TY - JOUR
T1 - A Weighted Difference of Anisotropic and Isotropic Total Variation Model for Image Processing
AU - Lou, Yifei
AU - Zeng, Tieyong
AU - Osher, Stanley
AU - Xin, Jack
N1 - Funding information:
^ Department of Mathematical Sciences, University of Texas at Dallas, Dallas, TX 75080 ([email protected]). The work of this author was partially supported by NSF grants DMS-0928427 and DMS-1222507.
^ Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong ([email protected]). The work of this author was partially supported by NSFC 11271049, RGC 211911, 12302714, and RFGs of HKBU.
^ Department of Mathematics, UCLA, Los Angeles, CA 90095 ([email protected]). The work of this author was supported by the Keck Foundation, ONR N000141410683, N000141110749, and NSF DMS-1118971.
^ Department of Mathematics, UC Irvine, Irvine, CA 92697 ([email protected]). The work of this author was partially supported by NSF grants DMS-0928427 and DMS-1222507.
Publisher copyright:
© 2015, Society for Industrial and Applied Mathematics
PY - 2015/9/10
Y1 - 2015/9/10
N2 - We propose a weighted difference of anisotropic and isotropic total variation (TV) as a regularization for image processing tasks, based on the well-known TV model and natural image statistics. Due to the form of our model, it is natural to compute via a difference of convex algorithm (DCA). We draw its connection to the Bregman iteration for convex problems and prove that the iteration generated from our algorithm converges to a stationary point with the objective function values decreasing monotonically. A stopping strategy based on the stable oscillatory pattern of the iteration error from the ground truth is introduced. In numerical experiments on image denoising, image deblurring, and magnetic resonance imaging (MRI) reconstruction, our method improves on the classical TV model consistently and is on par with representative state-of-the-art methods.
AB - We propose a weighted difference of anisotropic and isotropic total variation (TV) as a regularization for image processing tasks, based on the well-known TV model and natural image statistics. Due to the form of our model, it is natural to compute via a difference of convex algorithm (DCA). We draw its connection to the Bregman iteration for convex problems and prove that the iteration generated from our algorithm converges to a stationary point with the objective function values decreasing monotonically. A stopping strategy based on the stable oscillatory pattern of the iteration error from the ground truth is introduced. In numerical experiments on image denoising, image deblurring, and magnetic resonance imaging (MRI) reconstruction, our method improves on the classical TV model consistently and is on par with representative state-of-the-art methods.
KW - Anisotropic TV
KW - Bregman and split Bregman iterations
KW - Convergence to stationary points
KW - Difference of convex algorithm
KW - Isotropic TV
KW - Stable oscillatory errors
KW - Weighted difference
UR - http://www.scopus.com/inward/record.url?scp=84943549432&partnerID=8YFLogxK
U2 - 10.1137/14098435X
DO - 10.1137/14098435X
M3 - Journal article
AN - SCOPUS:84943549432
SN - 1936-4954
VL - 8
SP - 1798
EP - 1823
JO - SIAM Journal on Imaging Sciences
JF - SIAM Journal on Imaging Sciences
IS - 3
ER -