Back-projection Method Research Articles

Towards Automated Real-Time Detection and Location of Large-Scale Landslides through Seismic Waveform Back Projection

Rainfall-triggered landslides are one of the most deadly natural hazards in many regions. Seismic recordings have been used to examine source mechanisms and to develop monitoring systems of landslides. We present a semiautomatic algorithm for detecting and locating landslide events using both broadband and short-period recordings and have successfully applied our system to landslides in Taiwan. Compared to local earthquake recordings, the recordings of landslides usually show longer durations and lack distinctivePandSwave arrivals; therefore, the back projection method is adopted for the landslide detection and location. To identify the potential landslide events, the seismic recordings are band-passed from 1 to 3 Hz and the spectrum pattern in the time-frequency domain is used to distinguish landslides from other types of seismic sources based upon carefully selected empirical criteria. Satellite images before and after the detected and located landslide events are used for final confirmation. Our landslide detection and spatial-temporal location system could potentially benefit the establishment of rainfall-triggered landslide forecast models and provide more reliable constraints for physics-based landslide modeling. The accumulating seismic recordings of landslide events could be used as a training dataset for machine learning techniques, which will allow us to fully automate our system in the near future.

Study on Reciprocal Models for Magneto-Acousto-Electrical Tomography With Coil Detection

Magneto-Acousto-Electric Tomography with coil detection, known as Magneto-Acousto-Electric Tomography with Magnetic Induction (MAET-MI), is a non-contact resistivity-based imaging method that employs a coil to detect the induced current generated by the ultrasound in biological tissue, which lie under a static magnetic field. To reconstruct an image of the tissue's conductivity, we propose a reciprocal model to describe the relationship between the inducted voltage of a coil and its conductivity. Previous work on the reciprocal theorem demonstrates that reconstructing conductivity using this method is effective. The forward and inverse problem are usually not verified both numerically and experimentally. In this paper, different approaches are adopted to calculate the forward and the inverse problems for verification of the reciprocal model. This verifies that the reconstruction method based on electrode detection can be applied to MAET-MI. This means that the inverse problem of MAET-MI can be transformed into an inverse source reconstruction of a wave equation based on the coil detection. In the forward problem, the moment method is employed to calculate the Radon transform and generate the ultrasonic signals. For the inverse problem, the filtered back projection method is chosen to reconstruct the ultrasound sources, which are related to the curl of the current density in the reciprocal process. Based on the curl of the current density in the reciprocal process, four sets of correlation coefficients of the original and reconstructed images' model are all greater than 90%. The uniform error criterion is obtained via multiple reconstructions and comparison of multiple models. The reciprocal model exhibits a good uniformity and stability when describing the actual physical process. It also provides additional effective ideas for solving the inverse problem quickly to reconstruct the ultrasonic sources, which is corresponding to the actual distribution of the conductivity.

Development of geometrically ideal dose distribution as a reference for treatment planning in VMAT using filtered back-projection method

PurposeTo determine optimal dose distribution in the treatment planning of volumetric modulated arc therapy (VMAT), a virtually ideal dose distribution was developed as a reference by applying filtered back-projection method. MethodsDelineated structures in patient CT scans were identified using a treatment planning system. The projection of the planning target volume (PTV) was calculated along the X-ray direction for each angle of rotation. Each projection was Fourier transformed to the frequency space; a Shepp–Logan filter was applied, then an inverse Fourier transformation was performed. As the dose irradiation cannot assume a negative value, the filtered projections were shifted using the minimum value inside of the PTV. All values outside of the PTV were set to zero. The corrected filtered projections were then multiplied by the tissue-maximum ratio according to each voxel depth from the surface of the body to simulate X-ray attenuation. Finally, the distributions of multiple rotational angles were convolved to simulate the dose distribution of the VMAT. ResultsIdeal dose distributions were generated with sufficient uniformity inside of the PTV. Dose spreading except for the PTV due to external irradiation was reproduced in the case of a brain tumor. A reference dose distribution including OAR sparing was produced. The efficacy of this process as a target for optimum planning was confirmed. ConclusionUsing applied filtered back-projection, the ideal dose distribution, which excluded some device-oriented restrictions, was generated. This application will provide support for the determination of VMAT planning quality by providing reference dose distributions.

