Monograph & Editing

[1] Lu Shuai and Pereverzev Sergei V: Regularization Theory for Ill-posed Problems Selected Topics.
Walter de Gruyter GmbH, Berlin/Boston, Inverse and Ill-Posed Problems Series 58, 2013

[2] Cheng, Jin; Lu, Shuai; Yamamoto Masahiro Inverse Problems and Related Topics, Springer Proceedings in Mathematics & Statistics 310. Springer Nature Singapore Pte Ltd. 2020.

Research Papers in Journals

2021

[1] Lu, Shuai; Niu, Pingping; Werner, Frank; On the Asymptotical Regularization for Linear Inverse Problems in Presence of White Noise. SIAM/ASA J. Uncertain. Quantif. 9 (2021), no. 1, 1–28.

2020

[1] Zhao, Yubin; Mathé, Peter; Lu, Shuai ConvergenceAnalysis of Asymptotical Regularization and Runge-Kutta Integrators for Linear Inverse Problems under Variational Source Conditions. CSIAM Trans. Appl. Math. 1 (2020), no. 4, 693–714.

[2] Lu, Shuai; Mathé, Peter; Pereverzev, Sergei V. Randomized matrix approximation to enhance regularized projection schemes in inverse problems. Inverse Problems 36 (2020), no. 8, 085013, 20 pp.

[3] Lee, Wonjung; Sun, Yiqun; Lu, Shuai Hierarchical sparse observation models and informative prior for Bayesian inference of spatially varying parameters. J. Comput. Phys. 422 (2020), 109768, 18 pp.

[4] Isakov, Victor; Lu, Shuai; Xu, Boxi Linearized inverse Schrödinger potential problem at a large wavenumber. SIAM J. Appl. Math. 80 (2020), no. 1, 338–358.

[5] Lu, Shuai; Mathé, Peter; Pereverzev, Sergei V. Balancing principle in supervised learning for a general regularization scheme. Appl. Comput. Harmon. Anal. 48 (2020), no. 1, 123–148.

2019

[1] Lu, Shuai; Mathé, Peter; Pereverzyev, Sergiy, Jr. Analysis of regularized Nyström subsampling for regression functions of low smoothness. Anal. Appl. (Singap.) 17 (2019), no. 6, 931–946.

[2] Wang, Wei; Lu, Shuai; Hofmann, Bernd; Cheng, Jin Tikhonov regularization with ℓ0-term complementing a convex penalty: ℓ1-convergence under sparsity constraints. J. Inverse Ill-Posed Probl. 27 (2019), no. 4, 575–590.

[3] Niu, Pingping; Lu, Shuai; Cheng, Jin On periodic parameter identification in stochastic differential equations. Inverse Probl. Imaging 13 (2019), no. 3, 513–543.

[4] Hömberg, Dietmar; Lu, Shuai; Yamamoto, Masahiro Uniqueness for an inverse problem for a nonlinear parabolic system with an integral term by one-point Dirichlet data. J. Differential Equations 266 (2019), no. 11, 7525–7544.

2018

[1] Isakov, Victor; Lu, Shuai Inverse source problems without (pseudo) convexity assumptions. Inverse Probl. Imaging 12 (2018), no. 4, 955–970.

[2] Litao Ding, Shuai Lu and Jin Cheng: Weak-norm posterior contraction  rate of the 4DVAR method for  linear severely ill-posed problems, Journal of Complexity 46, (2018), no. 1, pp. 1-18.

[3] Victor Isakov and Shuai Lu: Increasing stability in the inverse source problem with attenuation and many frequencies, SIAM J. Appl. Math., 78 (2018), no. 1, pp. 1-18.

2017

[1] Marco A. Iglesias, Kui Lin, Shuai Lu and Andrew M. Stuart: Filter based methods for statistical linear inverse problems,  Communications in Mathematical Sciences 15 (2017) no. 7, pp. 1867-1896.  (arXiv download)

[2] Jinchang Zheng, Jin Cheng, Peijun Li and Shuai Lu: Periodic surface identification with phase or phaseless near-field data, Inverse Problems 33, (2017) 115004 (35pp).

2016

[1] Cheng Jin, Isakov Victor and Lu Shuai: Increasing stability in the inverse source problem with many frequencies, J. Differential Equations 260 (2016) 4786–4804.

[2] Su Huan, Xu Feng, Lu Shuai and Jin Yaqiu: Iterative ADMM for Inverse FE–BI Problem: A Potential Solution to Radio Tomography of Asteroids, IEEE Transactions on Geoscience and Remote Sensing (2016), no.9, 5226-5238.

