I received the B.S. degree in School of Mathematics and Statistics from Northwestern Polytechnical University, Xi’an, China, in 2022, advised by Prof. Jianchao Bai. At present, I’m pursuing a Ph.D degree in School of Mathematical Sciences and Shen Yuan Honors College at Beihang University, Beijing, China, advised by Prof. Yong Xia.

Research

My research interests include

• Optimization theory and algorithms
• Line spectral estimation
• Compressive Sensing

Recent Publications

• A Unified Algorithmic Framework for Dynamic Compressive Sensing.
  X. Liu, Y. Xia. Signal Processing, 232 (2025), 109926. [DOI] [code]

• Cubic NK-SVD: An Algorithm for Designing Parametric Dictionary in Frequency Estimation.
  X. Liu, Y. Xia. Signal Processing, 235 (2025), 110029. [DOI] [code]

• Split-Merge: A Difference-based Approach for Dominant Eigenvalue Problem.
  X. Liu, Y. Xia. [arXiv 2025]

• Split-Merge Revisited: A Scalable Approach to Generalized Eigenvalue Problems.
  X. Liu, Y. Xia. [arXiv 2025]

• Revisiting Atomic Norm Minimization: A Sequential Approach for Atom Identification and Refinement.
  X. Liu*, J. Wei*, Y. Xia. [arXiv 2024]

Work Experience

• Augest 1, 2025 - Augest 31, 2025, Research Assistant, Hong Kong Baptist University, Hong Kong, China, supervised by Prof. Michael K. Ng (SIAM Fellow).

Conference Talks

• October 12-15, 2023, Report on “A Unified Algorithmic Framework for Dynamic Compressive Sensing”. The 21st Annual Meeting of CSIAM, FM04, Kunming, Yunnan. [slides]
• September 13-15, 2024, Report on “Cubic NK-SVD: An Algorithm for Designing Parametric Dictionary in Frequency Estimation”. The 1st ORSC conference on Data Science and Operations Research Intelligence, Beijing. [slides]

Academic Activities

• April, 2025 - now, Reviewer of Minimally Invasive Therapy & Allied Technologies.

Teaching Assistant

• Modern Optimization Methods, 2023, Fall, Beihang University
• Optimization Theory and Methods, 2024, Fall, Beihang University

CV

• cv