Standard Backprojection Research Articles

Statistical modelling and Bayesian inversion for a Compton imaging system: application to radioactive source localization.

Statistical modelling and Bayesian inversion for a Compton imaging system: application to radioactive source localization.

Model-Based X-Ray-Induced Acoustic Computed Tomography.

X-ray-induced acoustic computed tomography (XACT) provides X-ray absorption-based contrast with acoustic detection. For its clinical translation, XACT imaging often has a limited field of view. This can result in image artifacts and overall loss of quantification accuracy. In this article, we aim to demonstrate model-based XACT image reconstruction to address these problems. An efficient matrix-free implementation of the regularized LSQR (MF-LSQR)-based minimization scheme and a noniterative model back-projection (MBP) scheme for computing XACT reconstructions have been demonstrated in this article. The proposed algorithms have been numerically validated and then used to perform reconstructions from experimental measurements obtained from an XACT setup. While the commonly used back-projection (BP) algorithm produces limited-view and noisy artifacts in the region of interest (ROI), model-based LSQR minimization overcomes these issues. The model-based algorithms also reduce the ring artifacts caused due to the nonuniformity response of the multichannel data acquisition. Using the model-based reconstruction algorithms, we are able to obtain reasonable XACT reconstructions for acoustic measurements of up to 120° view. Although the MBP is more efficient than the model-based LSQR algorithm, it provides only the structural information of the ROI. Overall, it has been demonstrated that the model-based image reconstruction yields better image quality for XACT than the standard BP. Moreover, the combination of model-based image reconstruction with different regularization methods can solve the limited-view problem for XACT imaging (in many realistic cases where the full-view dataset is unavailable), and hence pave the way for future clinical translation.

Model-Based Reconstruction of Large Three-Dimensional Optoacoustic Datasets.

Iterative model-based algorithms are known to enable more accurate and quantitative optoacoustic (photoacoustic) tomographic reconstructions than standard back-projection methods. However, three-dimensional (3D) model-based inversion is often hampered by high computational complexity and memory overhead. Parallel implementations on a graphics processing unit (GPU) have been shown to efficiently reduce the memory requirements by on-the-fly calculation of the actions of the optoacoustic model matrix, but the high complexity still makes these approaches impractical for large 3D optoacoustic datasets. Herein, we show that the computational complexity of 3D model-based iterative inversion can be significantly reduced by splitting the model matrix into two parts: one maximally sparse matrix containing only one entry per voxel-transducer pair and a second matrix corresponding to cyclic convolution. We further suggest reconstructing the images by multiplying the transpose of the model matrix calculated in this manner with the acquired signals, which is equivalent to using a very large regularization parameter in the iterative inversion method. The performance of these two approaches is compared to that of standard back-projection and a recently introduced GPU-based model-based method using datasets from in vivo experiments. The reconstruction time was accelerated by approximately an order of magnitude with the new iterative method, while multiplication with the transpose of the matrix is shown to be as fast as standard back-projection.

13.1: Invited Paper: Multigrid Backprojection Super‐Resolution and Deep Filter Visualization

We introduce a novel deep‐learning architecture for image upscaling by large factors (e.g. 4x, 8x) based on examples of pristine high‐resolution images. Our target is to reconstruct high‐resolution images from their downscale versions. The proposed system performs a multi‐level progressive upscaling, starting from small factors (2x) and updating for higher factors (4x and 8x). The system is recursive as it repeats the same procedure at each level. It is also residual since we use the network to update the outputs of a classic upscaler. The network residuals are improved by Iterative Back‐Projections (IBP) computed in the features of a convolutional network. To work in multiple levels we extend the standard back‐projection algorithm using a recursion analogous to Multi‐Grid algorithms commonly used as solvers of large systems of linear equations. We finally show how the network can be interpreted as a standard upsampling‐and‐filter upscaler with a space‐variant filter that adapts to the geometry. This approach allows us to visualize how the network learns to upscale. Finally, our system reaches state of the art quality for models with relatively few number of parameters.