Backprojection Wiener deconvolution for computed tomographic reconstruction.

Analytical CT reconstruction is popular in practice because of its computational efficiency, but it suffers from low reconstruction quality when an insufficient number of projections are used. To address this issue, this paper presents a new analytical method of backprojection Wiener deconvolution (BPWD). BPWD executes backprojection first, and then applies a Wiener deconvolution to the whole backprojected image. The Wiener filter is derived from a ramp filter, enabling the proposed approach to perform reconstruction and denoising simultaneously. The use of a filter after backprojection does not differentiate between real sampled projections and interpolated ones, introducing reconstruction errors. Therefore a weighted ramp filter was applied to increase the contribution of real sampled projections in the reconstruction, thus improving reconstruction quality. Experiments on synthetic data and real phase-contrast x-ray images showed that the proposed approach yields better reconstruction quality compared to the classical filtered backprojection (FBP) method, with comparable reconstruction speed.

Designing and developing an in-house CCD based optical CT scanner for gel dosimetry

Introduction: Measurement of the complex 3D radiation dose distribution created with advanced radiotherapy techniques such as IMRT and SRS became very important. Polymer gel dosimetry (PGD) is proposed method to recording this dose distribution. MRI, X-ray CT, ultrasound, spectrophotometry and optical CT scanners can be used for readout of Polymer gel dosimeters. Although MRI is gold standard readout instrument, but it is costly and time- consuming. Optical CT is faster and has very lower cost than other methods. The aim of this work is designing and developing an in-house fast CCD based optical computed tomography scanner to extract the 3D radiation dose distribution that recorded in irradiated PGDs. Materials and Methods: in this work we used an array of high power LEDs by 650nm wave length as broad beam light source and a CCD camera as large area detector. The image projections of test object that immersed in a water tank and its rotational movement were controlled by a stepper motor was obtained. Image reconstruction carried out in MATLAB environment with the Filtered back projection method. Results: Reconstructed image quality is very promising. And it is comparable to results of the other works. Contrast to Noise Ratio (CNR) of reconstructed images without any filters in the back projection algorithm was 0.41. Using ramp filter with 0.2 cutoff frequency, gained a 1.1 in CNR and using Butterworth filter with cutoff frequency of 0.3 gained a CNR of 1.3. Increasing cutoff frequency for Butterworth filter will degrade noise properties of reconstructed image and CNR goes down to 0.82, which is comparable with similar works. Conclusion: Optical CT readout system is considered one of the best options for gel readings. If we can overcome the problems of reconstructed images with light rays, this system can be useful for fast and accurate readout of irradiated polymer gel dosimeters.

Richardson-Lucy deconvolution of time histograms for high-resolution non-line-of-sight imaging based on a back-projection method.

Non-line-of-sight (NLoS) imaging is a newly developed technique with widespread applications in recent years. At present, it is difficult for NLoS imaging to achieve a high-resolution reconstruction with an existing back-projection method. We propose a novel approach based on the Richardson-Lucy deconvolution of time histograms for high-resolution NLoS imaging. In our approach, the backscattering photons from a line-of-sight scene, often regarded as adverse factors, are used favorably as priors for the deconvolution of time histograms. All deconvoluted time histograms are back projected into the space to form a high-resolution NLoS reconstruction. The simulated and experimental results with the approach demonstrated that the reconstructions of NLoS objects are indeed with high resolution, even under a relatively high noise level.

