张量优化问题作为数值优化领域的一个重要研究课题，是信号处理、机器学习和医学成像等领域中重要的工具。Hankel张量分解和低秩逼近优化问题是张量优化的重要研究内容，在地震波数据处理中有广泛应用。目前，这类问题仍有大量关键问题亟待解决。本项目将采用张量分解与多项式优化相结合的技术，利用Hankel张量自身的特殊结构，开展对Hankel张量分解和低秩逼近问题的研究。内容包括：（1）采用可分离优化的分裂算法，设计求解张量分解和低秩逼近的高效优化算法；（2）结合快速傅里叶变换，设计处理Hankel张量分解和张量低秩逼近模型的快速算法；（3）将算法应用到地震数据的处理中，对地震数据的去噪和完整化等方面展开研究。本项目的实施，将为张量优化问题发展和实际问题解决提供重要理论依据与算法支持。

Tensor optimization problem is an important research topic in the field of numerical optimization and plays a significant role in the fields of signal processing, machine learning and medical imaging. Hankel tensor decomposition and low-rank approximation problems, which are widely used in the seismic data processing, are important research problems of tensor optimization. Typically, there are still many issues to be solved. In this project, we will study Hankel tensor decomposition and low-rank approximation by combining tensor decomposition and polynomial optimization techniques and using its special structure: (1) Designing efficient optimization algorithms for solving tensor decomposition and low-rank approximation by using separable splitting algorithms. (2) Developing fast algorithms for Hankel tensor decomposition and tensor low-rank approximation by using Fast Fourier Transform. (3) Applying these algorithms to the seismic data processing, such as the denoising and completion of seismic data. This project will provide important theory and algorithms for tensor optimization problems and practical problems.