BP algorithm for the multireceiver SAS

The imaging performance and efficiency are two important issues for the multireceiver synthetic aperture sonar (SAS). Back projection (BP) algorithm is characterised by the high performance and low efficiency. In this study, the authors first recall the standard BP algorithm based on the interpolation for the multireceiver SAS. Then, two improved BP algorithms based on the range Fourier transformation (FT) are presented. Considering the fact that the time delay in the time domain can be carried out by the phase shifting in the frequency domain, an FT shifting based BP algorithm avoiding the interpolation error is presented. Although this method produces the focusing result with high performance, it is very time consuming. In order to improve the imaging efficiency without loss of imaging performance, the authors propose an oversampling-based BP algorithm, which is based on the fact that the zero-padding in the frequency domain is equivalent to the interpolation in the time domain. After that, the computation complexity of three BP algorithms is analysed in detail. Finally, simulations and real data are exploited to validate the presented methods.

Through a Cinder Block Wall Refocusing Using SAR Back Projection Method

Through a cinder block wall imaging using a standard back projection method is studied by employing backscattering in the frequency range of 1-4 GHz. First, using the finite-element method, numerical backscatterings of metallic and dielectric targets behind a cinder block wall are calculated and the effects of the wall on images are investigated. It is shown that the target image is shifted, repeated, and distorted. Second, to refocus the images, the proper Green function is calculated. Basically, the 2-D scattering from a cinder block wall is addressed, analytically and asymptotically. The imaging formulation is modified, using the structure Green function phase. To calculate the Geen function, wall parameters should be evaluated beforehand. Third, to estimate the wall parameters, we proposed the estimation of those using measured wall reflections. Using analytical formulations, direct wall reflections are estimated theoretically and compared with those of measured ones. Using genetic algorithm (GA), wall parameters are extracted, correctly. Having the optimum parameters, the direct wall reflection is effectively subtracted, the Green function is calculated, and the target image is refocused successfully. Finally, using the experimental data, the effectiveness of our proposed approach is demonstrated.

Automatic registered back‐projection approach based on object orientation for airborne repeat‐track interferometric SAR

The requirements of the correction of motion errors and high accurate registration are difficult to satisfy for the independence of the aperture paths in airborne repeat-track interferometry. Here, according to the principle of the independence between the imaging scene and synthetic aperture radar (SAR) viewing geometry, the authors propose a new SAR imaging approach based on the idea of object orientation and back-projection (BP), where the complex motion compensation is effectively avoided and the image formation and registration are achieved simultaneously with high accuracy. In contrast to the standard BP algorithm, it greatly reduces the difficulty of registration brought by the irregular deviations. Moreover, it further successfully overcomes the influence introduced by the centre-beam approximation compared with frequency-domain algorithms. Experimental results both on simulated and actual SAR data are used to validate the proposed algorithm.

On the Processing of Very High Resolution Spaceborne SAR Data: A Chirp-Modulated Back Projection Approach

A new image formation algorithm is proposed for processing very high resolution spaceborne sliding-spotlight synthetic aperture radar (SAR) data. Because of along-track antenna steering, the Doppler bandwidth of the received SAR data is expanded significantly beyond one pulse repetition frequency interval. Furthermore, the range histories become spatially dependent in both dimensions and cannot be expressed exactly by a hyperbolic model. In our approach, we first reduce the Doppler bandwidth by a novel azimuth dechirp processing method in the range frequency domain. The data are then processed by the standard $\omega $ – $\kappa $ algorithm with a fixed effective velocity. Thereafter, the chirp modulation concept is imported to rebuild new data with much shorter apertures. Finally, a standard back-projection algorithm is employed to accumulate the signal pixel by pixel along the newly built aperture. Thus, the balance between processing efficiency and precision can be controlled by adjusting the length of the new apertures. In addition, a more accurate 2-D spectrum derivation is employed to enhance the processing precision, and a novel range-splitting method is presented to accommodate the range dependence of effective velocities. Furthermore, when implementing the back projection, the image grid—the region and granularity level of which are user defined—is placed on the earth’s surface instead of on the slant-range plane, and the routine geometry projection processing thus becomes dispensable.

A distributed ASTRA toolbox.

