Computed tomography noise reduction based on total variation minimization and morphological component analysis

Computer algorithms that simulate lower-doses computed tomography (CT) images from clinical-dose images are widely available. However, most operate in the projection domain and assume access to the reconstruction method. Access to commercial reconstruction methods may often not be available in medical research, making image-domain noise simulation methods useful. However, the introduction of non-linear reconstruction methods, such as iterative and deep learning-based reconstruction, makes noise insertion in the image domain intractable, as it is not possible to determine the noise textures analytically. To develop a deep learning-based image-domain method to generate low-dose CT images from clinical-dose CT (CDCT) images for non-linear reconstruction methods. We propose a fully image domain-based method, utilizing a series of three convolutional neural networks (CNNs), which, respectively, denoise CDCT images, predict the standard deviation map of the low-dose image, and generate the noise power spectra (NPS) of local patches throughout the low-dose image. All three models have U-net-based architectures and are partly or fully three-dimensional. As a use case for this study and with no loss of generality, we use paired low-dose and clinical-dose brain CT scans. A dataset of paired scans was retrospectively obtained. All images were acquired with a wide-area detector clinical system and reconstructed using its standard clinical iterative algorithm. Each pair was registered using rigid registration to correct for motion between acquisitions. The data was randomly partitioned into training ( samples), validation ( samples), and test ( samples) sets. The performance of each of these three CNNs was validated separately. For the denoising CNN, the local standard deviation decrease, and bias were determined. For the standard deviation map CNN, the real and estimated standard deviations were compared locally. Finally, for the NPS CNN, the NPS of the synthetic and real low-dose noise were compared inside and outside the skull. Two proof-of-concept denoising studies were performed to determine if the performance of a CNN- or a gradient-based denoising filter on the synthetic low-dose data versus real data differed. The denoising network had a median decrease in noise in the cerebrospinal fluid by a factor of and introduced a median bias of HU. The network for standard deviation map estimation had a median error of HU. The noise power spectrum estimation network was able to capture the anisotropic and shift-variant nature of the noise structure by showing good agreement between the synthetic and real low-dose noise and their corresponding power spectra. The two proof of concept denoising studies showed only minimal difference in standard deviation improvement ratio between the synthetic and real low-dose CT images with the median difference between the two being 0.0 and +0.05 for the CNN- and gradient-based filter, respectively. The proposed method demonstrated good performance in generating synthetic low-dose brain CT scans without access to the projection data or to the reconstruction method. This method can generate multiple low-dose image realizations from one clinical-dose image, so it is useful for validation, optimization, and repeatability studies of image-processing algorithms.

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

CT reconstruction from few-views with anisotropic edge-guided total variance

To reduce the cost of positron emission tomography (PET) scanning systems, image reconstruction algorithms for low-sampled data have been extensively studied. However, the current method based on total variation (TV) minimization regularization nested in the maximum likelihood-expectation maximization (MLEM) algorithm cannot distinguish true structures from noise resulting losing some fine features in the images. Thus, this work aims to recover fine features lost in the MLEM-TV algorithm from low-sampled data. A feature refinement (FR) approach previously developed for statistical interior computed tomography (CT) reconstruction is applied to PET imaging to recover fine features in this study. The proposed method starts with a constant initial image and the FR step is performed after each MLEM-TV iteration to extract the desired structural information lost during TV minimization. A feature descriptor is specifically designed to distinguish structure from noise and artifacts. A modified steepest descent method is adopted to minimize the objective function. After evaluating the impacts of different patch sizes on the outcome of the presented method, an optimal patch size of 7×7 is selected in this study to balance structure-detection ability and computational efficiency. Applying MLEM-TV-FR algorithm to the simulated brain PET imaging using an emission activity phantom, a standard Shepp-Logan phantom, and mouse results in the increased peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) as comparing to using the conventional MLEM-TV algorithm, as well as the substantial reduction of the used sampling numbers, which improves the computational efficiency. The presented algorithm can achieve image quality superior to that of the MLEM and MLEM-TV approaches in terms of the preservation of fine structure and the suppression of undesired artifacts and noise, indicating its useful potential for low-sampled data in PET imaging.

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.

