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Accurate detection and segmentation of brain tumors is critical for medical diagnosis. However, current supervised learning methods require extensively annotated images and the state-of-the-art generative models used in unsupervised methods often have limitations in covering the whole data distribution. In this paper, we propose a novel framework Two-Stage Generative Model (TSGM) that combines Cycle Generative Adversarial Network (CycleGAN) and Variance Exploding stochastic differential equation using joint probability (VE-JP) to improve brain tumor detection and segmentation. The CycleGAN is trained on unpaired data to generate abnormal images from healthy images as data prior. Then VE-JP is implemented to reconstruct healthy images using synthetic paired abnormal images as a guide, which alters only pathological regions but not regions of healthy. Notably, our method directly learned the joint probability distribution for conditional generation. The residual between input and reconstructed images suggests the abnormalities and a thresholding method is subsequently applied to obtain segmentation results. Furthermore, the multimodal results are weighted with different weights to improve the segmentation accuracy further. We validated our method on three datasets, and compared with other unsupervised methods for anomaly detection and segmentation. The DSC score of 0.8590 in BraTs2020 dataset, 0.6226 in ITCS dataset and 0.7403 in In-house dataset show that our method achieves better segmentation performance and has better generalization., Comment: 11 pages,9 figures,3 tables

In the field of parallel imaging (PI), alongside image-domain regularization methods, substantial research has been dedicated to exploring $k$-space interpolation. However, the interpretability of these methods remains an unresolved issue. Furthermore, these approaches currently face acceleration limitations that are comparable to those experienced by image-domain methods. In order to enhance interpretability and overcome the acceleration limitations, this paper introduces an interpretable framework that unifies both $k$-space interpolation techniques and image-domain methods, grounded in the physical principles of heat diffusion equations. Building upon this foundational framework, a novel $k$-space interpolation method is proposed. Specifically, we model the process of high-frequency information attenuation in $k$-space as a heat diffusion equation, while the effort to reconstruct high-frequency information from low-frequency regions can be conceptualized as a reverse heat equation. However, solving the reverse heat equation poses a challenging inverse problem. To tackle this challenge, we modify the heat equation to align with the principles of magnetic resonance PI physics and employ the score-based generative method to precisely execute the modified reverse heat diffusion. Finally, experimental validation conducted on publicly available datasets demonstrates the superiority of the proposed approach over traditional $k$-space interpolation methods, deep learning-based $k$-space interpolation methods, and conventional diffusion models in terms of reconstruction accuracy, particularly in high-frequency regions.

Magnetic resonance imaging (MRI) is known to have reduced signal-to-noise ratios (SNR) at lower field strengths, leading to signal degradation when producing a low-field MRI image from a high-field one. Therefore, reconstructing a high-field-like image from a low-field MRI is a complex problem due to the ill-posed nature of the task. Additionally, obtaining paired low-field and high-field MR images is often not practical. We theoretically uncovered that the combination of these challenges renders conventional deep learning methods that directly learn the mapping from a low-field MR image to a high-field MR image unsuitable. To overcome these challenges, we introduce a novel meta-learning approach that employs a teacher-student mechanism. Firstly, an optimal-transport-driven teacher learns the degradation process from high-field to low-field MR images and generates pseudo-paired high-field and low-field MRI images. Then, a score-based student solves the inverse problem of reconstructing a high-field-like MR image from a low-field MRI within the framework of iterative regularization, by learning the joint distribution of pseudo-paired images to act as a regularizer. Experimental results on real low-field MRI data demonstrate that our proposed method outperforms state-of-the-art unpaired learning methods.

