Three-Dimensional Microwave Imaging: Fast and Accurate Computations with Block Resolution Algorithms.

This paper considers the microwave imaging reconstruction problem, based on additive penalization and gradient-based optimization. Each evaluation of the cost function and of its gradient requires the resolution of as many high-dimensional linear systems as the number of incident fields, which represents a large amount of computations. Since all such systems involve the same matrix, we propose a block inversion strategy, based on the block-biconjugate gradient stabilized (BiCGStab) algorithm, with efficient implementations specific to the microwave imaging context. Numerical experiments performed on synthetic data and on real measurements show that savings in computing time can reach a factor of two compared to the standard, sequential, BiCGStab implementation. Improvements brought by the block approach are even more important for the most difficult reconstruction problems, that is, with high-frequency illuminations and/or highly contrasted objects. The proposed reconstruction strategy is shown to achieve satisfactory estimates for objects of the Fresnel database, even on the most contrasted ones.

System matrix computation vs storage on GPU: A comparative study in cone beam CT.

PURPOSE: Iterative reconstruction algorithms in computed tomography (CT) require a fast method for computing the intersection distances between the trajectories of photons and the object, also called ray tracing or system matrix computation. This work focused on the thin-ray model is aimed at comparing different system matrix handling strategies using graphical processing units (GPUs). METHODS: In this work, the system matrix is modeled by thin rays intersecting a regular grid of box-shaped voxels, known to be an accurate representation of the forward projection operator in CT. However, an uncompressed system matrix exceeds the random access memory (RAM) capacities of typical computers by one order of magnitude or more. Considering the RAM limitations of GPU hardware, several system matrix handling methods were compared: full storage of a compressed system matrix, on-the-fly computation of its coefficients, and partial storage of the system matrix with partial on-the-fly computation. These methods were tested on geometries mimicking a cone beam CT (CBCT) acquisition of a human head. Execution times of three routines of interest were compared: forward projection, backprojection, and ordered-subsets convex (OSC) iteration. RESULTS: A fully stored system matrix yielded the shortest backprojection and OSC iteration times, with a 1.52× acceleration for OSC when compared to the on-the-fly approach. Nevertheless, the maximum problem size was bound by the available GPU RAM and geometrical symmetries. On-the-fly coefficient computation did not require symmetries and was shown to be the fastest for forward projection. It also offered reasonable execution times of about 176.4 ms per view per OSC iteration for a detector of 512 × 448 pixels and a volume of 3843 voxels, using commodity GPU hardware. Partial system matrix storage has shown a performance similar to the on-the-fly approach, while still relying on symmetries. CONCLUSION: Partial system matrix storage was shown to yield the lowest relative performance. On-the-fly ray tracing was shown to be the most flexible method, yielding reasonable execution times. A fully stored system matrix allowed for the lowest backprojection and OSC iteration times and may be of interest for certain performance-oriented applications.

Protocol for Robust In Vivo Measurements of Erythrocyte Aggregation Using Ultrasound Spectroscopy.

Erythrocyte aggregation is a non-specific marker of acute and chronic inflammation. Although it is usual to evaluate this phenomenon from blood samples analyzed in laboratory instruments, in vivo real-time assessment of aggregation is possible with spectral ultrasound techniques. However, variable blood flow can affect the interpretation of acoustic measures. Therefore, flow standardization is required. Two techniques of flow standardization were evaluated with porcine and equine blood samples in Couette flow. These techniques consisted in either stopping the flow or reducing it. Then, the sensibility and repeatability of the retained method were evaluated in 11 human volunteers. We observed that stopping the flow compromised interpretation and repeatability. Conversely, maintaining a low flow provided repeatable measures and could distinguish between normal and high extents of erythrocyte aggregation. Agreement was observed between in vivo and ex vivo measures of the phenomenon (R2 = 82.7%, p value < 0.0001). These results support the feasibility of assessing in vivo erythrocyte aggregation in humans by quantitative ultrasound means.

Coronary Stent Artifact Reduction with an Edge-Enhancing Reconstruction Kernel - A Prospective Cross-Sectional Study with 256-Slice CT.

