An iterative tomosynthesis reconstruction using total variation combined with non-local means filtering.

In tomosynthesis imaging, a small number of projections are acquired from a limited scan angle which is insufficient to reconstruct the image without undesired artifacts. Iterative reconstruction algorithms have been widely used in order to combat this problem. In this study, an effective compressed sensing (CS) based iterative reconstruction algorithm was implemented by applying total variation minimization in TV <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2D</sub> and TV <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3D</sub> forms. ART + TV <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2D</sub> has shown superior results over ART. However, the effect of regularization in the axial dimension is missing in TV <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2D</sub> . A 3D phantom which roughly simulates a breast tomosynthesis image was designed to evaluate if TV <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3D</sub> has a superiority over ART and ART + TV <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2D</sub> in the sense of root mean square error (RMSE) of a specific layer of interest (LOI) and the entire phantom. Computer simulations show that ART + TV <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3D</sub> method substantially enhances the reconstructed image by generating fewer artifacts with smaller error rates.

Isotropic and anisotropic filtering norm-minimization: A generalization of the TV and TGV minimizations using NESTA

Patient radiation dose is a major issue in computerized tomography (CT) imaging. Therefore, many improvements to the classical reconstruction algorithms are suggested to achieve reasonable image quality with less patient dose. The aim of this work is to improve the well-known algebraic reconstruction algorithm (ART) in order to obtain good image quality with less or limited projection angles. We achieve this purpose by sequential application of ART update, total variation minimization (TV), and non-local means (NLM). Both TV and NLM are widely used in imaging algorithms with high performance. To show the improvement in ART by TV and NLM we used a Shepp-Logan phantom simulation and real data from digital tomosynthesis imaging system. Our results indicate that the proposed method provided superior results over two widely used methods, ART and ART+TV, in many senses including Structure SIMilarity (SSIM), signal to noise ratio (SNR) and root mean squared error (RMSE).

Despeckling of ultrasound images, as a very active topic research in medical image processing, plays an important or even indispensable role in subsequent ultrasound image processing. The non-local total variation (NLTV) method has been widely applied to denoising images corrupted by Gaussian noise, but it cannot provide satisfactory restoration results for ultrasound images corrupted by speckle noise. To address this problem, a novel non-local total variation despeckling method is proposed for speckle reduction. In the proposed method, the non-local gradient is computed on the images restored by the optimized Bayesian non-local means (OBNLM) method and it is introduced into the total variation method to suppress speckle in ultrasound images. Comparisons of the restoration performance are made among the proposed method and such state-of-the-art despeckling methods as the squeeze box filter (SBF), the non-local means (NLM) method and the OBNLM method. The quantitative comparisons based on synthetic speckled images show that the proposed method can provide higher Peak signal-to-noise ratio (PSNR) and structure similarity (SSIM) than compared despeckling methods. The subjective visual comparisons based on synthetic and real ultrasound images demonstrate that the proposed method outperforms other compared algorithms in that it can achieve better performance of noise reduction, artifact avoidance, edge and texture preservation.

Total variation (TV) based models are very popular in image denoising but suffer from some drawbacks. For example, local TV methods often cannot preserve edges and textures well when they face excessive smoothing. Non-local TV methods constitute an alternative, but their computational cost is huge. To overcome these issues, we propose an image denoising method named non-local patch graph total variation (NPGTV). Its main originality stands for the graph total variation method, which combines the total variation with graph signal processing. Schematically, we first construct a K-nearest graph from the original image using a non-local patch-based method. Then the model is solved with the Douglas-Rachford Splitting algorithm. By doing so, the image details can be well preserved while being denoised. Experiments conducted on several standard natural images illustrate the effectiveness of our method when compared to some other state-of-the-art denoising methods like classical total variation, non-local means filter (NLM), non-local graph based transform (NLGBT), adaptive graph-based total variation (AGTV).

Image denoising with conditional generative adversarial networks (CGAN) in low dose chest images

The authors present the results of comparing 3D transform and iterative reconstruction methods with measured PET data from the HEAD PENN-PET scanner, which has a very large axial acceptance angle of 27 deg. The algorithms compared are the 3D-reprojection (3DRP) method, the iterative algebraic reconstruction technique (ART), and the maximum likelihood (ML-EM) algorithm. For the iterative methods, alternatives to the cubic voxel basis functions are also implemented. The comparisons are based on a series of figures of merit, including the point-spread function, the contrast recovery coefficient, and signal to noise ratios (SNR). The results show that the ART method implemented with the new basis functions requires only 1 cycle through the data to produce images with measured SNR values comparable to or better than the 3DRP method. The ML-EM method requires 6 to 8 iterations for the test phantom used and produced images with significantly lower SNR values. These are in agreement with previous simulation studies. >