While iterative reconstruction algorithms for tomography have several advantages compared to standard backprojection methods, the adoption of such algorithms in large-scale imaging facilities is still limited, one of the key obstacles being their high computational load. Although GPU-enabled computing clusters are, in principle, powerful enough to carry out iterative reconstructions on large datasets in reasonable time, creating efficient distributed algorithms has so far remained a complex task, requiring low-level programming to deal with memory management and network communication. The ASTRA toolbox is a software toolbox that enables rapid development of GPU accelerated tomography algorithms. It contains GPU implementations of forward and backprojection operations for many scanning geometries, as well as a set of algorithms for iterative reconstruction. These algorithms are currently limited to using GPUs in a single workstation. In this paper, we present an extension of the ASTRA toolbox and its Python interface with implementations of forward projection, backprojection and the SIRT algorithm that can be distributed over multiple GPUs and multiple workstations, as well as the tools to write distributed versions of custom reconstruction algorithms, to make processing larger datasets with ASTRA feasible. As a result, algorithms that are implemented in a high-level conceptual script can run seamlessly on GPU-enabled computing clusters, up to 32 GPUs or more. Our approach is not limited to slice-based reconstruction, facilitating a direct portability of algorithms coded for parallel-beam synchrotron tomography to cone-beam laboratory tomography setups without making changes to the reconstruction algorithm.

All-Directions Through-the-Wall Radar Imaging Using a Small Number of Moving Transceivers

Through-the-wall radar imaging systems are utilized for mapping buildings' interiors and detecting static and moving objects hidden behind the walls. The current techniques rely on large linear antenna arrays with directional radiation pattern for obtaining high cross-range resolution, and their imaging capability is limited by the low array processing gain and field of view. This paper introduces a new technique for through-the-wall radar imaging in which the linear array is replaced by a dense 2-D synthetic array formed by an ad hoc network of moving transceivers with omnidirectional antennas. Applying this method enables imaging of building interiors from outside or inside with 360° field of view. As receivers move, the direct and reflected signals from a stationary transmitter are sampled at different positions within the roaming domain, and by combining such signal samples using an appropriate beam-forming technique, a large and dense array is synthesized to provide an accurate radar map of the buildings' interiors and hidden objects in all directions. To increase the system dynamic range, the direct signals between the transmitter (Tx) and receiver (Rx) antennas are reduced, utilizing orthogonal polarizations for Tx and Rx. To improve the range resolution and reduce the background noise, a new method based on the generalized pencil of function method is proposed. This method can accurately detect the locations of the reflecting points within the image which, in combination with the standard back-projection focusing, provides high-quality radar images. A finite-element method for a simple building structure and ray tracing for a large 3-D building structure are used to evaluate the performance of the proposed method.

Single image super-resolution using regularization of non-local steering kernel regression

One promising technique for single image super-resolution (SR) is reconstruction-based framework, where the key issue is to apply reasonable prior knowledge to well pose the solution to upsampled images. In this paper, we employ the non-local steering kernel regression (NLSKR) model to devise an effective regularization term for solving single image SR problem. The proposed regularization term is based on the complementary properties of local structural regularity and non-local self-similarity existing in natural images, aiming at preserving sharp edges and producing fine details in the resultant image. By integrating the regularization term into the standard back-projection framework, we solve a least squares minimization problem to seek the desired high-resolution (HR) image. Extensive experimental results on several public databases indicate that the proposed method produces promising results in terms of both objective and subjective quality assessments.

High-Resolution Imaging for Impulse-Based Forward-Looking Ground Penetrating Radar

Forward-Looking Ground Penetrating Radar (FLGPR) has multiple applications, one of which includes its use for detecting landmines and other buried improvised explosive devices (IEDs). The standard method for generating synthetic aperture radar (SAR) images for this radar is the backprojection (BP) algorithm, which has poor resolution and high sidelobe problems. In this paper, we consider using the Sparse Iterative Covariance-based Estimation (SPICE) algorithm and the Spare Learning via Iterative Minimization (SLIM) algorithm for generating sparse high-resolution images for FLGPR. A pre-processing step, which involves an orthogonal projection of the received data onto a subspace related to the region of interest is performed, for decreasing the dimension of the data and for clutter reduction. The SLIM and SPICE algorithms are user-parameter free, and are capable of providing SAR images with improved resolution. We also use the well-known CLEAN approach for imaging based on a proposed signal model in the time domain. We show using simulated data that the SPICE and SLIM algorithms provide higher resolution than CLEAN and the standard BP. Imaging using real data collected via the Synchronous Impulse Reconstruction (SIRE) radar, a multiple-input multiple-output (MIMO) FLGPR radar developed by the Army Research Laboratory (ARL), is also presented and used for analysis.