2015

[1] Min Zhong, Yiu Chung Hon and Shuai Lu: Multiscale support vector approach for solving ill-posed problems, J. Sci. Comput. 64 (2015), no. 2, 317–340.

[2] Gang Bao, Shuai Lu, William Rundell and Boxi Xu: A recursive algorithm for multi-frequency acoustic inverse source problems, SIAM J. Numer. Anal. 53 (2015), no. 3, 1608–1628.

[3] Kui Lin, Shuai Lu and Peter Mathé: Oracle-type posterior contraction rates in Bayesian inverse problems, Inverse Problems and Imaging 9 (2015), no. 3,895–915.

[4] Boxi Xu, Shuai Lu and Min Zhong: Multiscale support vector regression method in Sobolev spaces on bounded domains, Appl. Anal. 94 (2015), no. 3, 548–569.

2014

[1] Dietmar Hömberg, Shuai Lu, Kenichi Sakamoto and Masahiro Yamamoto: Parameter identification in non-isothermal nucleation and growth processes. Inverse Problems, 30 (2014) 035003 (24pp).  (WIAS-Preprint)

[2] Jin Cheng, Bernd Hofmann and Shuai Lu: The index function and Tikhonov regularization for ill-posed problems. Journal of Computational and Applied Mathematics, 265 (2014) 110–119.

[3] Caixuan Ren, Xiang Xu and Shuai Lu: Regularization by projection for a backward problem of the time-fractional diffusion equation. Journal of Inverse and Ill-posed Problems, 22 (2014), 121–139.

[4] Shuai Lu and Peter Mathé: Varying discrepancy principle as an adaptive parameter selection in statistical inverse problems. Journal of Complexity, 30 (2014), 290–308.

[5] Xinming Wu, Philipp Kügler and Shuai Lu: Identification of the exchange coefficient from indirect data for a coupled continuum pipe-flow model. Chinese Annals of Mathematics Ser. B, 35 (2014), 483-500.

2013

[1] Lu Shuai and Mathé Peter: Heuristic parameter selection based on functional minimization: optimality and model function approach. Mathematics of Computation, 82 (2013), 1609–1630.

[2] Lu Shuai, Valeriya Naumova and Sergei V Pereverzev: Legendre polynomials as a recommended basis for numerical differentiation in the presence of stochastic white noise. Journal of Inverse and Ill-posed Problems, 21 (2013), 193–216.

[3] Wang Wei, Lu Shuai, Mao Heng and Cheng Jin: Multi-parameter Tikhonov regularization with the $\ell^0$ sparsity constraint. Inverse Problems, 29 (2013) 065018 (18pp).

2012

[1] Lu Shuai and Flemming Jens: Convergence rates analysis of Tikhonov regularization for nonlinear ill-posed problems with noisy operators. Inverse Problems, 28 (2012) 104003 (19pp)

[2] Lu Shuai, Chen Nan, Hu Bang and Cheng Jin: On the inverse problems for the coupled continuum pipe flow model for flows in karst aquifers. Inverse Problems, 28 (2012) 065003 (16pp)

[3] Zhong Min, Lu Shuai and Cheng Jin: Multiscale analysis for ill-posed problems with semi-discrete Tikhonov regularization. Inverse Problems, 28 (2012) 065019 (19pp)

[4] Lu Shuai, Heng Yi and Mhamdi Adel: A fast algorithm for the solution of a 3D transient inverse heat conduction problem by means of conjugate gradient method via Tikhonov regularization. International Journal of Heat and Mass Transfer, 55 (2012) 7865–7872

[5] Cheng Jin, Lu Shuai and Yamamoto Masahiro: Reconstruction of the Stefan-Boltzmann coefficients in the heat transfer process. Inverse Problems, 28 (2012) 045007 (17pp)

[6] Lu Shuai, Xu Boxi and Xu Xiang: Unique continuation on a line for the Helmholtz equation. Applicable Analysis, 91 (2012), 1761–1771.

[7] Hu Bang and Lu Shuai: Numerical differentiation by a Tikhonov regularization method based on the discrete cosine transform. Applicable Analysis, 91 (2012), 719–736.

Before 2011

[14] Lu Shuai and Pereverzev Sergei V: Multi-parameter regularization and its numerical realization. Numerische Mathematik,  118 (2011), 1-31.

[13] Lu Shuai, Pereverzev Sergei V, Shao Yuanyuan and Tautenhahn Ulrich: Discrepancy curves for multi-parameter regularization. Journal of Inverse and Ill-Posed Problems, 18 (2010), 655–676.

