We present a novel approach to variational volume reconstruction from sparse, noisy slice data using the Deep Ritz method. Motivated by biomedical imaging applications such as MRI-based slice-to-volume reconstruction (SVR), our approach addresses three key challenges: (i) the reliance on image segmentation to extract boundaries from noisy grayscale slice images, (ii) the need to reconstruct volumes from a limited number of slice planes, and (iii) the computational expense of traditional mesh-based methods. We formulate a variational objective that combines a regression loss designed to avoid image segmentation by operating on noisy slice data directly with a modified Cahn-Hilliard energy incorporating anisotropic diffusion to regularize the reconstructed geometry. We discretize the phase field with a neural network, approximate the objective at each optimization step with Monte Carlo integration, and use ADAM to find the minimum of the approximated variational objective. While the stochastic integration may not yield the true solution to the variational problem, we demonstrate that our method reliably produces high-quality reconstructed volumes in a matter of seconds, even when the slice data is sparse and noisy.

Computed tomography (CT) is one of the most widely used non-invasive imaging modalities for medical diagnosis. In clinical practice, CT images are usually acquired with large slice thicknesses due to the high cost of memory storage and operation time, resulting in an anisotropic CT volume with much lower inter-slice resolution than in-plane resolution. Since such inconsistent resolution may lead to difficulties in disease diagnosis, deep learning-based volumetric super-resolution methods have been developed to improve inter-slice resolution. Most existing methods conduct single-image super-resolution on the through-plane or synthesize intermediate slices from adjacent slices; however, the anisotropic characteristic of 3D CT volume has not been well explored. In this paper, we propose a novel cross-view texture transfer approach for CT slice interpolation by fully utilizing the anisotropic nature of 3D CT volume. Specifically, we design a unique framework that takes high-resolution in-plane texture details as a reference and transfers them to low-resolution through-plane images. To this end, we introduce a multi-reference non-local attention module that extracts meaningful features for reconstructing through-plane high-frequency details from multiple in-plane images. Through extensive experiments, we demonstrate that our method performs significantly better in CT slice interpolation than existing competing methods on public CT datasets including a real-paired benchmark, verifying the effectiveness of the proposed framework. The source code of this work is available at https://github.com/khuhm/ACVTT.

Neurite Orientation Dispersion and Density Imaging (NODDI) microstructure estimation from diffusion magnetic resonance imaging (dMRI) is of great significance for the discovery and treatment of various neurological diseases. Current deep learning-based methods accelerate the speed of NODDI parameter estimation and improve the accuracy. However, most methods require the number and coordinates of gradient directions during testing and training to remain strictly consistent, significantly limiting the generalization and robustness of these models in NODDI parameter estimation. Therefore, it is imperative to develop methods that can perform robustly under varying diffusion gradient directions. In this paper, we propose a q-space sampling augmentation-based continuous representation learning framework (SamRobNODDI) to achieve robust and generalized NODDI. Specifically, a continuous representation learning method based on q-space sampling augmentation is introduced to fully explore the information between different gradient directions in q- space. Furthermore, we design a sampling consistency loss to constrain the outputs of different sampling schemes, ensuring that the outputs remain as consistent as possible, thereby further enhancing performance and robustness to varying q-space sampling schemes. SamRobNODDI is also a flexible framework that can be applied to different backbone networks. SamRobNODDI was compared against seven state-of-the-art methods across 18 diverse q-space sampling schemes. Extensive experimental validations have been conducted under both identical and diverse sampling schemes for training and testing, as well as across varying sampling rates, different loss functions, and multiple network backbones. Results demonstrate that the proposed SamRobNODDI has better performance, robustness, generalization, and flexibility in the face of varying q-space sampling schemes.&#xD.

