科研進展
   新聞動態
      科研進展
      綜合新聞
      傳媒掃描
現在位置:首頁 > 新聞動態 > 科研進展
相位恢複的理論及算法(許志強)
2022-01-07 | 编辑:

  確定最少觀測次數是相位恢複、矩陣恢複中的一個基本問題。采用代數簇的方法,給出了通過無相位觀測恢複幾乎所有信號所需最少觀測次數 [1],並進一步將其擴展到通過線性觀測恢複幾乎所有低秩矩陣所需最少觀測次數 [2]。對複稀疏信號的相位恢複問題,研究了L1模型的性能,成功將壓縮感知中的主要結果擴展到無相位觀測 [3],並給出了求解稀疏信號相位恢複的S-PhaseLiftOff模型及求解算法 [4]。框架在相位恢複中扮演重要角色。其中一個基本問題是達到p-勢能最小的框架位置,人們通過大量數值計算,猜想了其位置。我們證明了該猜想成立 [5]

  所提出的研究相位恢複的代數簇方法,促進了 Homomorphic Sensing 的發展,該理論研究重建信號的代數方法。解決了能否利用L1模型,能否通過O(k logd)次無相位觀測恢複k-稀疏信號的開問題。對于p-勢能最小化猜想的工作,文獻中提到 “While revising this manuscript, we became aware of the work by Zhiqiang Xu and Zili Xu [27], where they prove the rest of the conjecture” Advance Comp Math, 2020;  “the conjecture mentioned above from the paper [6] was proved true in [25].”  (SIAM J. DISCRETE MATH., 2020) 

   

   

1. Meng Huang, Yi Rong, Yang Wang and Zhiqiang Xu, Almost Everywhere Generalized Phase Retrieval, Applied and Computational Harmonic Analysis, Vol. 50, January 2021, Pages 16-33 

2. Yi Rong, Yang Wang and Zhiqiang Xu, Almost everywhere injectivity conditions for the matrix recovery problem, Applied and Computational Harmonic Analysis, Vol.50 January 2021, Pages 386-400 

3. Yu Xia and Zhiqiang Xu, The recovery of complex sparse signals from few phaseless measurements, Applied and Computational Harmonic Analysis, Volume 50,2021. 

4. Yu Xia and Zhiqiang Xu, Sparse phase retrieval via Phaseliftoff, IEEE Transactions on Signal Processing, Page(s): 2129-2143, Vol.69, 18, 2021.     

5. Zhiqiang Xu and Zili Xu, The minimizers of the p-frame potential, Applied and Computational Harmonic Analysis, Volume 52, May 2021, Pages 366-379 

附件下載:
 
 
【打印本頁】【關閉本頁】
電子政務平台   |   科技網郵箱   |   ARP系統   |   會議服務平台   |   聯系我們   |   友情鏈接