3D imaging for ground-penetrating radars via dictionarydimension reduction

Ground-penetrating radar (GPR) has been widely used in detecting or imaging subsurface targets. In many applications such as archaeology, utility imaging, or landmine detection, three-dimensional (3D) images of the subsurface region is required for better understanding of the sensed medium. However, a high-resolution 3D image requires wideband data collection both in spatial and time/frequency domains. Match filtering is the main tool for generating subsurface images. Applying match filtering with the data acquisition impulse response for each possible voxel in the 3D region with the collected data requires both a tremendous amount of computer memory and computational complexity. Hence, it is very costly to obtain 3D GPR images in most of the applications although 3D images are very demanded results. In this paper, a new 3D imaging technique is proposed that will first decrease the memory requirements for 3D imaging with possible implications for less computational complexity. The proposed method uses the shifted impulse response of the targets that are on the same depth as a function of scanning position. This similarity of target responses for data dictionaries for only 2D target slices is constructed with twice the length in scanning directions and this 2D dictionary is mainly used for generating 3D images. The proposed method directly saves memory due to dimension reduction in dictionary generation and also decreases computational load. Simulation results show generated 3D images with the proposed technique. Comparisons in both memory and computational load with the standard backprojection show that the proposed technique offers advantages in both areas.

SU‐E‐J‐163: Suppressing Motion Related Artifacts in 4D‐CT Or 4D‐CBCT Reconstruction Using Projections and Digitally Reconstructed Projections: Proof of Principle

Purpose:It has been always challenging to reconstruct good quality 4D‐CT or 4D‐CBCT when the data are under‐sampled for each individual phase. For example, CBCT data is often acquired with limited number of projections and while it is sufficient to reconstruct decent motion averaged images; reconstructing a 4D image from this limited data leads to motion induced artifacts. However, inherent in the projection data are both components that capture the moving and non‐moving parts of the image. In this work, we test the feasibility of using such a dataset to separate out the moving and non‐moving components and then reconstruct individual phase images to acquire a complete 4D reconstruction with reduced artifacts.Methods:To test our theory, we simulated a simple 2D+time respiratory phantom, and demonstrated the feasibility using a simple filtered backprojection algorithm along with the proposed motion suppression technique to reconstruct 2D+time images. However, the concepts can be expanded to 3D+time (i.e. 4D) datasets both using conventional CT or CBCT acquisition. The core of the technique rests on separating out the motion components from individual projection data by selecting the minimum intensity between projections and digitally reconstructed projections. This information is then later added back into the final images reconstructed at each individual phase to suppress motion artifacts.Results:Initial results on a 2D+time simulated phantom proves that severe under‐sampling artifacts can be eliminated and individual phase images can be reconstructed with high fidelity when compared to standard under‐sampled filtered backprojection.Conclusion:The technique is successfully demonstrated using simple backprojection, and hence computational complexity is comparable to standard backprojection (for CT) or FDK (for CBCT). Computational complexity will be significantly better when compared to traditional iterative methods that use regularization and penalty functions.NIH R01CA133539

Flow-scanning optical tomography.

We present a 3D tomography technique for in vivo observation of microscopic samples. The method combines flow in a microfluidic channel, illumination through a slit aperture, and a Fourier lens for simultaneous acquisition of multiple perspective angles in the phase-space domain. The technique is non-invasive and naturally robust to parasitic sample motion. 3D absorption is retrieved using standard back-projection algorithms, here a limited-domain inverse radon transform. Simultaneously, 3D differential phase contrast images are obtained by computational refocusing and comparison of complementary illumination angles. We implement the technique on a modified glass slide which can be mounted directly on existing optical microscopes. We demonstrate both amplitude and phase tomography on live, freely swimming C. elegans nematodes.

Model-Based Optoacoustic Image Reconstruction of Large Three-Dimensional Tomographic Datasets Acquired With an Array of Directional Detectors

Image quality in 3-D optoacoustic (photoacoustic) tomography is greatly influenced by both the measurement system, in particular the number and spatial arrangement of ultrasound sensors, and the ability to account for the spatio-temporal response of the sensor element(s) in the reconstruction algorithm. Herein we present a reconstruction procedure based on the inversion of a time-domain forward model incorporating the spatial impulse response due to the shape of the transducer, which is subsequently applied in a tomographic system based on a translation-rotation scan of a linear detector array. The proposed method was also adapted to cope with the data-intensive requirements of high-resolution volumetric optoacoustic imaging. The processing of 2 · 10 (4) individual signals resulted in well-resolved images of both ~ 200 μm absorbers in phantoms and complex vascular structures in biological tissue. The results reported herein demonstrate that the introduced model-based methodology exhibits a better contrast and resolution than standard back-projection and model-based algorithms that assume point detectors. Moreover, the capability of handling large datasets anticipates that model-based methods incorporating the sensor properties can become standard practice in volumetric opto acoustic image formation.