Backprojection to image slip

Waveform backprojection is a key technique of earthquake-source imaging, which has been widely used for extracting information of earthquake source evolution that cannot be obtained by kinematic source inversion. The technique enjoys considerable popularity, owing to the simplicity of its implementation and the robustness of its processing, but the physical meaning of backprojection images has remained elusive. In this study, we reviewed the mathematical representation of backprojection (BP) and hybrid backprojection (HBP) methods, following the pioneering work of Fukahata et al. (Geophys. J. Int. (2014) 196, 552–559), to clarify the physical implications of BP images. We found that signal intensity in BP and HBP images is scaled with the amplitude of the Greens function that corresponds to a unit-step slip, which results in the signal intensity being depth dependent. We propose variants of BP and HBP, which we call kinematic BP and HBP, respectively, to relate the BP signal intensity to slip motion of an earthquake by modifying the normalizing factors used in the original BP and HBP methods. The original BP and HBP images remain useful for assessing the spatiotemporal strength of the wave radiation, which scales with the amplitude of the Greens function, whereas the kinematic BP and HBP methods are suitable for imaging the slip motion that is responsible for the high-frequency radiation produced during the source-rupture process.

Coseismic Radiation of the 2008 Mw 7.9 Wenchuan Earthquake and Its Relationship to Fault Complexities

The long rupture length and complex fault geometries of the 2008 Mw 7.9 Wenchuan earthquake offer a great opportunity to investigate the relationship between coseismic radiation and fault complexities. In this study, we first improved the compressive-sensing back-projection method (CS-BP) with window time adjustment and parallel computation to enhance its spatial–temporal resolution and computational efficiency. Then we applied the CS-BP to invert for the coseismic radiation of the Wenchuan earthquake in multiple frequency bands. Our results show that the coseismic radiation of the Wenchuan earthquake is frequency-dependent and strongly associated with the fault geometries: low-frequency radiation sources are concentrated on smooth fault segments with large coseismic slip, while higher-frequency sources are mainly related to fault complexities (e.g., Xiaoyudong fault, Gaochuan fault-bend, Leigu fault-bend, and Nanba fault step-over). An acceleration of rupture speed from ~ 1.5 to ~ 3.0 km/s is also observed the near Xiaoyudong fault, where strong high-frequency energies were radiated. Finally, we discuss the role of rupture speed in mediating the relationship between coseismic radiation and fault complexities. On one hand, sudden changes of rupture speeds contribute to strong high-frequency radiation. On the other hand, fault complexities can also strongly affect the rupture speed: a sudden break of a large asperity is able to propel the acceleration, while rupture front may decelerate when it jumps across geometric barriers.

Hydraulic system fault diagnosis method based on a multi‐feature fusion support vector machine

Real-time fault prevention and diagnosis in hydraulic systems is one of the challenges in engineering applications. In order to solve the problems of feature extraction and pattern recognition of different types of fault signals such as leakage, blockage, and cavitation in the hydraulic system, this paper presents a fault diagnosis method based on a multi-feature fusion support vector machine. This method first extracts the typical features of the fault signal from the time domain, frequency domain, and time−frequency domain. Then use the information entropy to calculate the weight of each feature, select the feature with the larger weight to participate in the stock index diagnosis. Finally, a multi-classifier based on the support vector machine is used to realise the fault diagnosis of the hydraulic system. The experimental results show that this method can achieve high accuracy in the hydraulic system fault diagnosis when the Gaussian radial basis function is selected. Also, compared with the commonly used improved back-projection neural network fault diagnosis method, this method has more excellent diagnostic performance.

Statistical CT reconstruction using region-aware texture preserving regularization learning from prior normal-dose CT image

In some clinical applications, prior normal-dose CT (NdCT) images are available, and the valuable textures and structure features in them may be used to promote follow-up low-dose CT (LdCT) reconstruction. This study aims to learn texture information from the NdCT images and leverage it for follow-up LdCT image reconstruction to preserve textures and structure features. Specifically, the proposed reconstruction method first learns the texture information from those patches with similar structures in NdCT image, and the similar patches can be clustered by searching context features efficiently from the surroundings of the current patch. Then it utilizes redundant texture information from the similar patches as a priori knowledge to describe specific regions in the LdCT image. The advanced region-aware texture preserving prior is termed as ‘RATP’. The main advantage of the PATP prior is that it can properly learn the texture features from available NdCT images and adaptively characterize the region-specific structures in the LdCT image. The experiments using patient data were performed to evaluate the performance of the proposed method. The proposed RATP method demonstrated superior performance in LdCT imaging compared to the filtered back projection (FBP) and statistical iterative reconstruction (SIR) methods using Gaussian regularization, Huber regularization and the original texture preserving regularization.

