This paper proposes a deep learning-based denoising method for noisy low-dose computerized tomography (CT) images in the absence of paired training data. The proposed method uses a fidelity-embedded generative adversarial network (GAN) to learn a denoising function from unpaired training data of low-dose CT (LDCT) and standard-dose CT (SDCT) images, where the denoising function is the optimal generator in the GAN framework. This paper analyzes the f-GAN objective to derive a suitable generator that is optimized by minimizing a weighted sum of two losses: the Kullback-Leibler divergence between an SDCT data distribution and a generated distribution, and the 2 loss between the LDCT image and the corresponding generated images (or denoised image). The computed generator reflects the prior belief about SDCT data distribution through training. We observed that the proposed method allows the preservation of fine anomalous features while eliminating noise. The experimental results show that the proposed deep-learning method with unpaired datasets performs comparably to a method using paired datasets. A clinical experiment was also performed to show the validity of the proposed method for noise arising in the low-dose X-ray CT.

Quantitative susceptibility mapping (QSM) is a new medical imaging technique that can visualize magnetic susceptibility, changes of which in tissue indicate various disease processes involving iron transport. The inverse problem of QSM is to recover the susceptibility distribution of the human body from the measured local field that is expressed by the convolution of the susceptibility distribution with the magnetic field generated by a unit dipole. The inverse problem is ill-posed due to the presence of zeros at a cone in the Fourier representation of the unit dipole kernel. Reconstruction methods have been greatly improved to give better recovery of tissue susceptibility data for QSM, and various clinical applications have been pursued. However, rigorous mathematical analyses for the inverse problem, such as demonstrations of the existence and uniqueness of solutions and error characterizations, have not yet been presented. This paper provides for the first time not only a theoretical ground for QSM but also the underlying cause of streaking artifacts.

Metal streak artifacts in X‐ray computerized tomography (CT) are characterized here using the notion of the wavefront set from microlocal analysis. The metal artifacts are caused mainly from the mismatch of the forward model of the filtered back‐projection; the presence of metallic subjects in an imaging subject violates the model's assumption of the CT sinogram data being the Radon transform of an image. The increasing use of metallic implants has increased demand for the reduction of metal artifacts in the field of dental and medical radiography. However, it is a challenging issue due to the serious difficulties in analyzing the X‐ray data, which depends nonlinearly on the distribution of the metallic subject. In this paper, we, for the first time, provide a mathematical analysis to characterize the structure of metal streaking artifacts. The metal streaking artifacts are produced along the line tangent to boundaries of the metal region touching at least two different boundaries. We also found a sufficient condition for the nonexistence of the metal streaking artifacts. © 2017 Wiley Periodicals, Inc.

There is increasing demand in the field of dental and medical radiography for effective metal artifact reduction (MAR) in computed tomography (CT) because artifact caused by metallic objects causes serious image degradation that obscures information regarding the teeth and/or other biological structures. This paper presents a new MAR method that uses the Laplacian operator to reveal background projection data hidden in regions containing data from metal. In the proposed method, we attempted to decompose the projection data into two parts: data from metal only (metal data), and background data in the absence of metal. Removing metal data from the projections enables us to perform sparsity-driven reconstruction of the metal component and subsequent removal of the metal artifact. The results of clinical experiments demonstrated that the proposed MAR algorithm improves image quality and increases the standard of 3D reconstruction images of the teeth and mandible.