Rank Minimization with Structured Data Patterns

Viktor Larsson, Carl Olsson, Erik Bylow, Fredrik Kahl

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review

Abstract

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)
Original languageEnglish
Title of host publicationComputer Vision - ECCV 2014, PT III
PublisherSpringer
Pages250-265
Volume8691
Publication statusPublished - 2014
Event13th European Conference on Computer Vision (ECCV) - Zurich, SWITZERLAND
Duration: 2014 Sept 62014 Sept 12

Publication series

Name
Volume8691
ISSN (Print)1611-3349
ISSN (Electronic)0302-9743

Conference

Conference13th European Conference on Computer Vision (ECCV)
Period2014/09/062014/09/12

Subject classification (UKÄ)

  • Mathematics

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