Flat sheet of Zinc material as a filter for gamma photons in Tc-99mm SPECT imaging

Purpose of the Study: Scattered gamma photons in single photon emission computed tomography (SPECT) is one of the main issues that degrade the image quality. There are several types of scatter correction methods. However, none of the technique is applied in routine clinical Tc-99m SPECT imaging. Therefore, Zinc (Zn) material filter was constructed for pre-filtration of scattered gamma photons in Tc-99m single photon emission computed tomography (SPECT).Materials and Methods: Tc-99m radioactivity was administered into the Carlson’s phantom. Planar and tomographic data were acquired with and without hot regions insert, respectively, with and without material filter. Scatter to non-scatter ratio was measured from the photopeak region of Tc-99m spectra. Tomographic images were generated using filtered back projection method. Contours on images were drawn with ImageJ software. Images obtained with and without material filter were analysed in terms of detectability of hot regions.Results: Remarkable decrease (≈ 21%) in the ratio of scattered to non-scattered gamma photons with material filter was achieved. Detectability of smaller hot regions with material filter was enhanced. In terms of sizes of all hot regions, material filter results appear closer to the original sizes.Conclusion: Material filter technique could be applied in Tc-99m clinical SPECT, while organ phantom studies are needed.

Acoustic Tomography of Composite Materials of the Through-Transition Method

The article presents the image of the testing area for the through-transition method with an acoustic array. Using linear acoustic array in through-transition method, a set of data from different angles is obtained. Using this data set and the back projection method, the test area imaging is obtained, which is represented by a set of small local areas. The number of initial projections passing through each local area is calculated. Furthermore, the density function is determined and the resulting function, that is encoded whether in color or grayscale, is displayed on the monitor screen.

Quantification of temporal resolution improvement factor in SMART-RECON based time-resolved C-arm Cone beam computed tomography angiography (TR-CBCTA)

In a recently published paper by Li et al (2018 Phys. Med. Biol. 63 075001), reconstruction parameters were optimized for the so-called synchronized multiArtifact reduction with tomographic reconstruction (SMART-RECON) method to enable time-resolved Cone beam computed tomography angiography (TR-CBCTA) from a single short-scan CBCT data set. However, the paper did not quantitatively address how much temporal resolution can be improved by using the SMART-RECON algorithm in TR-CBCTA. The purpose of this note was to present a method to quantify this temporal resolution improvement factor and to use that method to quantify the improvement in temporal resolution using SMART-RECON and optimized reconstruction parameters. In the method proposed in this note, the potential temporal blurring caused by SMART-RECON was modeled as a convolution between a temporal Gaussian blurring kernel and the ground truth temporal enhancement curve. The width parameter of the resulting Gaussian blurring kernel was used as a surrogate metric for temporal resolution to quantify the achievable temporal resolution for the conventional filtered backprojection (FBP) and SMART-RECON methods. The ratio of the surrogate temporal resolutions for the two reconstruction methods was calculated to quantify the factor of temporal resolution improvement. The quantitative results show that the temporal resolution is improved by a factor of 4.5 using SMART-RECON compared with FBP.

Accurate Iterative FBP Reconstruction Method for Material Decomposition of Dual Energy CT.

