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This article presents a novel undersampled magnetic resonance imaging (MRI) technique that leverages the concept of Neural Radiance Field (NeRF). With radial undersampling, the corresponding imaging problem can be reformulated into an image modeling task from sparse-view rendered data; therefore, a high dimensional MR image is obtainable from undersampled k-space data by taking advantage of implicit neural representation. A multi-layer perceptron, which is designed to output an image intensity from a spatial coordinate, learns the MR physics-driven rendering relation between given measurement data and desired image. Effective undersampling strategies for high-quality neural representation are investigated. The proposed method serves two benefits: (i) The learning is based fully on single undersampled k-space data, not a bunch of measured data and target image sets. It can be used potentially for diagnostic MR imaging, such as fetal MRI, where data acquisition is relatively rare or limited against diversity of clinical images while undersampled reconstruction is highly demanded. (ii) A reconstructed MR image is a scan-specific representation highly adaptive to the given k-space measurement. Numerous experiments validate the feasibility and capability of the proposed approach.

This paper describes the mathematical structure of the ill-posed nonlinear inverse problem of low-dose dental cone-beam computed tomography (CBCT) and explains the advantages of a deep learning-based approach to the reconstruction of computed tomography images over conventional regularization methods. This paper explains the underlying reasons why dental CBCT is more ill-posed than standard computed tomography. Despite this severe ill-posedness, the demand for dental CBCT systems is rapidly growing because of their cost competitiveness and low radiation dose. We then describe the limitations of existing methods in the accurate restoration of the morphological structures of teeth using dental CBCT data severely damaged by metal implants. We further discuss the usefulness of panoramic images generated from CBCT data for accurate tooth segmentation. We also discuss the possibility of utilizing radiation-free intra-oral scan data as prior information in CBCT image reconstruction to compensate for the damage to data caused by metal implants.

Low-dose dental cone beam computed tomography (CBCT) has been increasingly used for maxillofacial modeling. However, the presence of metallic inserts, such as implants, crowns, and dental filling, causes severe streaking and shading artifacts in a CBCT image and loss of the morphological structures of the teeth, which consequently prevents accurate segmentation of bones. A two-stage metal artifact reduction method is proposed for accurate 3D low-dose maxillofacial CBCT modeling, where a key idea is to utilize explicit tooth shape prior information from intra-oral scan data whose acquisition does not require any extra radiation exposure. In the first stage, an image-to-image deep learning network is employed to mitigate metal-related artifacts. To improve the learning ability, the proposed network is designed to take advantage of the intra-oral scan data as side-inputs and perform multi-task learning of auxiliary tooth segmentation. In the second stage, a 3D maxillofacial model is constructed by segmenting the bones from the dental CBCT image corrected in the first stage. For accurate bone segmentation, weighted thresholding is applied, wherein the weighting region is determined depending on the geometry of the intra-oral scan data. Because acquiring a paired training dataset of metal-artifact-free and metal artifact-affected dental CBCT images is challenging in clinical practice, an automatic method of generating a realistic dataset according to the CBCT physics model is introduced. Numerical simulations and clinical experiments show the feasibility of the proposed method, which takes advantage of tooth surface information from intra-oral scan data in 3D low dose maxillofacial CBCT modeling.

We present a fully automated method of integrating intraoral scan (IOS) and dental cone-beam computerized tomography (CBCT) images into one image by complementing each image's weaknesses. Dental CBCT alone may not be able to delineate precise details of the tooth surface due to limited image resolution and various CBCT artifacts, including metal-induced artifacts. IOS is very accurate for the scanning of narrow areas, but it produces cumulative stitching errors during full-arch scanning. The proposed method is intended not only to compensate the low-quality of CBCT-derived tooth surfaces with IOS, but also to correct the cumulative stitching errors of IOS across the entire dental arch. Moreover, the integration provide both gingival structure of IOS and tooth roots of CBCT in one image. The proposed fully automated method consists of four parts; (i) individual tooth segmentation and identification module for IOS data (TSIM-IOS); (ii) individual tooth segmentation and identification module for CBCT data (TSIM-CBCT); (iii) global-to-local tooth registration between IOS and CBCT; and (iv) stitching error correction of full-arch IOS. The experimental results show that the proposed method achieved landmark and surface distance errors of 112.4 $\mu$m and 301.7 $\mu$m, respectively.

Identification of 3D cephalometric landmarks that serve as proxy to the shape of human skull is the fundamental step in cephalometric analysis. Since manual landmarking from 3D computed tomography (CT) images is a cumbersome task even for the trained experts, automatic 3D landmark detection system is in a great need. Recently, automatic landmarking of 2D cephalograms using deep learning (DL) has achieved great success, but 3D landmarking for more than 80 landmarks has not yet reached a satisfactory level, because of the factors hindering machine learning such as the high dimensionality of the input data and limited amount of training data due to ethical restrictions on the use of medical data. This paper presents a semi-supervised DL method for 3D landmarking that takes advantage of anonymized landmark dataset with paired CT data being removed. The proposed method first detects a small number of easy-to-find reference landmarks, then uses them to provide a rough estimation of the entire landmarks by utilizing the low dimensional representation learned by variational autoencoder (VAE). Anonymized landmark dataset is used for training the VAE. Finally, coarse-to-fine detection is applied to the small bounding box provided by rough estimation, using separate strategies suitable for mandible and cranium. For mandibular landmarks, patch-based 3D CNN is applied to the segmented image of the mandible (separated from the maxilla), in order to capture 3D morphological features of mandible associated with the landmarks. We detect 6 landmarks around the condyle all at once, instead of one by one, because they are closely related to each other. For cranial landmarks, we again use VAE-based latent representation for more accurate annotation. In our experiment, the proposed method achieved an averaged 3D point-to-point error of 2.91 mm for 90 landmarks only with 15 paired training data.

Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance imaging, interior tomography, and sparse-view computed tomography, where deep learning techniques have achieved excellent performances. Although deep learning methods appear to overcome the limitations of existing mathematical methods when handling various underdetermined problems, there is a lack of rigorous mathematical foundations that would allow us to elucidate the reasons for the remarkable performance of deep learning methods. This study focuses on learning the causal relationship regarding the structure of the training data suitable for deep learning, to solve highly underdetermined inverse problems. We observe that a majority of the problems of solving underdetermined linear systems in medical imaging are highly non-linear. Furthermore, we analyze if a desired reconstruction map can be learnable from the training data and underdetermined system.

Machine learning-based analysis of medical images often faces several hurdles, such as the lack of training data, the curse of dimensionality problem, and the generalization issues. One of the main difficulties is that there exists computational cost problem in dealing with input data of large size matrices which represent medical images. The purpose of this paper is to introduce a framelet-pooling aided deep learning method for mitigating computational bundle, caused by large dimensionality. By transforming high dimensional data into low dimensional components by filter banks with preserving detailed information, the proposed method aims to reduce the complexity of the neural network and computational costs significantly during the learning process. Various experiments show that our method is comparable to the standard unreduced learning method, while reducing computational burdens by decomposing large-sized learning tasks into several small-scale learning tasks.