A Convex Approach to Low Rank Matrix Approximation with Missing Data

  • Carl Olsson
  • Magnus Oskarsson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5575)


Many computer vision problems can be formulated as low rank bilinear minimization problems. One reason for the success of these problems is that they can be efficiently solved using singular value decomposition. However this approach fails if the measurement matrix contains missing data.

In this paper we propose a new method for estimating missing data. Our approach is similar to that of L 1 approximation schemes that have been successfully used for recovering sparse solutions of under-determined linear systems. We use the nuclear norm to formulate a convex approximation of the missing data problem. The method has been tested on real and synthetic images with promising results.


Singular Value Decomposition Measurement Matrix Nuclear Norm Photometric Stereo Miss Data Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Carl Olsson
    • 1
  • Magnus Oskarsson
    • 1
  1. 1.Centre for Mathematical SciencesLund UniversityLundSweden

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