[12] Lu Shuai, Pereverzev Sergei V and Tautenhahn Ulrich: A model function method in regularized total least squares. Applicable Analysis, 89 (2010), 1693-1703.

[11] Lu Shuai, Pereverzev Sergei V, Shao Yuanyuan and Tautenhahn Ulrich: On the generalized discrepancy principle for Tikhonov regularization in Hilbert scales. Journal of Integral Equations and Application, 22 (2010), 483-517.

[10] Heng Yi, Lu Shuai, Mhamdi Adel and Pereverzev Sergei V: Model function approach in the modified L-curve method for the choice of regularization parameter. Inverse Problems, 26 (2010) 055006 (13pp). Corresponding author

[9] Lu Shuai, Pereverzev Sergei V and Tautenhahn Ulrich: Regularized total least squares: computational aspects and error bounds. SIAM Journal on Matrix Analysis and Applications, 31 (2009), 918-941.

[8] Lu Shuai and Pereverzev Sergei V: Sparse recovery by the standard Tikhonov method. Numerische Mathematik, 112 (2009), 403-424.

[7] Lu Shuai and Pereverzev Sergei V: Sparse reconstruction by means of the standard Tikhonov regularization. Journal of Physics: Conference Series, 135 (2008) 012066 (8pp).

[6] Lu Shuai, Pereverzev Sergei V and Tautenhahn Ulrich: Dual regularized total least squares and multi-parameter regularization. Computational Methods in Applied Mathematics, 8 (2008), 253-262.

[5] Lazarov Raytcho D, Lu Shuai and Pereverzev Sergei V: On the balancing principle for some problems of Numerical Analysis. Numerische Mathematik, 106 (2007), 659-689. Corresponding author

[4] Lu Shuai, Pereverzev Sergei V and Ramlau Ronny: An analysis of Tikhonov regularization for nonlinear ill-posed problems under general smoothness assumption. Inverse Problems, 23 (2007), 217-230.

[3] Lu Shuai and Pereverzev Sergei V: Numerical Differentiation from a view point of Regularization Theory. Mathematics of Computation, 75 (2006), 1853-1870.

[2] Cai Zhijie, Chen Deqiang and Lu Shuai: Reconstruction of a fractal rough surface. Physica D, 213 (2006), 25-30.

[1] Lu Shuai and Wang Yanbo: First and Second Order Numerical Differentiation with Tikhonov Regularization. Numerical Mathematics(A Journal of Chinese Universities), 26 (2004), 62-74 (Chinese). Translated to Frontiers of Mathematics in China, 1 (2006), 354-367 (English).

Research Papers in Book chapters

[1] Lu Shuai and Pereverzev Sergei V: Multiparameter regularization in Downward Continuation of Satellite Data. Handbook of Geomathematics, Volume 2, 813-832. Springer-Verlag Berlin Heidelberg 2010.

[2] Lu, Shuai; Pereverzyev, Sergiy, Jr.; Sampath, Sivananthan Multiparameter regularization for construction of extrapolating estimators in statistical learning theory. Multiscale signal analysis and modeling, 347–366, Springer, New York, 2013.

[3] Hömberg, Dietmar; Lu, Shuai; Sakamoto, Kenichi; Yamamoto, Masahiro Nucleation rate identification in binary phase transition. The impact of applications on mathematics, 227–243, Math. Ind. (Tokyo), 1, Springer, Tokyo, 2014.

[4] Wu, Zehui; Lu, Shuai Relaxing alternating direction method of multipliers (ADMM) for linear inverse problems. New trends in parameter identification for mathematical models, 317–345, Trends Math., Birkhäuser/Springer, Cham, 2018.

[5] Cheng, Jin; Choulli, Mourad; Lu, Shuai An Inverse Conductivity Problem in Multifrequency Electric Impedance Tomography. J. Cheng et al. (eds.), Inverse Problems and Related Topics, Springer Proceed ings in Mathematics & Statistics 310 (2020), 3-30.

[6] Isakov, Victor; Lu, Shuai On the Inverse Source Problem with Boundary Data at ManyWave Numbers. J. Cheng et al. (eds.), Inverse Problems and Related Topics, Springer Proceedings in Mathematics & Statistics 310 (2020), 59-80.

Thesis

 

Ph.D. Disseration: (Defensed on June 14, 2007 with distinction,
Univeristy of Linz, Austria)

A balancing principle for the choice of the regularization parameter

(Supervisor: Prof. Pereverzyev; Gutachter: Prof. Engl)