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- Title
A regularised deep matrix factorised model of matrix completion for image restoration.
- Authors
Li, Zhemin; Xu, Zhi‐Qin John; Luo, Tao; Wang, Hongxia
- Abstract
It has been an important approach of using matrix completion to perform image restoration. Most previous works on matrix completion focus on the low‐rank property by imposing explicit constraints on the recovered matrix, such as the constraint of the nuclear norm or limiting the dimension of the matrix factorisation component. Recently, theoretical works suggest that deep linear neural network has an implicit bias towards low rank on matrix completion. In this work, a regularised deep matrix factorised (RDMF) model for image restoration is proposed, which utilises the implicit bias of the low rank of deep neural networks and the explicit bias of total variation. RDMF is a powerful and flexible framework for inverse problems in image processing while the combination of implicit and explicit regularisation represents the intrinsic characteristics of a natural image. The effectiveness of the RDMF model with extensive experiments are demonstrated, in which the method surpasses the recently proposed models in common examples, especially for the restoration from very few observations. This work sheds light on a more general framework for solving other inverse problems by combining the implicit bias of deep learning with explicit regularisation.
- Subjects
IMAGE reconstruction; ARTIFICIAL neural networks; LOW-rank matrices; IMPLICIT bias; INVERSE problems
- Publication
IET Image Processing (Wiley-Blackwell), 2022, Vol 16, Issue 12, p3212
- ISSN
1751-9659
- Publication type
Article
- DOI
10.1049/ipr2.12553