Regularization For Reconstruction Research Articles

A content-adaptive unstructured grid based regularized CT reconstruction method with a SART-type preconditioned fixed-point proximity algorithm

The goal of this study is to develop a new computed tomography (CT) image reconstruction method, aiming at improving the quality of the reconstructed images of existing methods while reducing computational costs. Existing CT reconstruction is modeled by pixel-based piecewise constant approximations of the integral equation that describes the CT projection data acquisition process. Using these approximations imposes a bottleneck model error and results in a discrete system of a large size. We propose to develop a content-adaptive unstructured grid (CAUG) based regularized CT reconstruction method to address these issues. Specifically, we design a CAUG of the image domain to sparsely represent the underlying image, and introduce a CAUG-based piecewise linear approximation of the integral equation by employing a collocation method. We further apply a regularization defined on the CAUG for the resulting ill-posed linear system, which may lead to a sparse linear representation for the underlying solution. The regularized CT reconstruction is formulated as a convex optimization problem, whose objective function consists of a weighted least square norm based fidelity term, a regularization term and a constraint term. Here, the corresponding weighted matrix is derived from the simultaneous algebraic reconstruction technique (SART). We then develop a SART-type preconditioned fixed-point proximity algorithm to solve the optimization problem. Convergence analysis is provided for the resulting iterative algorithm. Numerical experiments demonstrate the superiority of the proposed method over several existing methods in terms of both suppressing noise and reducing computational costs. These methods include the SART without regularization and with the quadratic regularization, the traditional total variation (TV) regularized reconstruction method and the TV superiorized conjugate gradient method on the pixel grid.

The effect of Q.Clear reconstruction on quantification and spatial resolution of 18F-FDG PET in simultaneous PET/MR

BackgroundQ.Clear is a block sequential regularized expectation maximization penalized-likelihood reconstruction algorithm for Positron Emission Tomography (PET). It has shown high potential in improving image reconstruction quality and quantification accuracy in PET/CT system. However, the evaluation of Q.Clear in PET/MR system, especially for clinical applications, is still rare. This study aimed to evaluate the impact of Q.Clear on the 18F-fluorodeoxyglucose (FDG) PET/MR system and to determine the optimal penalization factor β for clinical use.MethodsA PET National Electrical Manufacturers Association/ International Electrotechnical Commission (NEMA/IEC) phantom was scanned on GE SIGNA PET/MR, based on NEMA NU 2-2012 standard. Metrics including contrast recovery (CR), background variability (BV), signal-to-noise ratio (SNR) and spatial resolution were evaluated for phantom data. For clinical data, lesion SNR, signal to background ratio (SBR), noise level and visual scores were evaluated. PET images reconstructed from OSEM + TOF and Q.Clear were visually compared and statistically analyzed, where OSEM + TOF adopted point spread function as default procedure, and Q.Clear used different β values of 100, 200, 300, 400, 500, 800, 1100 and 1400.ResultsFor phantom data, as β value increased, CR and BV of all sizes of spheres decreased in general; images reconstructed from Q.Clear reached the peak SNR with β value of 400 and generally had better resolution than those from OSEM + TOF. For clinical data, compared with OSEM + TOF, Q.Clear with β value of 400 achieved 138% increment in median SNR (from 58.8 to 166.0), 59% increment in median SBR (from 4.2 to 6.8) and 38% decrement in median noise level (from 0.14 to 0.09). Based on visual assessment from two physicians, Q.Clear with β values ranging from 200 to 400 consistently achieved higher scores than OSEM + TOF, where β value of 400 was considered optimal.ConclusionsThe present study indicated that, on 18F-FDG PET/MR, Q.Clear reconstruction improved the image quality compared to OSEM + TOF. β value of 400 was optimal for Q.Clear reconstruction.

GSURE criterion for unsupervised regularized reconstruction in tomographic diffractive microscopy.

We propose an unsupervised regularized inversion method for reconstruction of the 3D refractive index map of a sample in tomographic diffractive microscopy. It is based on the minimization of the generalized Stein's unbiased risk estimator (GSURE) to automatically estimate optimal values for the hyperparameters of one or several regularization terms (sparsity, edge-preserving smoothness, total variation). We evaluate the performance of our approach on simulated and experimental limited-view data. Our results show that GSURE is an efficient criterion to find suitable regularization weights, which is a critical task, particularly in the context of reducing the amount of required data to allow faster yet efficient acquisitions and reconstructions.

