Research output per year
Research output per year
Carl Olsson, Marcus Carlsson, Erik Bylow
Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review
This paper considers the problem of finding a low rank matrix from observations of linear combinations of its elements. It is well known that if the problem fulfills a restricted isometry property (RIP), convex relaxations using the nuclear norm typically work well and come with theoretical performance guarantees. On the other hand these formulations suffer from a shrinking bias that can severely degrade the solution in the presence of noise. In this theoretical paper we study an alternative non-convex relaxation that in contrast to the nuclear norm does not penalize the leading singular values and thereby avoids this bias. We show that despite its non-convexity the proposed formulation will in many cases have a single stationary point if a RIP holds. Our numerical tests show that our approach typically converges to a better solution than nuclear norm based alternatives even in cases when the RIP does not hold.
Original language | English |
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Title of host publication | Proceedings - 2017 IEEE International Conference on Computer Vision Workshops, ICCVW 2017 |
Publisher | IEEE - Institute of Electrical and Electronics Engineers Inc. |
Pages | 1809-1817 |
Number of pages | 9 |
Volume | 2018-January |
ISBN (Electronic) | 9781538610343 |
DOIs | |
Publication status | Published - 2018 Jan 19 |
Event | 16th IEEE International Conference on Computer Vision Workshops, ICCVW 2017 - Venice, Italy Duration: 2017 Oct 22 → 2017 Oct 29 |
Conference | 16th IEEE International Conference on Computer Vision Workshops, ICCVW 2017 |
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Country/Territory | Italy |
City | Venice |
Period | 2017/10/22 → 2017/10/29 |
Research output: Thesis › Doctoral Thesis (compilation)