PURPOSE: Metallic artifacts can result in an artificial thickening of the coronary stent wall which can significantly impair computed tomography (CT) imaging in patients with coronary stents. The objective of this study is to assess in vivo visualization of coronary stent wall and lumen with an edge-enhancing CT reconstruction kernel, as compared to a standard kernel. METHODS: This is a prospective cross-sectional study involving the assessment of 71 coronary stents (24 patients), with blinded observers. After 256-slice CT angiography, image reconstruction was done with medium-smooth and edge-enhancing kernels. Stent wall thickness was measured with both orthogonal and circumference methods, averaging thickness from diameter and circumference measurements, respectively. Image quality was assessed quantitatively using objective parameters (noise, signal to noise (SNR) and contrast to noise (CNR) ratios), as well as visually using a 5-point Likert scale. RESULTS: Stent wall thickness was decreased with the edge-enhancing kernel in comparison to the standard kernel, either with the orthogonal (0.97 ± 0.02 versus 1.09 ± 0.03 mm, respectively; p<0.001) or the circumference method (1.13 ± 0.02 versus 1.21 ± 0.02 mm, respectively; p = 0.001). The edge-enhancing kernel generated less overestimation from nominal thickness compared to the standard kernel, both with the orthogonal (0.89 ± 0.19 versus 1.00 ± 0.26 mm, respectively; p<0.001) and the circumference (1.06 ± 0.26 versus 1.13 ± 0.31 mm, respectively; p = 0.005) methods. The edge-enhancing kernel was associated with lower SNR and CNR, as well as higher background noise (all p < 0.001), in comparison to the medium-smooth kernel. Stent visual scores were higher with the edge-enhancing kernel (p<0.001). CONCLUSION: In vivo 256-slice CT assessment of coronary stents shows that the edge-enhancing CT reconstruction kernel generates thinner stent walls, less overestimation from nominal thickness, and better image quality scores than the standard kernel.

Evaluation of the OSC-TV iterative reconstruction algorithm for cone-beam optical CT.

PURPOSE: The present work evaluates an iterative reconstruction approach, namely, the ordered subsets convex (OSC) algorithm with regularization via total variation (TV) minimization in the field of cone-beam optical computed tomography (optical CT). One of the uses of optical CT is gel-based 3D dosimetry for radiation therapy, where it is employed to map dose distributions in radiosensitive gels. Model-based iterative reconstruction may improve optical CT image quality and contribute to a wider use of optical CT in clinical gel dosimetry. METHODS: This algorithm was evaluated using experimental data acquired by a cone-beam optical CT system, as well as complementary numerical simulations. A fast GPU implementation of OSC-TV was used to achieve reconstruction times comparable to those of conventional filtered backprojection. Images obtained via OSC-TV were compared with the corresponding filtered backprojections. Spatial resolution and uniformity phantoms were scanned and respective reconstructions were subject to evaluation of the modulation transfer function, image uniformity, and accuracy. The artifacts due to refraction and total signal loss from opaque objects were also studied. RESULTS: The cone-beam optical CT data reconstructions showed that OSC-TV outperforms filtered backprojection in terms of image quality, thanks to a model-based simulation of the photon attenuation process. It was shown to significantly improve the image spatial resolution and reduce image noise. The accuracy of the estimation of linear attenuation coefficients remained similar to that obtained via filtered backprojection. Certain image artifacts due to opaque objects were reduced. Nevertheless, the common artifact due to the gel container walls could not be eliminated. CONCLUSIONS: The use of iterative reconstruction improves cone-beam optical CT image quality in many ways. The comparisons between OSC-TV and filtered backprojection presented in this paper demonstrate that OSC-TV can potentially improve the rendering of spatial features and reduce cone-beam optical CT artifacts.

GPU-accelerated regularized iterative reconstruction for few-view cone beam CT.

PURPOSE: The present work proposes an iterative reconstruction technique designed for x-ray transmission computed tomography (CT). The main objective is to provide a model-based solution to the cone-beam CT reconstruction problem, yielding accurate low-dose images via few-views acquisitions in clinically acceptable time frames. METHODS: The proposed technique combines a modified ordered subsets convex (OSC) algorithm and the total variation minimization (TV) regularization technique and is called OSC-TV. The number of subsets of each OSC iteration follows a reduction pattern in order to ensure the best performance of the regularization method. Considering the high computational cost of the algorithm, it is implemented on a graphics processing unit, using parallelization to accelerate computations. RESULTS: The reconstructions were performed on computer-simulated as well as human pelvic cone-beam CT projection data and image quality was assessed. In terms of convergence and image quality, OSC-TV performs well in reconstruction of low-dose cone-beam CT data obtained via a few-view acquisition protocol. It compares favorably to the few-view TV-regularized projections onto convex sets (POCS-TV) algorithm. It also appears to be a viable alternative to full-dataset filtered backprojection. Execution times are of 1-2 min and are compatible with the typical clinical workflow for nonreal-time applications. CONCLUSIONS: Considering the image quality and execution times, this method may be useful for reconstruction of low-dose clinical acquisitions. It may be of particular benefit to patients who undergo multiple acquisitions by reducing the overall imaging radiation dose and associated risks.

Design of iterative ROI transmission tomography reconstruction procedures and image quality analysis.