Learning Deep Subspace Projection Prior for Dual-Camera Compressive Hyperspectral Imaging

Coded aperture snapshot spectral imaging (CASSI) captures the 3-D hyperspectral images (HSI) in the form of 2-D coded images. The dual-camera compressive hyperspectral imaging (DCCHI) can effectively improve the reconstruction quality by adding a parallel complementary panchromatic camera. Several regularization-based methods have been proposed for dual-camera reconstruction. However, the handcrafted priors of these methods are limited in representing the complex intrinsic structure of HSI. In this letter, we propose to learn deep subspace projection prior for dual-camera compressive reconstruction. We first design a deep subspace projection prior regularized dual-camera compressive reconstruction model and minimize it with alternative optimization. Then, we unfold the optimization process into a network. Specifically, the deep subspace projection prior learning leads to features with low-rank characteristics, which could efficiently exploit the spectral correlation of HSI. The dual-camera compressive reconstruction network is learned in an end-to-end manner. Extensive experiments substantiate the performance and efficiency of other start-of-the-art algorithms.

Beam-hardening corrections through a polychromatic projection model integrated to an iterative reconstruction algorithm

In this work, a novel physics-rich beam-hardening correction algorithm was developed for X-ray Computed Tomography. This method uses the spectrum information, the detector response, the filter geometry and a calibration curve. The correction, which does not require prior material knowledge, was embedded in an iterative reconstruction algorithm, and simulates the beam-hardening by estimating the X-ray spectrum at each voxel in the forward projection step. As a result, beam-hardening artifacts are inherently reduced in reconstructed images. For a regular reconstruction matrix of 512 pixels × 512 pixels, processing times of approximately ∼5 s per slice were obtained using a four GPU setup. This method was also compared to the dual-energy beam-hardening correction method proposed by Alvarez and Macovski, which it outperforms when high-Z elements are involved.

Self-paced learning-assisted regularization reconstruction method with data-adaptive prior for electrical capacitance tomography

The advent of electrical capacitance tomography provides a potential visualization-based measurement paradigm for process monitoring, but the large gap between the reconstructed images and the true images poses a great challenge to the application of the technology. To settle the formidable challenge, this study proposes a new two-stage self-paced learning-based reconstruction (SPLR) method. In the first stage, the random forest method is introduced to provide a prediction of the reference image. The reference image prior is data-adaptive and does not require any prior assumptions, which is different from common handcrafted priors. In the second stage, the self-paced learning (SPL) is introduced to build a new optimization problem equipped with the sparse prior and the reference image for formulating the inversion-based reconstruction problem (IBRP), which is solved by a new optimizer that only requires the gradient information, without inversion computation. The new SPLR algorithm achieves not only the fusion of the domain knowledge and the dada-adaptive knowledge learned from the given dataset but also the confluence of the supervised learning and the solution of the IBRP. Quantitative validation results on challenging cases illustrating the performance gain of the SPLR algorithm over the prevalent imaging techniques in terms of reconstruction quality and robustness are displayed.

On Hallucinations in Tomographic Image Reconstruction.

Tomographic image reconstruction is generally an ill-posed linear inverse problem. Such ill-posed inverse problems are typically regularized using prior knowledge of the sought-after object property. Recently, deep neural networks have been actively investigated for regularizing image reconstruction problems by learning a prior for the object properties from training images. However, an analysis of the prior information learned by these deep networks and their ability to generalize to data that may lie outside the training distribution is still being explored. An inaccurate prior might lead to false structures being hallucinated in the reconstructed image and that is a cause for serious concern in medical imaging. In this work, we propose to illustrate the effect of the prior imposed by a reconstruction method by decomposing the image estimate into generalized measurement and null components. The concept of a hallucination map is introduced for the general purpose of understanding the effect of the prior in regularized reconstruction methods. Numerical studies are conducted corresponding to a stylized tomographic imaging modality. The behavior of different reconstruction methods under the proposed formalism is discussed with the help of the numerical studies.

