Nonlocal Elastica Model for Sparse Reconstruction

In view of the exceptional ability of curvature in connecting missing edges and structures, we propose novel sparse reconstruction models via the Euler’s elastica energy. In particular, we firstly extend the Euler’s elastica regularity into the nonlocal formulation to fully take the advantages of th...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical imaging and vision Vol. 62; no. 4; pp. 532 - 548
Main Authors Yan, Mengyuan, Duan, Yuping
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2020
Springer Nature B.V
Subjects
Algorithms
Applications of Mathematics
Computer Science
Convexity
Elastica
Image Processing and Computer Vision
Mathematical Methods in Physics
Reconstruction
Redundancy
Sampling
Signal,Image and Speech Processing
Smoothness
Weighting functions
Euler’s elastica
Nonlocal regularization
Sparse reconstruction
ADMM
Online AccessGet full text

Cover

More Information
Summary:In view of the exceptional ability of curvature in connecting missing edges and structures, we propose novel sparse reconstruction models via the Euler’s elastica energy. In particular, we firstly extend the Euler’s elastica regularity into the nonlocal formulation to fully take the advantages of the pattern redundancy and structural similarity in image data. Due to its non-convexity, non-smoothness and nonlinearity, we regard both local and nonlocal elastica functional as the weighted total variation for a good trade-off between the runtime complexity and performance. The splitting techniques and alternating direction method of multipliers (ADMM) are used to achieve efficient algorithms, the convergence of which is also discussed under certain assumptions. The weighting function occurred in our model can be well estimated according to the local approach. Numerical experiments demonstrate that our nonlocal elastica model achieves the state-of-the-art reconstruction results for different sampling patterns and sampling ratios, especially when the sampling rate is extremely low.
ISSN:0924-9907
1573-7683
DOI:10.1007/s10851-019-00943-7