To develop a highly accelerated MRI technique for simultaneous quantification of blood flow and T₁ of the brain tissue. A dual-flip-angle phase-contrast stack-of-stars (DFA PC-SOS) sequence was developed for simultaneous acquisition of highly-undersampled data for the quantification of velocity of arterial blood and T₁ mapping of brain tissue. A deep learning-based algorithm, combining hybrid-feature hash encoding implicit neural representation with explicit sparse prior knowledge (INRESP), was used for image reconstruction. Magnitude and phase images were used for T₁ mapping and velocity measurements, respectively. The accuracy of the measurements was assessed in a quantitative phantom and six healthy volunteers. T₁ mapping obtained with DFA PC-SOS showed high correlation and consistency with reference measurements in phantom experiments (y = 0.916× + 4.71, R² = 0.9953, ICC = 0.9963). Blood flow measurements in healthy volunteers demonstrated strong correlation and consistency with reference values measured by SFA PC-SOS (y = 1.04×-0.187, R² = 0.9918, ICC = 0.9967). The proposed technique enabled an acceleration of 16× with high correlation and consistency with fully sampled data in volunteers (T₁: y = 1.06× + 1.44, R² = 0.9815, ICC = 0.9818; flow: y = 1.01×-0.0525, R² = 0.9995, ICC = 0.9998). This study demonstrates the feasibility of 16-fold accelerated simultaneous acquisition for flow quantification and T₁ mapping in the brain. The proposed technique provides a rapid and comprehensive assessment of cerebrovascular diseases with both vascular hemodynamics and surrounding brain tissue characteristics, and has potential to be used in routine clinical applications.

This study presents an unsupervised deep learning approach for computed tomography (CT) image reconstruction, leveraging the inherent similarities between deep neural network training and conventional iterative reconstruction methods. By incorporating forward and backward projection layers within the deep learning framework, we demonstrate the feasibility of reconstructing images from projection data without relying on ground-truth images. Our method is evaluated on the two-dimensional 2DeteCT dataset, showcasing superior performance in terms of mean squared error (MSE) and structural similarity index (SSIM) compared to traditional filtered backprojection (FBP) and maximum likelihood (ML) reconstruction techniques. Additionally, our approach significantly reduces reconstruction time, making it a promising alternative for real-time medical imaging applications. Future work will focus on extending this methodology to three-dimensional reconstructions and enhancing the adaptability of the projection geometry.

This study presents an unsupervised deep learning approach for computed tomography (CT) image reconstruction, leveraging the inherent similarities between deep neural network training and conventional iterative reconstruction methods. By incorporating forward and backward projection layers within the deep learning framework, we demonstrate the feasibility of reconstructing images from projection data without relying on ground-truth images. Our method is evaluated on the two-dimensional 2DeteCT dataset, showcasing superior performance in terms of mean squared error (MSE) and structural similarity index (SSIM) compared to traditional filtered backprojection (FBP) and maximum likelihood (ML) reconstruction techniques. Additionally, our approach significantly reduces reconstruction time, making it a promising alternative for real-time medical imaging applications. Future work will focus on extending this methodology to three-dimensional reconstructions and enhancing the adaptability of the projection geometry.

Reconstructing high-quality images from corrupted measurements remains a fundamental challenge in medical imaging. Recently, deep unrolling (DUN) methods have emerged as a promising solution, combining the interpretability of traditional iterative algorithms with the powerful representation capabilities of deep learning. However, their performance is often limited by weak information flow between iterative stages and a constrained ability to capture global features across stages-limitations that tend to worsen as the number of iterations increases.
Approach: In this work, we propose a memory-enhanced and multi-domain learning-based deep unrolling network for interpretable, high-fidelity medical image reconstruction. First, a memory-enhanced module is designed to adaptively integrate historical outputs across stages, reducing information loss. Second, we introduce a cross-stage spatial-domain learning transformer (CS-SLFormer) to extract both local and non-local features within and across stages, improving reconstruction performance. Finally, a frequency-domain consistency learning (FDCL) module ensures alignment between reconstructed and ground truth images in the frequency domain, recovering fine image details.
Main Results: Comprehensive experiments evaluated on three representative medical imaging modalities (PET, MRI, and CT) show that the proposed method consistently outperforms state-of-the-art (SOTA) approaches in both quantitative metrics and visual quality. Specifically, our method achieved a PSNR of 37.835 dB and an SSIM of 0.970 in 1 $\%$ dose PET reconstruction.
Significance: This study expands the use of model-driven deep learning in medical imaging, demonstrating the potential of memory-enhanced deep unrolling frameworks for high-quality reconstructions.