Myocardial blood flow values based on 15O-water PET are insensitive to image reconstruction settings

Abstract Funding Acknowledgements Type of funding sources: None. Background For 15O-water PET, a cutoff hyperemic myocardial blood flow (MBF) value of 2.3 mL/g/min for significant ischemia has been established (1). For other tracers, different studies show a wide range of proposed cutoff values. The use of uniform absolute cutoff values for pathological hyperemic MBF or flow reserve in clinical decision making requires robust quantification of MBF, with comparable values across scanners, centres, and reconstruction methods. Purpose The aim of the present work was to assess the effect of different reconstruction methods on quantitative MBF values based on 15O-water PET. Methods 20 patients referred for assessment of ischemia underwent 4 min dynamic stress PET scans starting simultaneously with automated bolus injection of 400 MBq 15O-water on a digital PET/CT scanner. Images were reconstructed using 17 different reconstruction methods, with the clinical reconstruction used as reference: time-of-flight (TOF) ordered subsets expectation maximization (OSEM) with 3 iterations and 16 subsets, including point spread function recovery (PSF) and a 5 mm gaussian post-filter. Parameters that were varied were number of iterations (1-6), filter (3, 5 or 8 mm), exclusion of TOF and PSF, and using regularized reconstruction with 7 different values of the regularization parameter beta. Images were analyzed fully automatically using aQuant software, resulting in parametric MBF images and polar maps as well as regional MBF values. Correlation and agreement of MBF values based on each reconstruction were compared using regression and Bland-Altman analysis as well as Wilcoxon tests. Results Whole left ventricle MBF values ranged from 1.1 to 3.9 mL/g/min. Visually, there were only small differences in MBF images or polar maps between methods (Figure 1). Correlation between whole left ventricle MBF values based on the various reconstruction algorithms was high (r > 0.99). At the regional level, correlation coefficients were always > 0.94 (Figure 2). No significant bias was found between any of the reconstruction methods and the standard method (p > 0.65). Regression slopes relative to the standard method ranged from 0.993 to 1.080. Changes in reconstruction settings did not alter diagnosis in any patient. Conclusion Changes in reconstruction settings such as filter size, number of iterations, inclusion of time-of-flight or resolution recovery, and regularization, have negligible impact on MBF values based on 15O-water PET analyzed using the automated software. This is likely due to the fact that MBF is determined by the clearance rate of 15O-water rather than its uptake rate such as for other PET tracers, in addition to the used segmentation routines. These results also indicate that quantitative MBF measurements using 15O-water are likely to be robust across different types of PET scanners and hospitals, which is highly important for reliable clinical use of cut-off values for ischemia.

Core Imaging Library - Part II: multichannel reconstruction for dynamic and spectral tomography.

The newly developed core imaging library (CIL) is a flexible plug and play library for tomographic imaging with a specific focus on iterative reconstruction. CIL provides building blocks for tailored regularized reconstruction algorithms and explicitly supports multichannel tomographic data. In the first part of this two-part publication, we introduced the fundamentals of CIL. This paper focuses on applications of CIL for multichannel data, e.g. dynamic and spectral. We formalize different optimization problems for colour processing, dynamic and hyperspectral tomography and demonstrate CIL’s capabilities for designing state-of-the-art reconstruction methods through case studies and code snapshots.This article is part of the theme issue ‘Synergistic tomographic image reconstruction: part 2’.

Implementation of a Framelet-Based Spectral Reconstruction for Multi-Slice Spiral CT

