There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

In the presence of metal implants, metal artifacts are introduced to x-ray computed tomography CT images. Although a large number of metal artifact reduction (MAR) methods have been proposed in the past decades, MAR is still one of the major problems in clinical x-ray CT. In this paper, we develop a convolutional neural network (CNN)-based open MAR framework, which fuses the information from the original and corrected images to suppress artifacts. The proposed approach consists of two phases. In the CNN training phase, we build a database consisting of metal-free, metal-inserted and pre-corrected CT images, and image patches are extracted and used for CNN training. In the MAR phase, the uncorrected and pre-corrected images are used as the input of the trained CNN to generate a CNN image with reduced artifacts. To further reduce the remaining artifacts, water equivalent tissues in a CNN image are set to a uniform value to yield a CNN prior, whose forward projections are used to replace the metal-affected projections, followed by the FBP reconstruction. The effectiveness of the proposed method is validated on both simulated and real data. Experimental results demonstrate the superior MAR capability of the proposed method to its competitors in terms of artifact suppression and preservation of anatomical structures in the vicinity of metal implants.

Convolutional Neural Network Based Metal Artifact Reduction in X-Ray Computed Tomography

Methods to overcome metal artifacts in computed tomography (CT) images have been researched and developed for nearly 40 years. When X-rays pass through a metal object, depending on its size and density, different physical effects will negatively affect the measurements, most notably beam hardening, scatter, noise, and the non-linear partial volume effect. These phenomena severely degrade image quality and hinder the diagnostic power and treatment outcomes in many clinical applications. In this paper, we first review the fundamental causes of metal artifacts, categorize metal object types, and present recent trends in the CT metal artifact reduction (MAR) literature. To improve image quality and recover information about underlying structures, many methods and correction algorithms have been proposed and tested. We comprehensively review and categorize these methods into six different classes of MAR: metal implant optimization, improvements to the data acquisition process, data correction based on physics models, modifications to the reconstruction algorithm (projection completion and iterative reconstruction), and image-based post-processing. The primary goals of this paper are to identify the strengths and limitations of individual MAR methods and overall classes, and establish a relationship between types of metal objects and the classes that most effectively overcome their artifacts. The main challenges for the field of MAR continue to be cases with large, dense metal implants, as well as cases with multiple metal objects in the field of view. Severe photon starvation is difficult to compensate for with only software corrections. Hence, the future of MAR seems to be headed toward a combined approach of improving the acquisition process with dual-energy CT, higher energy X-rays, or photon-counting detectors, along with advanced reconstruction approaches. Additional outlooks are addressed, including the need for a standardized evaluation system to compare MAR methods.

Metal Artifact Reduction in CT: Where Are We After Four Decades?

In this paper, coexistence and stability of multiple equilibrium points of fractional-order recurrent neural networks are addressed. Several sufficient conditions are derived for ascertaining the existence of $ {\prod _{i=1}^{n}(2K_{i}+1)}$ equilibrium points ( $ {K_{i}\geq 0}$ ) and the local Mittag–Leffler stability of $ {\prod _{i=1}^{n}(K_{i}+1)}$ equilibrium points of them by using the geometrical properties of activation functions and algebraic properties of nonsingular ${M}$ -matrix. In contrast with many existing results, the derived results cover both mono-stability and multistability, and the activation functions herein could be nonmonotonic and nonlinear in any open interval. In addition, three numerical examples are elaborated to substantiate the efficacy and characteristics of the theoretical results.

Multiple Mittag–Leffler Stability of Fractional-Order Recurrent Neural Networks

In this paper, we propose a new metal artifacts reduction algorithm based on fractional-order total-variation sinogram inpainting model for X-ray computed tomography (CT). The numerical algorithm for our fractional-order framework is also analyzed. Simulations show that, both quantitatively and qualitatively, our method is superior to conditional interpolation methods and the classic integral-order total variation model.

A new CT metal artifacts reduction algorithm based on fractional-order sinogram inpainting

We propose a novel metal artifact reduction method based on a fractional-order curvature driven diffusion model for X-ray computed tomography. Our method treats projection data with metal regions as a damaged image and uses the fractional-order curvature-driven diffusion model to recover the lost information caused by the metal region. The numerical scheme for our method is also analyzed. We use the peak signal-to-noise ratio as a reference measure. The simulation results demonstrate that our method achieves better performance than existing projection interpolation methods, including linear interpolation and total variation.

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Efficient CT metal artifact reduction based on fractional-order curvature diffusion.

Low-dose computed tomography (LDCT) scans, which can effectively alleviate the radiation problem, will degrade the imaging quality. In this paper, we propose a novel LDCT reconstruction network that unrolls the iterative scheme and performs in both image and manifold spaces. Because patch manifolds of medical images have low-dimensional structures, we can build graphs from the manifolds. Then, we simultaneously leverage the spatial convolution to extract the local pixel-level features from the images and incorporate the graph convolution to analyze the nonlocal topological features in manifold space. The experiments show that our proposed method outperforms both the quantitative and qualitative aspects of state-of-the-art methods. In addition, aided by a projection loss component, our proposed method also demonstrates superior performance for semi-supervised learning. The network can remove most noise while maintaining the details of only 10% (40 slices) of the training data labeled.

MAGIC: Manifold and Graph Integrative Convolutional Network for Low-Dose CT Reconstruction.

Multi-task short-term reactive and active load forecasting method based on attention-LSTM model

The current mainstream computed tomography (CT) reconstruction methods based on deep learning usually need to fix the scanning geometry and dose level, which significantly aggravates the training costs and requires more training data for real clinical applications. In this paper, we propose a parameter-dependent framework (PDF) that trains a reconstruction network with data originating from multiple alternative geometries and dose levels simultaneously. In the proposed PDF, the geometry and dose level are parameterized and fed into two multilayer perceptrons (MLPs). The outputs of the MLPs are used to modulate the feature maps of the CT reconstruction network, which condition the network outputs on different geometries and dose levels. The experiments show that our proposed method can obtain competitive performance compared to the original network trained with either specific or mixed geometry and dose level, which can efficiently save extra training costs for multiple geometries and dose levels.

Yan Liu

Papers

A new CT metal artifacts reduction algorithm based on fractional-order sinogram inpainting

Efficient CT metal artifact reduction based on fractional-order curvature diffusion.

MAGIC: Manifold and Graph Integrative Convolutional Network for Low-Dose CT Reconstruction.

Multi-task short-term reactive and active load forecasting method based on attention-LSTM model

CT Reconstruction With PDF: Parameter-Dependent Framework for Data From Multiple Geometries and Dose Levels