MO‐D‐108‐10: 3D Reconstruction of Scintillation Light Emission From Mono‐Energetic Proton Beams Using a Limited Projection Approach: A Simulation Study

Purpose: Large‐volume scintillator detectors show promise for fast, highresolution measurements of proton treatment fields, but previous work has been limited to observing 2D projections of the 3D scintillation light distribution. The purpose of this work is to develop a 3D reconstruction method for a scintillation dosimetry system consisting of a tank of liquid scintillator imaged by CCD cameras. Methods: To reconstruct the scintillation light produced by proton beams in 3D, we applied the maximum‐a‐posteriori (MAP) algorithm using projections from three views (2 orthogonal side projections and 1 forward projection). However, the small number of viewing angles in our system limits the efficiency of this approach. In this study, we exploited the axial symmetry of proton beams to create an improved initial estimation of the light distribution. Monte Carlo calculations were performed to simulate the light emission from a volume of liquid scintillator irradiated with proton pencil beams. Projection images of the light emission were calculated from the simulated data with known camera and scintillator artifacts. We compared the MAP reconstructed emissions obtained using a standard backprojection initial estimate with those using our proposed profile‐based initial estimation. Results: From our simulations, the root mean square (RMS) error of the MAP reconstruction was 5.6% using the backprojection estimate. It was reduced to 4.9% using the profile‐based estimate. In addition, our new approach also reduced visual artifacts in the low dose region. Using the profile‐based estimate, reconstruction converged at about 6 iterations. Using the backprojection estimate, 14 iterations were required for convergence. Conclusion: The proposed method allows more accurate 3D reconstruction with fewer artifacts and requiring fewer iterations. The application is useful in proton beam calibration and has the potential to make 3D quality assurance possible for intensity modulated proton therapy.

Terahertz radiation for tomographic inspection

Three-dimensional (3-D) terahertz computed tomography has already been performed with three different reconstruction methods (standard back-projection algorithm and two iterative analyses) to reconstruct 3-D objects. A Gaussian beam model is developed according to the physical properties of terahertz waves such as the energy distribution within the propagation path. This model is included as a new convolution filter into the tomographic reconstruction methods in order to analyze the impact of a such effect and then to enhance quality and accuracy of the resulting images. We demonstrate the improvements of the optimized reconstructions for applied 3-D terahertz tomography.

GPU-BASED ω-K TOMOGRAPHIC PROCESSING BY 1D NON-UNIFORM FFTS

We present an ω-k approach based on the use of a 1D NonUniform FFT (NUFFT) routine, of NER (Non-Equispaced Results) type, programmed on a GPU in CUDA language, amenable to realtime applications. A Matlab main program links, via mex files, a compiled parallel (CUDA) routine implementing the NUFFT. The approach is shown to be an extension of an already developed parallel algorithm based on standard backprojection processing to account also for near-field data. The implementation of the GPU-based, parallel NUFFT routine is detailed and the computational advantages of the developed approach are highlighted against other confronted sequential or parallel (on multi-core CPU) procedures. Furthermore, the benefits of the ω-k, NUFFT-based processing are pointed out by both comparing its accuracy and computational convenience against other interpolators, and by providing numerical results. By comparing the computational performance of the algorithm against a multi-core, Matlab implementation, the speedup has been about 20 for a medium size image. The performance of the approach has been pointed out in the applicative case of vegetation imaging against experimental data of a boxtree (Buxus tree), also under a source of temporal decorrelation (wind).

An Autofocus Method for Backprojection Imagery in Synthetic Aperture Radar

In this letter, we present an autofocus routine for backprojection imagery from spotlight-mode synthetic aperture radar data. The approach is based on maximizing image sharpness and supports the flexible collection and imaging geometries of BP, including wide-angle apertures and the ability to image directly onto a digital elevation map. While image-quality-based autofocus approaches can be computationally intensive, in the backprojection setting, we demonstrate a natural geometric interpretation that allows for optimal single-pulse phase corrections to be derived in closed form as the solution of a quartic polynomial. The approach is applicable to focusing standard backprojection imagery, as well as providing incremental focusing in sequential imaging applications based on autoregressive backprojection. An example demonstrates the efficacy of the approach applied to real data for a wide-aperture backprojection image.