Spectral CT utilizes spectral information of X-ray sources to reconstruct energy-resolved X-ray images and has wide medical applications. Compared with conventional energy-integrated CT scanners, however, spectral CT faces serious technical difficulties in hardware, and hence its clinical use has been expensive and limited. The goal of this paper is to present a software solution and an implementation of a framelet-based spectral reconstruction algorithm for multi-slice spiral scanning based on a conventional energy-integrated CT hardware platform. In the present work, we implement the framelet-based spectral reconstruction algorithm using compute unified device architecture (CUDA) with bowtie filtration. The platform CUDA enables fast execution of the program, while the bowtie filter reduces radiation exposure. We also adopt an order-subset technique to accelerate the convergence. The multi-slice spiral scanning geometry with these additional features will make the framelet-based spectral reconstruction algorithm more powerful for clinical applications. The method provides spectral information from just one scan with a standard energy-integrating detector and produces color CT images, spectral curves of the attenuation coefficient at every point inside the object, and photoelectric images, which are all valuable imaging tools in cancerous diagnosis. The proposed algorithm is tested with a Catphan phantom and real patient data sets for its performance. In experiments with the Catphan 504 phantom, the synthesized color image reveals changes in the level of colors and details and the yellow color in Teflon indicates a special spectral property which is invisible in regular CT reconstruction. In experiments with clinical images, the synthesized color images provide some extra details which are helpful for clinical diagnosis, for example, details about the renal pelvis and lumbar join. The numerical studies indicate that the proposed method provides spectral image information which can reveal fine structures in clinical images and that the algorithm is efficient regarding to the computational time. Thus, the proposed algorithm has a great potential in practical application.

Subspace-constrained approaches to low-rank fMRI acceleration

Acceleration methods in fMRI aim to reconstruct high fidelity images from under-sampled k-space, allowing fMRI datasets to achieve higher temporal resolution, reduced physiological noise aliasing, and increased statistical degrees of freedom. While low levels of acceleration are typically part of standard fMRI protocols through parallel imaging, there exists the potential for approaches that allow much greater acceleration. One such existing approach is k-t FASTER, which exploits the inherent low-rank nature of fMRI. In this paper, we present a reformulated version of k-t FASTER which includes additional L2 constraints within a low-rank framework.We evaluated the effect of three different constraints against existing low-rank approaches to fMRI reconstruction: Tikhonov constraints, low-resolution priors, and temporal subspace smoothness. The different approaches are separately tested for robustness to under-sampling and thermal noise levels, in both retrospectively and prospectively-undersampled finger-tapping task fMRI data. Reconstruction quality is evaluated by accurate reconstruction of low-rank subspaces and activation maps.The use of L2 constraints was found to achieve consistently improved results, producing high fidelity reconstructions of statistical parameter maps at higher acceleration factors and lower SNR values than existing methods, but at a cost of longer computation time. In particular, the Tikhonov constraint proved very robust across all tested datasets, and the temporal subspace smoothness constraint provided the best reconstruction scores in the prospectively-undersampled dataset. These results demonstrate that regularized low-rank reconstruction of fMRI data can recover functional information at high acceleration factors without the use of any model-based spatial constraints.

Anatomy-guided PET reconstruction using l 1 bowsher prior

Advances in simultaneous positron emission tomography/magnetic resonance imaging (PET/MRI) technology have led to an active investigation of the anatomy-guided regularized PET image reconstruction algorithm based on MR images. Among the various priors proposed for anatomy-guided regularized PET image reconstruction, Bowsher’s method based on second-order smoothing priors sometimes suffers from over-smoothing of detailed structures. Therefore, in this study, we propose a Bowsher prior based on the -norm and an iteratively reweighting scheme to overcome the limitation of the original Bowsher method. In addition, we have derived a closed solution for iterative image reconstruction based on this non-smooth prior. A comparison study between the original and proposed Bowsher priors was conducted using computer simulation and real human data. In the simulation and real data application, small lesions with abnormal PET uptake were better detected by the proposed Bowsher prior methods than the original Bowsher prior. The original Bowsher leads to a decreased PET intensity in small lesions when there is no clear separation between the lesions and surrounding tissue in the anatomical prior. However, the proposed Bowsher prior methods showed better contrast between the tumors and surrounding tissues owing to the intrinsic edge-preserving property of the prior which is attributed to the sparseness induced by -norm, especially in the iterative reweighting scheme. Besides, the proposed methods demonstrated lower bias and less hyper-parameter dependency on PET intensity estimation in the regions with matched anatomical boundaries in PET and MRI. Therefore, these methods will be useful for improving the PET image quality based on the anatomical side information.

Refractive three-dimensional reconstruction for underwater stereo digital image correlation.

