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An Oracle Gradient Regularized Newton Method for Quadratic Measurements Regression

2023-12-25 16:17

报告人: 樊军

报告人单位: 河北工业大学

时间: 2023年12月28日下午14:30—16:30

地点: bat365正版唯一官网北洋园校区bat365中文官网登录入口58号教学楼223会议室

开始时间: 2023年12月28日下午14:30—16:30

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摘要:Recently, recovering an unknown signal from quadratic measurements has gained popularity because it includes many interesting applications as special cases such as phase retrieval, fusion frame phase retrieval, and positive operator-valued measure. In this paper, by employing the least squares approach to reconstruct the signal, we establish the non-asymptotic statistical property showing that the gap between the estimator and the true signal is vanished in the noiseless case and is bounded in the noisy case by an error rate of , where and are the number of measurements and the dimension of the signal, respectively. We develop a gradient regularized Newton method (GRNM) to solve the least squares problem and prove that it converges to a unique local minimum at a superlinear rate under certain mild conditions. In addition to the deterministic results, GRNM can reconstruct the true signal exactly for the noiseless case and achieve the above error rate with a high probability for the noisy case. Numerical experiments demonstrate the GRNM performs nicely in terms of high order of recovery accuracy, faster computational speed, and strong recovery capability.


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