Diffusion models have emerged as a leading methodology for image generation and have proven successful in the realm of magnetic resonance imaging (MRI) reconstruction. However, existing reconstruction methods based on diffusion models are primarily formulated in the image domain, making the reconstruction quality susceptible to inaccuracies in coil sensitivity maps (CSMs). k-space interpolation methods can effectively address this issue but conventional diffusion models are not readily applicable in k-space interpolation. To overcome this challenge, we introduce a novel approach called SPIRiT-Diffusion, which is a diffusion model for k-space interpolation inspired by the iterative self-consistent SPIRiT method. Specifically, we utilize the iterative solver of the self-consistent term (i.e., k-space physical prior) in SPIRiT to formulate a novel stochastic differential equation (SDE) governing the diffusion process. Subsequently, k-space data can be interpolated by executing the diffusion process. This innovative approach highlights the optimization model's role in designing the SDE in diffusion models, enabling the diffusion process to align closely with the physics inherent in the optimization model, a concept referred to as model-driven diffusion. We evaluated the proposed SPIRiT-Diffusion method using a 3D joint intracranial and carotid vessel wall imaging dataset. The results convincingly demonstrate its superiority over image-domain reconstruction methods, achieving high reconstruction quality even at a substantial acceleration rate of 10.

Diffusion model is the most advanced method in image generation and has been successfully applied to MRI reconstruction. However, the existing methods do not consider the characteristics of multi-coil acquisition of MRI data. Therefore, we give a new diffusion model, called SPIRiT-Diffusion, based on the SPIRiT iterative reconstruction algorithm. Specifically, SPIRiT-Diffusion characterizes the prior distribution of coil-by-coil images by score matching and characterizes the k-space redundant prior between coils based on self-consistency. With sufficient prior constraint utilized, we achieve superior reconstruction results on the joint Intracranial and Carotid Vessel Wall imaging dataset., Comment: submitted to ISMRM

Recently, score-based diffusion models have shown satisfactory performance in MRI reconstruction. Most of these methods require a large amount of fully sampled MRI data as a training set, which, sometimes, is difficult to acquire in practice. This paper proposes a fully-sampled-data-free score-based diffusion model for MRI reconstruction, which learns the fully sampled MR image prior in a self-supervised manner on undersampled data. Specifically, we first infer the fully sampled MR image distribution from the undersampled data by Bayesian deep learning, then perturb the data distribution and approximate their probability density gradient by training a score function. Leveraging the learned score function as a prior, we can reconstruct the MR image by performing conditioned Langevin Markov chain Monte Carlo (MCMC) sampling. Experiments on the public dataset show that the proposed method outperforms existing self-supervised MRI reconstruction methods and achieves comparable performances with the conventional (fully sampled data trained) score-based diffusion methods.

Diffusion models with continuous stochastic differential equations (SDEs) have shown superior performances in image generation. It can serve as a deep generative prior to solving the inverse problem in magnetic resonance (MR) reconstruction. However, low-frequency regions of $k$-space data are typically fully sampled in fast MR imaging, while existing diffusion models are performed throughout the entire image or $k$-space, inevitably introducing uncertainty in the reconstruction of low-frequency regions. Additionally, existing diffusion models often demand substantial iterations to converge, resulting in time-consuming reconstructions. To address these challenges, we propose a novel SDE tailored specifically for MR reconstruction with the diffusion process in high-frequency space (referred to as HFS-SDE). This approach ensures determinism in the fully sampled low-frequency regions and accelerates the sampling procedure of reverse diffusion. Experiments conducted on the publicly available fastMRI dataset demonstrate that the proposed HFS-SDE method outperforms traditional parallel imaging methods, supervised deep learning, and existing diffusion models in terms of reconstruction accuracy and stability. The fast convergence properties are also confirmed through theoretical and experimental validation. Our code and weights are available at https://github.com/Aboriginer/HFS-SDE., Comment: accepted for IEEE TMI

Deep learning methods driven by the low-rank regularization have achieved attractive performance in dynamic magnetic resonance (MR) imaging. However, most of these methods represent low-rank prior by hand-crafted nuclear norm, which cannot accurately approximate the low-rank prior over the entire dataset through a fixed regularization parameter. In this paper, we propose a learned low-rank method for dynamic MR imaging. In particular, we unrolled the semi-quadratic splitting method (HQS) algorithm for the partially separable (PS) model to a network, in which the low-rank is adaptively characterized by a learnable null-space transform. Experiments on the cardiac cine dataset show that the proposed model outperforms the state-of-the-art compressed sensing (CS) methods and existing deep learning methods both quantitatively and qualitatively., Comment: journal