Measuring the three-dimensional (3D) deformation of submerged objects through different media with the stereo digital image correlation (stereo-DIC) method involves the refractive optical imaging problem where the non-linear transmission of light is induced by a change of medium density. The problem invalidates the underlying single viewpoint assumption of the perspective model in regular stereo-DIC, thereby resulting in erroneous measurements of 3D shape and deformation. In this work, we propose a refractive stereo-DIC method that overcomes the problem by considering light refraction in 3D reconstruction. We formulate a full refractive reconstruction geometry description based on Snell's law of flat refraction and the regular triangulation. This allows the true shape to be effectively reconstructed by tracing and establishing the refracted ray-paths based on the regular 3D reconstruction, without reformulating the camera model and image formation. The refractive stereo-DIC is finally established by integrating the refractive 3D reconstruction into the regular DIC framework for measuring accurate 3D shape and deformation of submerged objects. We experiment the proposed approach with underwater 3D shape and deformation measurements. Both results prove its feasibility and correctness, further heralding our approach as a flexible solution that could readily extend the stereo-DIC to fluid-immersed 3D deformation characterization.

Multiscale wavelet-based regularized reconstruction algorithm for three-dimensional compressed sensing magnetic resonance imaging

Nowadays, the most dynamic and safe imaging technique used in hospitals to diagnose is magnetic resonance imaging (MRI). In clinical applications, such as follow-up of patients with planning surgery, radiation therapy, therapy response in bone metastases assessment and treatment for brain disorders, repeated MRI scans are performed. Unfortunately, the slow acquisitions of MRI drive cost high by limiting patient throughput as well as limiting the potential indications for use. A mathematical framework called compressed sensing (CS) to accelerate MRI acquisition is used for generating undersampled measurements. Then, the iterative nonlinear numerical method is required for perfect reconstruction from highly undersampled measurements. In this work, the multiscale wavelet domain regularization prior-based iterative reconstruction algorithm is developed to address the above-mentioned reconstruction problem, in which multiscale wavelet domain generalized Gaussian mixture model is utilized for the regularization prior. The regularization-based algorithm is applied to generate three-dimensional (3D) high-quality MRI volume from multichannel k-space measurements in a compressed sensing framework. Several experiments using one synthetic and one real 3D CS multichannel k-space data were used to evaluate and validate the performance of the proposed algorithm. The total variation (TV)-based and soft-thresholding (ST) based-reconstruction methods were implemented to compare with the proposed algorithm. Extensive experimental results demonstrated that the proposed method has improved results in terms of visual quality and quantitative measurements compared to the existing methods.

An improved patch-based regularization method for PET image reconstruction

Statistical reconstruction methods based on penalized maximum likelihood (PML) are being increasingly used in positron emission tomography (PET) imaging to reduce noise and improve image quality. Wang and Qi proposed a patch-based edge-preserving penalties algorithm that can be implemented in three simple steps: a maximum-likelihood expectation-maximization (MLEM) image update, an image smoothing step, and a pixel-by-pixel image fusion step. The pixel-by-pixel image fusion step, which fuses the MLEM updated image and the smoothed image, involves a trade-off between preserving the fine structural features of an image and suppressing noise. Particularly when reconstructing images from low-count data, this step cannot preserve fine structural features in detail. To better preserve these features and accelerate the algorithm convergence, we proposed to improve the patch-based regularization reconstruction method. Our improved method involved adding a total variation (TV) regularization step following the MLEM image update in the patch-based algorithm. A feature refinement (FR) step was then used to extract the lost fine structural features from the residual image between the TV regularized image and the fused image based on patch regularization. These structural features would then be added back to the fused image. With the addition of these steps, each iteration of the image should gain more structural information. A brain phantom simulation experiment and a mouse study were conducted to evaluate our proposed improved method. Brain phantom simulation with added noise were used to determine the feasibility of the proposed algorithm and its acceleration of convergence. Data obtained from the mouse study were divided into event count sets to validate the performance of the proposed algorithm when reconstructing images from low-count data. Five criteria were used for quantitative evaluation: signal-to-noise ratio (SNR), covariance (COV), contrast recovery coefficient (CRC), regional relative bias, and relative variance. The bias and variance of the phantom brain image reconstructed using the patch-based method were 0.421 and 5.035, respectively, and this process took 83.637 seconds. The bias and variance of the image reconstructed by the proposed improved method, however, were 0.396 and 4.568, respectively, and this process took 41.851 seconds. This demonstrates that the proposed algorithm accelerated the reconstruction convergence. The CRC of the phantom brain image reconstructed using the patch-based method was iterated 20 times and reached 0.284, compared with the proposed method, which reached 0.446. When using a count of 5,000 K data obtained from the mouse study, both the patch-based method and the proposed method reconstructed images similar to the ground truth image. The intensity of the ground truth image was 88.3, and it was located in the 102nd row and the 116th column. However, when the count was reduced to below 40 K, and the patch-based method was used, image quality was significantly reduced. This effect was not observed when the proposed method was used. When a count of 40 K was used, the image intensity was 58.79 when iterated 100 times by the patch-based method, and it was located in the 102nd row and the 116th column, while the intensity when iterated 50 times by the proposed method was 63.83. This suggests that the proposed method improves image reconstruction from low-count data. This improved method of PET image reconstruction could potentially improve the quality of PET images faster than other methods and also produce better reconstructions from low-count data.