Compared with traditional CT, dual energy CT (DECT) has the capability to improve material differentiation and reduce beam hardening artifacts, and thus has wide prospects of applications. In this paper, by linearizing the polychromatic projections with their first-order Taylor expansions, we derive an iterative reconstruction method for DECT. The method updates the basis material images by adding the residual images reconstructed from the residual projections to the current estimated basis material images, i.e., the iteration process of the proposed method is carried out in image domain, so it is applicable to both geometrically consistent and inconsistent projections. In addition, as the filtered back-projection method is used in the reconstruction of the residual images, the proposed method has a high degree of parallelism. Both numerical simulation and real-data experiments are performed, and the results confirm the effectiveness of the proposed reconstruction method.

Source Models of the 2012 Haida Gwaii (Canada) and 2015 Illapel (Chile) Earthquakes and Numerical Simulations of Related Tsunamis

Seismological observations provide essential input parameters for numerical tsunami simulations. Here, we present source mechanism parameters, finite-fault source rupture models and numerical tsunami simulation results for the destructive October 28, 2012 Haida Gwaii-Canada (Mw 7.7) and September 16, 2015 Illapel-Chile (Mw 8.3) earthquakes and resulting tsunamis. These two earthquakes were controlled by active tectonic features along the subduction zones that had developed in response to the convergent movements of lithospheric plates. The faulting geometry (strike, dip, and rake angles), focal depth, fault dimensions, average and maximum slip values on the fault planes and seismic moments of the earthquakes are estimated by analyzing teleseismic long-period P- and SH-waves and broadband P-waveforms and using waveform inversion and hybrid back-projection methods. The obtained slip models of the earthquakes reveal heterogeneous slip distributions on fault planes with long source durations (~ 80 s and 150 s) and low stress drop values (10–15 bars). Numerical simulations of tsunami wave propagation are further performed using the uniform and non-uniform slip models and nonlinear long-wave equations in spherical coordinates. The shape and arrival times of leading tsunami waves are adequately constrained particularly with the heterogeneous slip distribution models. The general characteristics of synthetic tsunami waveforms (e.g., amplitude, shape, arrival time) calculated using the non-uniform slip model, are more consistent with the observed tsunami records than those of a uniform slip model. It is further seen that simulation results using preliminary and fast slip models for both earthquakes give only approximate early tsunami estimates; tsunami wave heights and arrival times to the coasts are mostly not well simulated. The results indicate that tsunami simulations based on finite-fault source slip models likely contribute to the determination of tsunamigenic coastal regions by revealing locations, arrival times, amplitudes, and directions of tsunami waves within a close approximation to observed records off-shore and far from the source region. They provide sufficient information to facilitate tsunami warning and mitigation challenges after the destructive earthquakes. We further suggest that joint inversions of GPS, tsunami, teleseismic and strong ground motion records and higher resolution bathymetry data are needed in order to obtain better correlations between observed and synthetic tsunami data, especially for the later arriving waves.

Analytical expressions for the reconstructed image of a homogeneous cylindrical sample exhibiting a beam hardening artifact in X-ray computed tomography

BACKGROUND:Cylindrical phantoms are often imaged by X-ray computed tomography (CT) to evaluate the extent of beam hardening (or cupping artifact) resulting from a polychromatic X-ray source.OBJECTIVE:Our goal was to derive analytical expressions for the reconstructed image of a homogeneous cylindrical phantom exhibiting a cupping artifact, to permit a quantitative comparison with experimental cupping data.METHODS:A filtered backprojection method was employed to obtain the analytical cupping profile for the phantom, assuming that the projection data could be approximated as a power series with respect to the sample penetration thickness.RESULTS:The cupping profile was obtained analytically as a series of functions by employing Ramachandran filtering with an infinite Nyquist wavenumber. The quantitative relationship between the power series of the projection and the nth moment of the linear attenuation coefficient spectrum of the phantom was also determined. Application of the obtained cupping profile to the evaluation of the practical reconstruction filters with a finite Nyquist wavenumber and to the best choice of the contrast agent was demonstrated.CONCLUSIONS:The set of exact solutions derived in this work should be applicable to the analysis of cylindrical phantom experiments intended to evaluate CT systems.