Dual-head small-animal positron emission tomography (DHAPET) has characteristics of high detection sensitivity and flexible system configurations. However, the system geometry may result in severe parallax errors and undetected events along the trans-axial directions, thus reducing the image quality. With the advancement of detector hardware, time-of-flight (TOF) of photons can be detected, which has demonstrated significant improvement in image quality, and can greatly benefit its use in research studies and clinics. Algorithms like total variation (TV) minimization methods that aim to compensate the effects of data truncation can be employed to reconstruct images with better resolution and quality. In this work, we will numerically compute the DHAPET system response matrix that includes TOF information and propose a TOF-PET reconstruction algorithm based on TV-minimization. By applying both TOF information and TV minimization in the iterative algorithm, the reconstructed images can be anticipated to have improved quality with better spatial resolution.

Computed tomography (CT) is capable of generating detailed cross-sectional images of the scanned objects non-destructively. So far, CT has become an increasingly vital tool for 3D modelling of cultural relics. Compressed sensing (CS)-based CT reconstruction algorithms, such as the algebraic reconstruction technique (ART) regularized by total variation (TV), enable accurate reconstructions from sparse-view data, which consequently reduces both scanning time and costs. However, the implementation of the ART-TV is considerably slow, particularly in cone-beam reconstruction. In this paper, we propose an efficient and high-quality scheme for cone-beam CT reconstruction based on the traditional ART-TV algorithm. Our scheme employs Joseph's projection method for the computation of the system matrix. By exploiting the geometric symmetry of the cone-beam rays, we are able to compute the weight coefficients of the system matrix for two symmetric rays simultaneously. We then employ multi-threading technology to speed up the reconstruction of ART, and utilize graphics processing units (GPUs) to accelerate the TV minimization. Experimental results demonstrate that, for a typical reconstruction of a 512 × 512 × 512 volume from 60 views of 512 × 512 projection images, our scheme achieves a speedup of 14 × compared to a single-threaded CPU implementation. Furthermore, high-quality reconstructions of ART-TV are obtained by using Joseph's projection compared with that using traditional Siddon's projection.

In some computed tomography (CT) applications, limited-angle projections are used for image reconstruction, and traditional reconstruction methods, such as filtered back-projection (FBP) or simultaneous algebraic reconstruction technique (SART), cannot reconstruct high-quality CT images without prior knowledge assistance. For limited-angle CT reconstruction, total variation minimization (TVM) method is not conductive to recovering image structures. Image reconstruction methods based on anisotropic total variation (ATV) and reweighted anisotropic total variation (RwATV) can significantly reduce the shading artifacts using prior knowledge of the scanning angular range and image sparsity. However, using the knowledge of image sparsity does not further improve image quality in some applications. In this paper, we propose a new reconstruction method based on anisotropic relative total variation (ARTV) for limited-angle CT reconstruction. In ARTV, the windowed inherent variation (WIV) indicates the strength of structure information and WIV values are adaptively determined by local structure information. In limited-angle CT, particular scanning angular range urges us into exerting different strengths on different directions of ARTV. Experiments on FORBILD HEAD phantom, a thoracic image and real projections of a walnut are performed to test the new method. Experimental results show that the destroyed structures are recovered to some extent, and we acquire higher image quality compared to some existing limited-angle CT reconstruction methods.

Electrocardiographic mapping (ECGM) is to estimate the cardiac activities from the measured body surface potentials (BSPs), in which the epicardial potentials (EPs) is often reconstructed. One of the challenges in ECGM problem is its ill-posedness, and regularization techniques are needed to obtain the clinically reasonable solutions. The total variation (TV) method has been validated in keeping the sharp edges and has found some preliminary applications in ECG inverse problem. In this study, we applied and compared two algorithms: lagged diffusivity (LD) fixed point iteration and primal dual-interior point method (PD-IPM), to implement TV regularization method in ECGM problem. With a realistic heart-lung-torso model, the TV methods are tested and compared to the L2-norm regularization methods in zero- and first-order. The simulation results demonstrate that the TV method can generate better EPs compared to the zero-order Tikhonov method. Compared to the first-order Tikhonov method, the TV’s results are much sharper. For the two algorithms in TV method, the LD algorithm seems more robust than the PD-IPM in ECGM problem, though the PD-IPM converges faster.KeywordsBoundary Element MethodElectrical Impedance TomographyFixed Point IterationTotal Variation RegularizationTikhonov MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In the long-distance space target detection, the technique of laser reflection tomography (LRT) shows great power and attracts more attention for further study and real use. However, space targets are often non-cooperative, and normally a 360° complete view of reflection projections cannot be obtained. Therefore, this article firstly introduces an improved LRT system design with more advanced laser equipment for long-distance non-cooperative detection to ensure the high quality of the lidar beam and the lidar projection data. Then, the LRT image reconstruction is proposed and focused on the laser image reconstruction method utilizing the total variation (TV) minimization approach based on the sparse algebraic reconstruction technique (ART) model, in order to reconstruct the laser image in a sparse or incomplete view of projections. At last, comparative experiments with the system are performed to validate the advantages of this method with the LRT system. In both near and far field experiments, the effectiveness and superiority of the proposed method are verified for different types of projection data through comparison to typical methods.