Whole-body 18-F-FDG-PET in patients with leptomeningeal disease and correlation with MRI.

Studies evaluating leptomeningeal disease on whole-body 18F-FDG PET are lacking. The purpose was to evaluate PET imaging of leptomeningeal disease and investigate the incremental utility of newer PET reconstructions in leptomeningeal disease. PET imaging of 56 patients with leptomeningeal disease detected initially on MRI (n = 53) or cytopathology (n = 35) were retrospectively reviewed. Regular 3-dimensional iterative reconstruction (3D IR, n = 56) and advanced reconstruction (AdvRecon, n = 41) PET images were evaluated by readers blinded to clinical and MRI findings for uptake involving cauda equina, posterior fossa and spinal cord. Spinal cord uptake pattern was classified as normal (uptake < liver), uptake = liver, conus uptake > liver, conus and cervical cord uptake > liver and multifocal/diffuse uptake > liver. SUVmax ratios of conus/liver, conus/left atrium and conus/cervical cord were compared between 3D IR and AdvRecon datasets. Cauda equina uptake was seen in 64% and 78% on 3D IR and AdvRecon; posterior fossa uptake was seen in 52% and 54% on 3D IR and AdvRecon, respectively. Twelve percent had cauda equina or posterior fossa uptake visible only on AdvRecon. On 3D IR, normal spinal cord uptake was most common (27%); on AdvRecon, conus and cervical cord uptake > liver was most common (32%). Seven of 11 patients with normal spinal cord uptake on 3D IR were upgraded to increased uptake on AdvRecon. AdvRecon showed significantly higher conus/liver, conus/blood pool and conus/cervical cord SUVmax ratios (P < 0.0001). Abnormal uptake in cauda equina, posterior fossa and spinal cord uptake are visible on FDG PET in leptomeningeal disease with increased conspicuity advanced PET reconstructions.

An Efficient One-Step Method for Spectral CT Based on an Approximate Linear Model

Spectral computed tomography (spectral CT) is a medical and biomedical imaging technique which uses the spectral information of the attenuated X-ray beam. Energy-resolved photon-counting detector is a promising technique for improved spectral CT imaging and allows to obtain material selective images. Two different kind of approaches can be used to solve the problem of spectral reconstruction consisting of material decomposition and tomographic reconstruction: the “two steps” methods which are most often projection-based methods, and the “one step” methods. While the projection-based methods are interesting for the fast computational time, the one-step methods link directly the material image domain and the multienergy sinograms domain, which is an advantage to introduce spatial prior information in the material image domain. In this work we propose a proximal operator associated to a data fidelity term (based on an empirical linear forward model) for multimaterial decomposition. This proximal operator, which has a closed-form solution, makes it possible to propose fast regularized reconstruction methods for spectral CT, in particular for data of photon-counting detectors with many energy bins. We propose a one-step method based on the alternating direction method of multipliers (ADMM) and this proximal operator. We present promising results on dual material image reconstructions obtained from simulated and experimental data. We show qualitative and quantitative comparisons with two previously published multimaterial decomposition methods.