Practical simulations of low-dose CT images have a possibility of being helpful means for optimization of the CT exposure dose. Because current methods reported by several researchers are limited to specific vendor platforms and generally rely on raw sinogram data that are difficult to access, we have developed a new computerized scheme for producing simulated low-dose CT images from real high-dose images without use of raw sinogram data or of a particular phantom. Our computerized scheme for low-dose CT simulation was based on the addition of a simulated noise image to a real high-dose CT image reconstructed by the filtered back-projection algorithm. First, a sinogram was generated from the forward projection of a high-dose CT image. Then, an additional noise sinogram resulting from use of a reduced exposure dose was estimated from a predetermined noise model. Finally, a noise CT image was reconstructed with a predetermined filter and was added to the real high-dose CT image to create a simulated low-dose CT image. The noise power spectrum and modulation transfer function of the simulated low-dose images were very close to those of the real low-dose images. In order to confirm the feasibility of our method, we applied this method to clinical cases which were examined with the high dose initially and then followed with a low-dose CT. In conclusion, our proposed method could simulate the low-dose CT images from their real high-dose images with sufficient accuracy and could be used for determining the optimal dose setting for various clinical CT examinations.

The total variation (TV) minimization image reconstruction algorithm for inverting the divergent-beam x-ray transform is applied to image reconstruction in circular cone-beam computed tomography (CT). Reconstructions for the disk phantom are shown and compared with that of projection onto convex sets (POCS). The preliminary results appear to show that TV-minimization yields accurate image reconstructions that are robust against data inconsistencies due to noise or mismatch in the system matrix.

Tensor completion has attracted attention because of its promising ability and generality. However, there are few studies on noisy scenarios which directly solve an optimization problem consisting of a "noise inequality constraint". In this paper, we propose a new tensor completion and denoising model including tensor total variation and tensor nuclear norm minimization with a range of values and noise inequalities. Furthermore, we developed its solution algorithm based on a primal-dual splitting method, which is computationally efficient as compared to tensor decomposition based non-convex optimization. Lastly, extensive experiments demonstrated the advantages of the proposed method for visual data retrieval such as for color images, movies, and 3D-volumetric data.

This paper introduced a novel method to reconstruct low-dose computed tomography (LDCT) images based on weighted total variation minimization. Previous work has shown that a CT image can be reconstructed from under-sampling data by minimizing the total variation (TV) of the image with some constraints. However, due to the piecewise constant assumption, the conventional TV minimization algorithm often suffers over-smooth on the edges of the resulted image. Considering the anisotropic property of the edge voxels in an image, we proposed a weighted total variation (WTV) minimization algorithm to achieve high-quality LDCT image reconstruction from under-sampling sinogram data. The proposed algorithm was evaluated by computer simulation, where the Shepp-Logan phantom was used. In noise free cases, 20 projection views were enough to accurately reconstruct the phantom image by the WTV approach while the filtered backprojection (FBP) reconstruction failed. In noise cases, different levels of Poisson noise were added to the noise-free sinogram. The local signal to noise ratio (SNR) and global SNR were computed to evaluate the robustness of the WTV algorithm to the noise. The simulation results showed that the WTV algorithm can have much higher global SNR compared to the conventional TV. The relationship between the number of views of WTV algorithm and the mean square error (MSE) of the reconstructed images was also discussed in this paper in order to find the minimum projection numbers required to obtain an adequate reconstruction image for low-dose CT applications.

Positron emission tomography (PET) and computed tomography (CT) play a vital role in tumor-related medical diagnosis, assessment, and treatment planning. However, full-dose PET and CT pose the risk of excessive radiation exposure to patients, whereas low-dose images compromise image quality, impacting subsequent tumor recognition and diseasediagnosis. To solve such problems, we propose a Noise-Assisted Hybrid Attention Network (NAHANet) to reconstruct full-dose PET and CT images from low-dose PET (LDPET) and CT (LDCT) images to reduce patient radiation risks while ensuring the performance of subsequent tumor recognition. NAHANet contains two branches: the noise feature prediction branch (NFPB) and the cascaded reconstruction branch. Among them, NFPB providing noise features for the cascade reconstruction branch. The cascaded reconstruction branch comprises a shallow feature extraction module and a reconstruction module which contains a series of cascaded noise feature fusion blocks (NFFBs). Among these, the NFFB fuses the features extracted from low-dose images with the noise features obtained by NFPB to improve the feature extraction capability. To validate the effectiveness of the NAHANet method, we performed experiments using two public available datasets: the Ultra-low Dose PET Imaging Challenge dataset and Low Dose CT Grand Challengedataset. As a result, the proposed NAHANet achieved higher performance on common indicators. For example, on the CT dataset, the PSNR and SSIM indicators were improved by 4.1dB and 0.06 respectively, and the rMSE indicator was reduced by 5.46 compared with the LDCT; on the PET dataset, the PSNR and SSIM was improved by 3.37dB and 0.02, and the rMSE was reduced by 9.04 compared with theLDPET. This paper proposes a transformer-based denoising algorithm, which utilizes hybrid attention to extract high-level features of low dose images and fuses noise features to optimize the denoising performance of the network, achieving good performance improvements on low-dose CT and PETdatasets.

