Semi-supervised learning performs accurate segmentation by effectively leveraging unlabeled data. Most existing methods struggle to capture complex global data distribution, which is particularly important for medical images characterized by intricate background structures and ambiguous boundaries. Class prototypes are commonly used to represent the essential semantic representation of each class. Most prototype methods construct a single prototype vector per class using convolutional neural networks (CNNs), thereby neglecting both distribution modeling and intra-class variability. To address these issues, we propose a diffusion and spatial prototype learning method (DSP) for semi-supervised medical image segmentation. Firstly, the Image-to-Segmentation Diffusion Model (ISDM) generates pseudo-labels rich in distribution information from the original image. Secondly, the diffusion network is combined with a Convolutional Segmentation Network (CSN) to simultaneously learn data distribution and anatomical details. Thirdly, class prototypes are constructed at the voxel level and combined with the diffusion model to make them spatially aware and incorporate global distribution information. Extensive experiments on three benchmark medical image datasets (left atrium and brain tumor) show that our method achieves state-of-the-art performance, validating its effectiveness. Code is available at: https://github.com/Lianyuan-Yu/DSP.

Semi-supervised learning leverages insights from unlabeled data to enhance generalizability of the model, thereby decreasing the dependence on extensive labeled datasets. Most existing methods overly focus on local representations while neglecting the learning of global structures. On the one hand, given that labeled and unlabeled images are presumed to originate from the same distribution, it is probable that similar regional features observed in both types of images correspond to the same label. Current label propagation techniques, which predominantly propagate label information through the construction of graph structures or similarity matrices, heavily depend on localized information and are prone to converge to local optima. In contrast, optimal transport considers the entire distribution. This facilitates more comprehensive and efficient label propagation. On the other hand, current consistency regularization-based methods focus on the local view, we believe learning from a global geometric view may capture more information. Geometric moment information of the sample itself can constrain the overall geometric structure. Inspired by these observations, this paper introduces a semi-supervised medical image segmentation framework that integrates optimal transport and central moment consistency regularization (OTCMC) from a global perspective. Firstly, we pass label information from labeled data to unlabeled data by optimal transport. Secondly, we incorporate central moment consistency regularization to focus the network on the geometric structure of images. Our method achieves the state-of-the-art (SOTA) performance on a series of datasets, including the NIH pancreas, left atrium, brain tumor, and skin lesion dermoscopy datasets.

Rician noise reduction is an essential issue in magnetic resonance imaging (MRI). Recently, learning‐based methods have achieved great success in dealing with image restoration problems, which provide fast inference and good performance. One limitation of these methods, however, is that the training procedure is usually noise‐level dependent, i.e. the trained models are bound to a specific noise level and lack the ability to automatically adapt to different noise levels. In this study, the authors propose a variational model for Rician noise removal by integrating a noise adaption function into the field of experts image prior, which can adapt to different noise levels. Instead of directly solving the energy minimisation problem, the authors unroll the gradient descent step of the energy functional for several iterations, the time‐dependent parameters of which can be learned through a supervised training process. The authors call this methodology as the noise adaptive trainable non‐linear reaction–diffusion model. The proposed methodology is robustness against noise level changing and noise distributions. Experimental results over ‐, ‐ and PD‐weighted MRI data set demonstrate that the proposed model can achieve superior performance compared with other methods in terms of both the peak signal‐to‐noise ratio and the structural similarity index.

Random walk is a popular and efficient algorithm for image segmentation, especially for extracting regions of interest (ROIs). One difficulty with the random walk algorithm is the requirement for solving a huge sparse linear system when applied to large images. Another limitation is its sensitivity to seeds distribution, i.e., the segmentation result depends on the number of seeds as well as their placement, which puts a burden on users. In this paper, we first propose a continuous random walk model with explicit coherence regularization (CRWCR) for the extracted ROI, which helps to reduce the seeds sensitivity, so as to reduce the user interactions. Then, a very efficient algorithm to solve the CRWCR model will be developed, which helps to remove the difficulty of solving huge linear systems. Our algorithm consists of two stages: initialization by performing one-dimensional random walk sweeping based on user-provided seeds, followed by the alternating direction scheme, i.e., Peaceman-Rachford scheme for further correction. The first stage aims to provide a good initial guess for the ROI, and it is very fast since we just solve a limited number of one-dimensional random walk problems. Then, this initial guess is evolved to the ideal solution by applying the second stage, which should also be very efficient since it fits well for GPU computing, and 10 iterations are usually sufficient for convergence. Numerical experiments are provided to validate the proposed model as well as the efficiency of the two-stage algorithm.

Computed laminography (CL) is a prospective nondestructive testing technique for flat object inspection in industrial applications. However, CL image reconstruction is a challenging task because incomplete projection data are acquired from the CL scan. When a conventional computed tomography (CT) reconstruction method is applied to cone beam CL data, the vertical edges (singularities in the z-direction) in the reconstructed image would be blurred. On the contrary, the horizontal edges (singularities within slices) can be quite accurately reconstructed. Based on this key observation, an edge information diffusion method is developed, which fixes the horizontal edges and propagates their values within the slices. An effective CL reconstruction method is then proposed for flat object inspection by combining the edge information diffusion procedure, which plays the role of regularization, with conventional CT image reconstruction algorithms. Experiments on both simulated data and real data are performed to verify the effectiveness of the proposed method. The results show that the proposed method can effectively suppress the inter-slice aliasing and blurring caused by incompleteness of the CL scan data, and that it outperforms other state-of-the-art methods.