Imaging Based on Correlation Function for Buried Objects Identification

Ground-penetrating radar is usually employed to detect such buried objects beneath the ground as pipes, cables, and mines. There exist several methods for monitoring the buried objects, some of which require a relatively long time and heavy computations to create an appropriate image. The signal sent to the environment is reflected due to the characteristic features of the environment, which eventually leads to detection of the buried objects. For detection of the near ground surface targets, there is a very poor distinguishability between the signal reflected from the buried objects and the one from the ground itself. Buried objects in this case are detectable using ultra-wide band signals in the frequency domain. Comparing the reflected signals from the ground with those from the objects in the aforementioned case, one can detect the buried objects. In this paper, the reflected signal from the ground is canceled using the time-gating method. To detect the buried objects, the signals reflected from different position zones are compared with each other based on the concept of correlation function which is suggested in this paper. The results of this paper are also compared with those of the reflected-power and back-projection methods. We demonstrate that by employing the proposed method, it is possible to detect all buried objects in these environmental conditions.

Regularization strategies in statistical image reconstruction of low-dose x-ray CT: A review.

Statistical image reconstruction (SIR) methods have shown potential to substantially improve the image quality of low-dose x-ray computed tomography (CT) as compared to the conventional filtered back-projection (FBP) method. According to the maximum a posteriori (MAP) estimation, the SIR methods are typically formulated by an objective function consisting of two terms: (a) a data-fidelity term that models imaging geometry and physical detection processes in projection data acquisition, and (b) a regularization term that reflects prior knowledge or expectations of the characteristics of the to-be-reconstructed image. SIR desires accurate system modeling of data acquisition, while the regularization term also has a strong influence on the quality of reconstructed images. A variety of regularization strategies have been proposed for SIR in the past decades, based on different assumptions, models, and prior knowledge. In this paper, we review the conceptual and mathematical bases of these regularization strategies and briefly illustrate their efficacies in SIR of low-dose CT.

Robust Recovery of Temporal Overlap Between Network Activity Using Transient-Informed Spatio-Temporal Regression.

Functional magnetic resonance imaging is a non-invasive tomographic imaging modality that has provided insights into system-level brain function. New analysis methods are emerging to study the dynamic behavior of brain activity. The innovation-driven co-activation pattern (iCAP) approach is one such approach that relies on the detection of timepoints with a significant transient activity to subsequently retrieve spatially and temporally overlapping large-scale brain networks. To recover temporal profiles of the iCAPs for further time-resolved analysis, spatial patterns are fitted back to the activity-inducing signals. In this crucial step, spatial dependences can hinder the recovery of temporal overlapping activity. To overcome this effect, we propose a novel back-projection method that optimally fits activity-inducing signals given a set of transient timepoints and spatial maps of iCAPs, thus taking into account both spatial and temporal constraints. Validation on simulated data shows that transient-based constraints improve the quality of fitted time courses. Further evaluation on experimental data demonstrates that overfitting and underfitting are prevented by the use of optimized spatio-temporal constraints. Spatial and temporal properties of resulting iCAPs support that brain activity is characterized by the recurrent co-activation and co-deactivation of spatially overlapping large-scale brain networks. This new approach opens new avenues to explore the brain's dynamic core.

Backprojection inverse filtration for laminographic reconstruction

Traditional tomography uses circular trajectories and here, filtered backprojection often works well. However, for objects with large aspect ratios, rotational tomography is often not feasible. In these cases, other trajectories can be more appropriate. For generic trajectories, filtered backprojection methods might not work well and full iterative reconstruction can be computationally demanding. In this study, the authors thus propose a third paradigm that combines aspects of both of these techniques. They use interpolation and backprojection techniques to generate an initial estimate of an object's internal structure using projection images taken at different orientations. Depending on the scanning geometry used to calculate the tomographic projections, this initial estimate can be understood as a blurred (filtered) approximation of the actual structure. For each scanning geometry, they specify the equivalent blurring operator that would provide the same estimate directly from a representation of the object's internal structure. They then use iterative techniques to invert this filtering operation, thus estimating the internal structure from the estimate of its blurred representation.