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Rank Minimization with Structured Data Patterns

In English

Författare

Summary, in English

The problem of finding a low rank approximation of a given measurement matrix is of key interest in computer vision. If all the elements of the measurement matrix are available, the problem can be solved using factorization. However, in the case of missing data no satisfactory solution exists. Recent approaches replace the rank term with the weaker (but convex) nuclear norm. In this paper we show that this heuristic works poorly on problems where the locations of the missing entries are highly correlated and structured which is a common situation in many applications. Our main contribution is the derivation of a much stronger convex relaxation that takes into account not only the rank function but also the data. We propose an algorithm which uses this relaxation to solve the rank approximation problem on matrices where the given measurements can be organized into overlapping blocks without missing data. The algorithm is computationally efficient and we have applied it to several classical problems including structure from motion and linear shape basis estimation. We demonstrate on both real and synthetic data that it outperforms state-of-the-art alternatives. (1)

Publiceringsår

2014

Språk

Engelska

Sidor

250-265

Publikation/Tidskrift/Serie

Computer Vision - ECCV 2014, PT III

Volym

8691

Dokumenttyp

Konferensbidrag

Förlag

Springer

Ämne

  • Mathematics

Conference name

13th European Conference on Computer Vision (ECCV)

Conference date

2014-09-06 - 2014-09-12

Status

Published

ISBN/ISSN/Övrigt

  • ISSN: 0302-9743
  • ISSN: 1611-3349