arXiv subjects

Zhongjie Lu

Publications and source records attributed to Zhongjie Lu.

5 recordsLinked to original sources

arXiv2024

Auxiliary iterative schemes for the discrete operators on de Rham complex

The main difficulty in solving the discrete source or eigenvalue problems of the operator $ d^*d $ with iterative methods is to deal with its huge kernel, for example, the $ \nabla \times \nabla \times $ and $- \nabla ( \nabla \cdot ) $ operator. In this paper, we construct a kind of auxiliary schemes for their discrete systems based on Hodge Laplacian on de Rham complex. The spectra of the new schemes are Laplace-like. Then many efficient iterative methods and preconditioning techniques can be applied to them. After getting the solutions of the auxiliary schemes, the desired solutions of the original systems can be recovered or recognized through some simple operations. We sum these up as a new framework to compute the discrete source and eigenvalue problems of the operator $ d^*d $ using iterative method. We also investigate two preconditioners for the auxiliary schemes, ILU-type method and Multigrid method. Finally, we present plenty of numerical experiments to verify the efficiency of the auxiliary schemes.

math.NA↗

arXiv2024

Solving discrete constrained problems on de Rham complex

The main difficulty in solving the discrete constrained problem is its poor and even ill condition. In this paper, we transform the discrete constrained problems on de Rham complex to Laplace-like problems. This transformation not only make the constrained problems solvable, but also make it easy to use the existing iterative methods and preconditioning techniques to solving large-scale discrete constrained problems.

math.NA↗

arXiv2021

A sparse approximate inverse for triangular matrices based on Jacobi iteration

In this paper, we propose a simple sparse approximate inverse for triangular matrices (SAIT). Using the Jacobi iteration method, we obtain an expression of the exact inverse of triangular matrix, which is a finite series. The SAIT is constructed based on this series. We apply the SAIT matrices to iterative methods with ILU preconditioners. The two triangular solvers in the ILU preconditioning procedure are replaced by two matrix-vector multiplications, which can be fine-grained parallelized. We test this method by solving some linear systems and eigenvalue problems with preconditioned iterative methods.

math.NA↗

arXiv2021

Comprehensive and Clinically Accurate Head and Neck Organs at Risk Delineation via Stratified Deep Learning: A Large-scale Multi-Institutional Study

Accurate organ at risk (OAR) segmentation is critical to reduce the radiotherapy post-treatment complications. Consensus guidelines recommend a set of more than 40 OARs in the head and neck (H&N) region, however, due to the predictable prohibitive labor-cost of this task, most institutions choose a substantially simplified protocol by delineating a smaller subset of OARs and neglecting the dose distributions associated with other OARs. In this work we propose a novel, automated and highly effective stratified OAR segmentation (SOARS) system using deep learning to precisely delineate a comprehensive set of 42 H&N OARs. SOARS stratifies 42 OARs into anchor, mid-level, and small & hard subcategories, with specifically derived neural network architectures for each category by neural architecture search (NAS) principles. We built SOARS models using 176 training patients in an internal institution and independently evaluated on 1327 external patients across six different institutions. It consistently outperformed other state-of-the-art methods by at least 3-5% in Dice score for each institutional evaluation (up to 36% relative error reduction in other metrics). More importantly, extensive multi-user studies evidently demonstrated that 98% of the SOARS predictions need only very minor or no revisions for direct clinical acceptance (saving 90% radiation oncologists workload), and their segmentation and dosimetric accuracy are within or smaller than the inter-user variation. These findings confirmed the strong clinical applicability of SOARS for the OAR delineation process in H&N cancer radiotherapy workflows, with improved efficiency, comprehensiveness, and quality.

eess.IV↗

arXiv2018

Diagnostic Classification Of Lung Nodules Using 3D Neural Networks

Lung cancer is the leading cause of cancer-related death worldwide. Early diagnosis of pulmonary nodules in Computed Tomography (CT) chest scans provides an opportunity for designing effective treatment and making financial and care plans. In this paper, we consider the problem of diagnostic classification between benign and malignant lung nodules in CT images, which aims to learn a direct mapping from 3D images to class labels. To achieve this goal, four two-pathway Convolutional Neural Networks (CNN) are proposed, including a basic 3D CNN, a novel multi-output network, a 3D DenseNet, and an augmented 3D DenseNet with multi-outputs. These four networks are evaluated on the public LIDC-IDRI dataset and outperform most existing methods. In particular, the 3D multi-output DenseNet (MoDenseNet) achieves the state-of-the-art classification accuracy on the task of end-to-end lung nodule diagnosis. In addition, the networks pretrained on the LIDC-IDRI dataset can be further extended to handle smaller datasets using transfer learning. This is demonstrated on our dataset with encouraging prediction accuracy in lung nodule classification.

cs.CV↗