报告题目：Tensor Recovery from Quantized Measurements Based on Modewise Operators
报告人：侯景耀副研究员
报告时间：2025年5月10日（星期六）14:30—15:30
报告地点：数学科学学院201会议室
摘要：The problem of tensor recovery from quantized measurements aims to reconstruct a low-rank tensor based on its quantized linear inner-product measurements, which has diverse applications in achieving compressed representation or efficient transmission of high-order tensors. Existing methodologies for this problem rely on computing the product between the vectorization of the underlying tensor and a scale-matched random Gaussian measurement matrix that is significantly larger than the original tensor. The challenge lies in addressing both storage and transmission problems associated with such a random measurement matrix, which may exceed those posed by the original tensor. The present study introduces a multi-stage modewise measurement strategy into quantized measurements, thereby facilitating the utilization of multiple smaller-sized measurement matrices to effectively alleviate this issue. An iterative projected back projection recovery algorithm is proposed to match such quantized multi-stage modewise measurements within the framework of higher-order singular value decomposition (HOSVD). By developing the tensor limited projection distortion (LPD) property and combining it with the restricted isometry property (RIP), we establish sufficient conditions on both the linear sampling operator and quantizer to ensure that our approach enables reconstruction of low-rank tensors. 

报告人简介：侯景耀，西华师范大学数学与信息学院副研究员，硕士生导师，美国数学会《Mathematical Reviews》特邀评论员。2021年12月获西南大学数学与统计学院博士学位，2023.09-2024.08在香港浸会大学跟随吴国宝(Michael Kwok-Po Ng)教授从事博士后研究。2023年入选四川省“天府峨眉计划”青年人才项目。主要从事压缩感知、高维数据恢复等方向的研究。荣获第三届川渝科技学术大会暨四川科技学术大会优秀论文三等奖、四川省现场统计学会第二届优秀科研成果奖教师组二等奖、重庆市优秀博士学位论文。以第一或通讯作者身份在《IEEE TPAMI》、《IEEE TIT》、《SIAM Journal on Imaging Sciences》、《Inverse Problems》、《Information and Inference: A Journal of the IMA》等国际知名期刊上发表SCI论文10余篇。主持国家自然科学基金1项，四川省自然科学基金1项。

编辑：王苗   审核：蒋毅   终审：屈加文