主要研究方向为偏微分方程、统计学及其在图像处理中的应用。在基于偏微分方程与变分法的图像处理问题以及医学图像分割、融合反问题的基础理论与算法研究方面,取得了系列研究成果。
代表性论文:
[1]. Lihua
Min,
Zhe Zhang, Zhengmeng Jin*, Selective segmentation of inhomogeneous images based
on local clustering and global smoothness, Journal of the Franklin Institute,
2025. (SCI收录)
[2]. Zhengmeng
Jin, Yue Ma, Lihua Min*, Minling Zheng, Variational image dehazing with
a novel underwater dark channel prior, Inverse Problems and Imaging, 2025,
19(2): 334-354. (SCI收录)
[3]. Zhengmeng
Jin, Wang Hao, Michael K. Ng and Lihua Min*, Regularized CNN with
geodesic active contour and edge predictor for image, SIAM Journal on Imaging
Sciences, 2024, 17(4): 2392- 2417. (SCI收录)
[4]. Lihua
Min,
Xiaoyu Lian, Zhengmeng Jin* and Minling Zheng, A Retinex-based selective
segmentation model for inhomogeneous images, Journal of Mathematical
Imaging and Vision, , 2023, 65: 437–452. (SCI收录)
[5]. Zhengmeng
Jin, Jie Wang, Lihua Min* and Minling Zheng, An adaptive total generalized
variational model for speckle reduction in ultrasound images, Journal of
the Franklin Institute, 2022, 359: 8377–8394. (SCI收录)
[6].
Lihua Min , Qiang Cui*,
Zhengmeng Jin and Tieyong Zeng, Inhomogeneous image segmentation based on local
constant and global smoothness priors, Digital Signal Processing, 2021, 111:102989,17
pages. (SCI收录)
[7]. Zhengmeng
Jin, Junkang Zhang, Lihua Min* and Michael Ng, A variational model for spatially
weighting in image fusion, SIAM Journal on Imaging Sciences, 2021, 14(2):
441–469. (SCI收录)
[8].
Lihua Min Zhenhua Li*,
Zhengmeng Jin and Qiang Cui, Color edge preserving image colorization with a
coupled natural vectorial total variation, Computer Vision and Image
Understanding, 2020, 196, 102981, 9 pages. (SCI收录)
[9]. Zhengmeng
Jin, Yimeng Wu, Lihua Min* and Michael Ng, A Retinex-based total variation
approach for image segmentation and bias correction, Applied Mathematical
Modelling, 2020,79: 52-67. (SCI收录)
[10]. Zhengmeng
Jin*, Lihua Min, Michael K. Ng and Minling Zheng,Image colorization
by fusion of color transfers based on DFT and variance features,Computers and
Mathematics with Applications, 2019, 77: 2553-2567 (SCI收录)
[11]. Lihua
Min
and Xiaohong Qin*, Stability of rarefaction wave for compressible Navier-Stokes
equations on the half Line, Acta Mathematicae Applicatae Sinica, English
Series, 2016, 32(1): 175–186. (SCI收录)
[12]. Lihua
Min*,
Liouville type theorem for higher order Hardy-Henon system of inequalities.
Mathematical Inequalities & Applications, 2014, 17(4): 1427–1439. (SCI收录)
[13]. Lihua
Min*
and Xiaoping Yang, Finite speed of propagation and algebraic time decay of
solutions to a generalized thin film equation. Communications on Pure and
Applied Analysis, 2014, 13(2): 543-566. (SCI收录)
[14]. Lihua
Min*,
Xiaoping Yang and Dong Ye, Well-posedness for a fourth order nonlinear equation
related to image processing. Nonlinear Analysis: Real World Applications, 2014,
17: 192-202. (SCI收录)
[15]. Lihua
Min*,
Xiaoping Yang and Changfeng Gui, Entropy estimates and large time behavior of
solutions to a fourth order nonlinear degenerate equation, Communications in
Contemporary Mathematics, 2013, 15(4): 1250066, 23 pages. (SCI收录)
科研项目:
[1].
国家自然科学基金青年基金项目:一类四阶退化偏微分方程解的非负性和唯一性研究(No.11401318),22万,2015.01-2017.12,主持;
[2].
江苏省高校自然科学研究面上项目:高阶退化非线性偏微分方程解的性态研究(No.14KJB110020),3万,2014.08-2016.12,主持;
[3].
南京邮电大学引进人才科研启动项目:图像处理中几类四阶非线性 PDE 解的理论研究(No. NY214023),5万,2014.06-2017.05,主持;
[4].
江苏省普通高校研究生科研创新计划资助项目:高阶非线性图像偏微分方程解的性态研究 ( No.
CXZZ11_0257),3 万, 2011.04-2013.04,主持;
[5].
江苏省高校自然科学研究面上项目:基于变分偏微分方程的图像着色方法研究(No.15KJB110018),3万,2015.07-2017.06,主要参加人(排名第2);
[6].
国家自然科学基金青年基金项目:非局部扩散趋化方程组的定性研究(No. 11701290) ,23万,2018.01-2020.12,主要参加人(排名第2);
[7].
江苏省省自然科学基金项目:非局部扩散趋化-流体方程组的定性研究(No. BK20170896),20万,2017.07-2020.06,主要参加人(排名第2);
[8].
江苏省高校自然科学研究面上项目:多种群趋化模型解的定性研究(No. 17KJB110012),3万,2017.09-2019.08,主要参加人(排名第2);
[9]. 国家自然科学基金面上项目:基于变分偏微分方程的MRI医学图像着色理论与算法研究(No.11671004),48万,2017.01-2020.12,主要参加人(排名第4).
[10]. 基于几何变分的MR医学图像选择性分割理论与算法研究(No.12271262),国家自然科学基金(面上项目),2023.01-2026.12,主要参加人(排名第4).