The authors present the results of comparing 3-D transform and iterative reconstruction methods with measured PET data from the HEAD PENN-PET scanner, which has a very large axial acceptance angle of 27/spl deg/. The algorithms compared are the 3-D-reprojection (3DRP) method, the iterative algebraic reconstruction technique (ART), and the maximum likelihood (ML-EM) algorithm. For the iterative methods, alternatives to the cubic voxel basis functions are also implemented. The comparisons are based on a series of figures of merit, including the point-spread function, the contrast recovery coefficient, and signal-to-noise ratios (SNR). The results show that the ART method implemented with the new basis functions requires only one cycle through the data to produce images with measured SNR values comparable to or better than the 3DRP method. The ML-EM method was run for 10 iterations and produced images with lower SNR values for the test phantom used. With the exception of the ML-EM results, these are in agreement with the authors' previous simulation studies.

Magnetic particle imaging (MPI) is a relatively new method to image the spatial distribution of magnetic nanoparticle (MNP) tracers administered to the body with high spatial and temporal resolution using an inhomogeneous magnetic field. The spatial information of the MNP's is encoded using a field free point (FFP), or a field free line (FFL), in which the magnetic field vanishes at a point, or on a line, respectively. FFL scanning has the advantage of improved sensitivity compared to FFP scanning as a result of higher signal-to-noise ratio. The trajectory traversed by the FFL or FFP is an important parameter of the MPI system and should be selected to achieve the best imaging quality in minimum scan time, while considering hardware constraints and patient safety. In this study, we analyzed the image quality of different FFL trajectories for a large field of view (FOV) using simulations, to provide a baseline information for FFL scanning MPI system design. We simulated a human-sized FFL scanning MPI configuration to image a circular FOV with 160mm diameter, and compared Radial, Spiral, Uniform Spiral, Flower, and Lissajous trajectories with different trajectory densities scanned by the FFL for constant scan time. We analyzed the system matrices of the trajectories in terms of mutual coherence and homogeneity of the spatial sensitivity. We calculated the maximum electric fields induced on a homogeneous conductive body by the selection field (SF) and the focus field (FF) to compare the trajectories based on the nerve stimulation threshold. The images were obtained using the system matrix reconstruction approach with two different image reconstruction methods. In the first one, we used the conventional image reconstruction method, algebraic reconstruction technique (ART), which gives a regularized least-squares solution. In the second one, we used the state-of-the-art alternating direction method of multipliers (ADMM), which minimizes a weighted sum of the l1 -norm and the total variation (TV) of the images. The Radial and Spiral trajectories resulted in a poor imaging performance at low trajectory densities due to relatively high coherency and poor sensitivity of the measurements, respectively. For ART reconstruction, the highest image quality with the lowest trajectory density was achieved with the Uniform Spiral trajectory. Uniform Spiral, Flower, and Lissajous trajectories yielded comparable performance with ADMM reconstruction. The rotating SF induced higher electric field amplitude compared to the FF. Consequently, maximum allowable gradient at the same trajectory density was greater for the Radial trajectory compared to the other trajectories. For a large FOV coverage, the Uniform Spiral trajectory offers a good compromise between image quality and imaging time, taking safety and hardware limitations into account. The Radial trajectory, especially using l1 -norm and TV priors in the reconstruction, may be favorable in case the SF induced electric field is higher than that of the FF at the same frequency (e.g., relatively small FOV coverage). In general, ADMM reconstruction resulted in higher contrast and resolution compared to ART, leading to lighter requirements on the density of the trajectory.

We explore the use of the recently proposed ‘total nuclear variation’ (TVN) as a regularizer for reconstructing multi-channel, spectral CT images. This convex penalty is a natural extension of the total variation (TV) to vector-valued images and has the advantage of encouraging common edge locations and a shared gradient direction among image channels. We show how it can be incorporated into a general, data-constrained reconstruction framework and derive update equations based on the first-order, primal-dual algorithm of Chambolle and Pock. Early simulation studies based on the numerical XCAT phantom indicate that the inter-channel coupling introduced by the TVN leads to better preservation of image features at high levels of regularization, compared to independent, channel-by-channel TV reconstructions.