A computational and experimental study is conducted to examine how directivity associated with a finite aperture sensor affects photoacoustic tomography (PAT) image reconstruction. Acoustic signals for the simulation work were computed using a discrete particle approach from three numerical phantoms including a vasculature. The theoretical framework and a Monte Carlo approach for construction of a tissue configuration are discussed in detail. While simulating forward data, the directivity of the sensor was taken into account. The image reconstruction was accomplished using system matrix based methods like l2 norm Tikhonov regularization, l1 norm regularization and total variation (TV) minimization. Accordingly, two different system matrices were constructed- (i) assuming transducer as a point detector (PD) and (ii) retaining properties of a finite detector with directivity (FDWD). Image reconstruction was also performed utilizing experimentally measured PA signals. Both the computational and experimental results demonstrate that blur-free PAT imaging can be achieved with the FDWD method. Additionally, TV minimization provides marginally better image reconstruction compared to the other schemes.

Computed tomography (CT) technology has been rapidly developed and widely used in the medical field, at the same time, it has also attracted people’s attention to its radiation dose. Although reducing the dose of X-rays can greatly reduce a patient’s chance of developing cancer, the lower the dose, the worse the quality of the generated image, generating speckle noise and streaking artifacts that can seriously affect the diagnostic results. Therefore, low-dose CT images need to be optimized and enhanced to facilitate expert diagnosis. Based on WGAN-VGG, this paper proposes an improved generative adversarial network for CT image denoising. The algorithm improves the loss functions of the generator and discriminator, and introduces noise loss, which constitutes a composite perceptual loss function with perceptual loss. This method not only prevents over fitting of results and low PSNR and SSIM, but also can better measure the internal similarity between images, so that the visual texture details of the image can achieve a more detailed restoration effect, which is helpful to reduce noise and see clearer details. Experiments have shown that the algorithm accelerates the convergence of loss function, effectively improves the problems of difficult training of generative adversarial network and slow convergence of loss function, and can better remove noise and restore more image details at the same time.

In recent years, there has been increased interest in low-dose X-ray cone beam computed tomography (CBCT) in many fields, including dentistry, guided radiotherapy and small animal imaging. Despite reducing the radiation dose, low-dose CBCT has not gained widespread acceptance in routine clinical practice. In addition to performing more evaluation studies, developing a fast and high-quality reconstruction algorithm is required. In this work, we propose an iterative reconstruction method that accelerates ordered-subsets (OS) reconstruction using a power factor. Furthermore, we combine it with the total-variation (TV) minimization method. Both simulation and phantom studies were conducted to evaluate the performance of the proposed method. Results show that the proposed method can accelerate conventional OS methods, greatly increase the convergence speed in early iterations. Moreover, applying the TV minimization to the power acceleration scheme can further improve the image quality while preserving the fast convergence rate.

Computed tomography (CT) images with a low-dose protocol generally have severe mottle noise and streak artifacts. In this paper, we propose a novel diffusion method named “artifact suppressed nonlinear diffusion filtering (ASNDF),” to process low-dose CT (LDCT) images. Different from other diffusion filtering methods, the proposed ASNDF not only includes image gradient as the main cue to construct a diffusion coefficient function, but also incorporates the local variances of image to be diffused and residual image between two adjacent diffusions. In detail, the classical PM diffusion is first performed to get the initial residual image, and then from the second iteration, the LDCT image is processed according to the ASNDF processing. Simulated data, clinical data and rat data are conducted to evaluate the proposed method, and the comparison experiments with other competing methods show that the proposed ASNDF method makes an improvement in artifact suppression and structure preservation, and offers a sound alternative to process LDCT images from most current CT systems.

High Quality 4-dimensional Cone Beam CT by Deforming Prior Images