.
RESEARCH PAPER
.
SCIENCE CHINA
Information Sciences
doi: 10.1007/s11432-015-5419-2
c
Science China Press and Springer-Verlag Berlin Heidelberg 2016 info.scichina.com link.springer.com
Nonconvex plus quadratic penalized low-rank and
sparse decomposition for noisy image alignment
Xiai CHEN
1,2
, Zhi HAN
1,2
*
, Yao WANG
3
, Yandong TANG
1,2
&HaibinYU
1,2
1
State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences,
Shenyang 110016,China;
2
University of Chinese Academy of Sciences, Beijing 100049,China;
3
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049,China
Received May 24, 2015; accepted July 8, 2015
Abstract This paper proposes a general method for dealing with the problem of recovering the low-rank
structure, in which the data can be deformed by some unknown transformations and corrupted by sparse
or nonsparse noises. Nonconvex penalization method is used to remedy the drawbacks of existing convex
penalization method and a quadratic penalty is further used to better tackle the nonsparse noises in the data.
We exploits the local linear approximation (LLA) method for turning the resulting nonconvex penalization
problem into a series of weighted convex penalization problems and these subproblems are efficiently solved via
the augmented Lagrange multiplier (ALM). Besides comparing with the method of robust alignment by sparse
and low-rank decomposition for linearly correlated images (RASL), we also propose a nonconvex penalized low-
rank and sparse decomposition (NLSD) model as comparison. Numerical experiments are conducted on both
controlled and uncontrolled data to demonstrate the outperformance of the proposed method over RASL and
NLSD.
Keywords low-rank decomposition, nonconvex relaxation, quadratic penalized, batch image alignment, sparse
or nonsparse noise
Citation Chen X A, Han Z, Wang Y, et al. Nonconvex plus quadratic penalized low-rank and sparse decompo-
sition for noisy image alignment. Sci China Inf Sci, 2016, 59, doi: 10.1007/s11432-015-5419-2
1 Introduction
In recent years, with the development of Internet technology, massive amounts of image and video data
are available to us. All these high-dimensional data pose steep challenges to existing vision algorithms in
automatically extracting the hidden low-dimensional structures despite changing of viewpoints, illumina-
tions, occlusions, nonsparse noises, or even no alignment. Undone these nuisance factors in the processing
stage is of great importance in obtaining the true intrinsic structures of the data.
The classical Principal Component Analysis (PCA) [1, 2] is the most widely used statistical tool for
high-dimensional data analysis and dimensionality reduction today. But it also has been shown that PCA
technique only works well when the perturbation is i.i.d Gaussian, which means that it is not robust to
gross errors or outliers. The recent proposed Robust PCA [3] method utilizes a convex program that
* Corresponding author (email: hanzhi@sia.cn)
剩余12页未读，继续阅读
资源评论