Magnetic resonance imaging reconstruction via non‐convex total variation regularization

AbstractMagnetic resonance imaging (MRI) reconstruction model based on total variation (TV) regularization can deal with problems such as incomplete reconstruction, blurred boundary, and residual noise. In this article, a non‐convex isotropic TV regularization reconstruction model is proposed to overcome the drawback. Moreau envelope and minmax‐concave penalty are firstly used to construct the non‐convex regularization of L2 norm, then it is applied into the TV regularization to construct the sparse reconstruction model. The proposed model can extract the edge contour of the target effectively since it can avoid the underestimation of larger nonzero elements in convex regularization. In addition, the global convexity of the cost function can be guaranteed under certain conditions. Then, an efficient algorithm such as alternating direction method of multipliers is proposed to solve the new cost function. Experimental results show that, compared with several typical image reconstruction methods, the proposed model performs better. Both the relative error and the peak signal‐to‐noise ratio are significantly improved, and the reconstructed images also show better visual effects. The competitive experimental results indicate that the proposed approach is not limited to MRI reconstruction, but it is general enough to be used in other fields with natural images.

Improving the Accuracy of Automatic Reconstruction of 3D Complex Buildings Models from Airborne Lidar Point Clouds

Due to high requirements of variety of 3D spatial data applications with respect to data amount and quality, automatized, efficient and reliable data acquisition and preprocessing methods are needed. The use of photogrammetry techniques—as well as the light detection and ranging (LiDAR) automatic scanners—are among attractive solutions. However, measurement data are in the form of unorganized point clouds, usually requiring transformation to higher order 3D models based on polygons or polyhedral surfaces, which is not a trivial process. The study presents a newly developed algorithm for correcting 3D point cloud data from airborne LiDAR surveys of regular 3D buildings. The proposed approach assumes the application of a sequence of operations resulting in 3D rasterization, i.e., creation and processing of a 3D regular grid representation of an object, prior to applying a regular Poisson surface reconstruction method. In order to verify the accuracy and quality of reconstructed objects for quantitative comparison with the obtained 3D models, high-quality ground truth models were used in the form of the meshes constructed from photogrammetric measurements and manually made using buildings architectural plans. The presented results show that applying the proposed algorithm positively influences the quality of the results and can be used in combination with existing surface reconstruction methods in order to generate more detailed 3D models from LiDAR scanning.

Optimization of [18F]PSMA-1007 PET-CT using regularized reconstruction in patients with prostate cancer

BackgroundProstate-specific membrane antigen (PSMA) radiotracers such as [18F]PSMA-1007 used with positron emission tomography-computed tomography (PET-CT) is promising for initial staging and detection of recurrent disease in prostate cancer patients. The block-sequential regularization expectation maximization algorithm (BSREM) is a new PET reconstruction algorithm, which provides higher image contrast while also reducing noise. The aim of the present study was to evaluate the influence of different acquisition times and different noise-suppressing factors in BSREM (β values) in [18F]PSMA-1007 PET-CT regarding quantitative data as well as a visual image quality assessment.We included 35 patients referred for clinical [18F]PSMA-1007 PET-CT. Four megabecquerels per kilogramme were administered and imaging was performed after 120 min. Eighty-four image series per patient were created with combinations of acquisition times of 1–4 min/bed position and β values of 300–1400. The noise level in normal tissue and the contrast-to-noise ratio (CNR) of pathological uptakes versus the local background were calculated. Image quality was assessed by experienced nuclear medicine physicians.ResultsThe noise level in the liver, spleen, and muscle was higher for low β values and low acquisition times (written as activity time products (ATs = administered activity × acquisition time)) and was minimized at maximum AT (16 MBq/kg min) and maximum β (1400). There was only a small decrease above AT 10. The median CNR increased slowly with AT from approximately 6 to 12 and was substantially lower at AT 4 and higher at AT 14–16. At AT 4–6, many images were regarded as being of unacceptable quality. For AT 8, β values of 700–900 were considered of acceptable quality.ConclusionsAn AT of 8 (for example as in our study, 4 MB/kg with an acquisition time of 2 min) with a β value of 700 performs well regarding noise level, CNR, and visual image quality assessment.