Efficient Matrix Sensing Using Rank-1 Gaussian Measurements

  • Kai Zhong
  • Prateek Jain
  • Inderjit S. DhillonEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9355)


In this paper, we study the problem of low-rank matrix sensing where the goal is to reconstruct a matrix exactly using a small number of linear measurements. Existing methods for the problem either rely on measurement operators such as random element-wise sampling which cannot recover arbitrary low-rank matrices or require the measurement operator to satisfy the Restricted Isometry Property (RIP). However, RIP based linear operators are generally full rank and require large computation/storage cost for both measurement (encoding) as well as reconstruction (decoding).

In this paper, we propose simple rank-one Gaussian measurement operators for matrix sensing that are significantly less expensive in terms of memory and computation for both encoding and decoding. Moreover, we show that the matrix can be reconstructed exactly using a simple alternating minimization method as well as a nuclear-norm minimization method. Finally, we demonstrate the effectiveness of the measurement scheme vis-a-vis existing RIP based methods.


Matrix sensing Matrix completion Inductive learning Alternating minimization 


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Supplementary material

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Supplementary material (pdf 468 KB)


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of Texas at AustinAustinUSA
  2. 2.Microsoft ResearchBangaloreIndia

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