. Rotating polar-coordinate technique was introduced into ART in this paper, forming Polar-ART (PART) algorithm. PART is 2.7 times as fast as ART with nearly the same quantitative accuracy and it does not need as much memory as ART, which is proved by experiments on 60Co container CT inspection system. A drawback of PART is the loss of resolution in reconstructed images.

Wavelet inversion of the k-plane transform and its application

We establish an inversion formula and a convolution–backprojection algorithm for the k-plane transform ( 0 < k < n ) based on the wavelet theory. If k = n − 1 , the proposed convolution–backprojection algorithm provides a novel method for the inversion of the Radon transform. We demonstrate that the proposed algorithm is easy to implement for global image reconstruction as well as local image reconstruction with the Lemarie–Mayer's wavelets.