PURPOSE: An iterative edge-preserving CT reconstruction algorithm for high-resolution imaging of small regions of the field of view is investigated. It belongs to a family of region-of-interest reconstruction techniques in which a low-cost pilot reconstruction of the whole field of view is first performed and then used to deduce the contribution of the region of interest to the projection data. These projections are used for a high-resolution reconstruction of the region of interest (ROI) using a regularized iterative algorithm, resulting in significant computational savings. This paper examines how the technique by which the pilot reconstruction of the full field of view is obtained affects the total runtime and the image quality in the region of interest. METHODS: Previous contributions to the literature have each focused on a single approach for the pilot reconstruction. In this paper, two such approaches are compared: the filtered backprojection and a low-resolution regularized iterative reconstruction method. ROI reconstructions are compared in terms of image quality and computational cost over simulated and physical phantom (Catphan600) studies, in order to assess the compromises that most impact the quality of the ROI reconstruction. RESULTS: With the simulated phantom, new artifacts that appear in the ROI images are caused by significant errors in the pilot reconstruction. These errors include excessive coarseness of the pilot image grid and beam-hardening artifacts. With the Catphan600 phantom, differences in the imaging model of the scanner and that of the iterative reconstruction algorithm cause dark border artifacts in the ROI images. CONCLUSIONS: Inexpensive pilot reconstruction techniques (analytical algorithms, very-coarse-grid penalized likelihood) are practical choices in many common cases. However, they may yield background images altered by edge degradation or beam hardening, inducing projection inconsistency in the data used for ROI reconstruction. The ROI images thus have significant streak and speckle artifacts, which adversely affect the resolution-to-noise compromise. In these cases, edge-preserving penalized-likelihood methods on not-too-coarse image grids prove to be more robust and provide the best ROI image quality.

Reconstruction of real tomographic data using algebraic methods.

We propose an algebraic image reconstruction method that can cope with the size and features of datasets produced by actual scanners, such as angular flying focal spot and detector offset. Image reconstruction is performed by minimizing a penalized least squares objective function by means of a preconditioned conjugate gradient (PCG) algorithm. Efficient implementation of the matrix-vector products that represent projection and backprojection operations is crucial to reconstruction speed, as such operations are performed at least once per iteration. For this purpose, we developed an efficient storage scheme for the projection matrix that allowed fast matrix-vector products. These features, along with an appropriate choice of the preconditioning matrix, yielded a numerically efficient method which produces results with better quality than those provided by usual filtered backprojection techniques.

Penalized-likelihood region-of-interest CT reconstruction by local object supersampling.

We present an iterative 2D tomographic reconstruction procedure for a 2D region of interest (ROI), in which high resolution is required. This method is based on an irregular sampling of the image, the ROI being defined on a fine grid while the rest of the image--the "background"--is sampled on a much coarser grid. The background and the ROI are reconstructed simultaneously from the full set of acquired line integrals. This approach significantly reduces the computational cost of projection and backprojection operations. We also show that this procedure yields images of quality equivalent to full high-resolution reconstruction within the ROI, with dramatic runtime savings.

On global and local convergence of half-quadratic algorithms.

This paper provides original results on the global and local convergence properties of half-quadratic (HQ) algorithms resulting from the Geman and Yang (GY) and Geman and Reynolds (GR) primal-dual constructions. First, we show that the convergence domain of the GY algorithm can be extended with the benefit of an improved convergence rate. Second, we provide a precise comparison of the convergence rates for both algorithms. This analysis shows that the GR form does not benefit from a better convergence rate in general. Moreover, the GY iterates often take advantage of a low cost implementation. In this case, the GY form is usually faster than the GR form from the CPU time viewpoint.

Reduction of Beam-Hardening Artifacts in X-Ray CT.

Our goal is to decrease the importance of beam- hardening artifacts in X-ray computed tomography by address- ing the polyenergetic nature of the X-ray source. We use the same physical model as De Man and al [1]. We next adopt an estimation framework for the reconstruction: the attenuation coefficients are determined by a likelihood-based estimator. This approach leads to minimization of an objective function which exhibits a complex structure. Nonetheless, we develop a numerical procedure with satisfactory numerical efficiency : we use a nonlinear conjugate gradient method. The three major contributions of this communication are : the positivity of the solution ensured by a change of variables, the convergence properties of the algorithm, and a satisfying computation time.

Three-dimensional edge-preserving image enhancement for computed tomography.

Computed tomography (CT) images exhibit a variable amount of noise and blur, depending on the physical characteristics of the apparatus and the selected reconstruction method. Standard algorithms tend to favor reconstruction speed over resolution, thereby jeopardizing applications where accuracy is critical. In this paper, we propose to enhance CT images by applying half-quadratic edge-preserving image restoration (or deconvolution) to them. This approach may be used with virtually any CT scanner, provided the overall point-spread function can be roughly estimated. In image restoration, Markov random fields (MRFs) have proven to be very flexible a priori models and to yield impressive results with edge-preserving penalization, but their implementation in clinical routine is limited because they are often viewed as complex and time consuming. For these practical reasons, we focused on numerical efficiency and developed a fast implementation based on a simple three-dimensional MRF model with convex edge-preserving potentials. The resulting restoration method provides good recovery of sharp discontinuities while using convex duality principles yields fairly simple implementation of the optimization. Further reduction of the computational load can be achieved if the point-spread function is assumed to be separable. Synthetic and real data experiments indicate that the method provides significant improvements over standard reconstruction techniques and compares well with convex-potential Markov-based reconstruction, while being more flexible and numerically efficient.