Denoising reconstructed Computed Tomography (CT) images without access to raw projection data remains a significant difficulty in medical imaging, particularly when utilizing sharp or medium reconstruction kernels that generate high-frequency noise. This work introduces an innovative method that integrates quaternion mathematics with bilateral filtering to resolve this issue. The proposed Quaternion Bilateral Filter (QBF) effectively maintains anatomical structures and mitigates noise caused by the kernel by expressing CT scans in quaternion form, with the red, green, and blue channels encoded together. Compared to conventional methods that depend on raw data or grayscale filtering, our approach functions directly on reconstructed sharp kernel images. It converts them to mimic the quality of soft-kernel outputs, obtained with kernels such as B30f, using paired data from the same patients. The efficacy of the QBF is evidenced by both full-reference metrics (Structural Similarity Index Measure (SSIM), Peak Signal-to-Noise Ratio (PSNR), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE)) and no-reference perceptual metrics (Naturalness Image Quality Evaluator (NIQE), Blind Referenceless Image Spatial Quality Evaluator (BRISQUE), and Perception-based Image Quality Evaluator (PIQE)). The results indicate that the QBF demonstrates improved denoising efficacy compared to traditional Bilateral Filter (BF), Non-Local Means (NLM), wavelet, and Convolutional Neural Network (CNN)-based processing, achieving an SSIM of 0.96 and a PSNR of 36.3 on B50f reconstructions. Additionally, segmentation-based visual validation verifies that QBF-filtered outputs maintain essential structural details necessary for subsequent diagnostic tasks. This study emphasizes the importance of quaternion-based filtering as a lightweight, interpretable, and efficient substitute for deep learning models in post-reconstruction CT image enhancement.

To validate a deep learning (DL) reconstruction technique for faster post-contrast enhanced coronal Volume Interpolated Breath-hold Examination (VIBE) sequences and assess its image quality compared to conventionally acquired coronal VIBE sequences. This prospective study included 151 patients undergoing clinically indicated upper abdominal MRI acquired on 3 T scanners. Two coronal T1 fat-suppressed VIBE sequences were acquired: a DL-reconstructed sequence (VIBE_DL) and a standard sequence (VIBE_SD). Three radiologists independently evaluated six image quality parameters: overall image quality, perceived signal-to-noise ratio, severity of artifacts, liver edge sharpness, liver vessel sharpness, and lesion conspicuity, using a 4-point Likert scale. Inter-reader agreement was assessed using Gwet's AC2. Ordinal mixed-effects regression models were used to compare VIBE_DL and VIBE_SD. Acquisition times were 10.2 s for VIBE_DL compared to 22.3 s for VIBE_SD. VIBE_DL demonstrated superior overall image quality (OR 1.95, 95 % CI: 1.44-2.65, p < 0.001), reduced image noise (OR 3.02, 95 % CI: 2.26-4.05, p < 0.001), enhanced liver edge sharpness (OR 3.68, 95 % CI: 2.63-5.15, p < 0.001), improved liver vessel sharpness (OR 4.43, 95 % CI: 3.13-6.27, p < 0.001), and better lesion conspicuity (OR 9.03, 95 % CI: 6.34-12.85, p < 0.001) compared to VIBE_SD. However, VIBE_DL showed increased severity of peripheral artifacts (OR 0.13, p < 0.001). VIBE_DL detected 137/138 (99.3 %) focal liver lesions, while VIBE_SD detected 131/138 (94.9 %). Inter-reader agreement ranged from good to very good for both sequences. The DL-reconstructed VIBE sequence significantly outperformed the standard breath-hold VIBE in image quality and lesion detection, while reducing acquisition time. This technique shows promise for enhancing the diagnostic capabilities of contrast-enhanced abdominal MRI.

Reconstructing high-fidelity MR images from undersampled k-space data remains a challenging problem in MRI. While Mamba variants for vision tasks offer promising long-range modeling capabilities with linear-time complexity, their direct application to MRI reconstruction inherits two key limitations: (1) insensitivity to high-frequency anatomical details; and (2) reliance on redundant multi-directional scanning. To address these limitations, we introduce High-Fidelity Mamba (HiFi-Mamba), a novel dual-stream Mamba-based architecture comprising stacked W-Laplacian (WL) and HiFi-Mamba blocks. Specifically, the WL block performs fidelity-preserving spectral decoupling, producing complementary low- and high-frequency streams. This separation enables the HiFi-Mamba block to focus on low-frequency structures, enhancing global feature modeling. Concurrently, the HiFi-Mamba block selectively integrates high-frequency features through adaptive state-space modulation, preserving comprehensive spectral details. To eliminate the scanning redundancy, the HiFi-Mamba block adopts a streamlined unidirectional traversal strategy that preserves long-range modeling capability with improved computational efficiency. Extensive experiments on standard MRI reconstruction benchmarks demonstrate that HiFi-Mamba consistently outperforms state-of-the-art CNN-based, Transformer-based, and other Mamba-based models in reconstruction accuracy while maintaining a compact and efficient model design.