TY - JOUR
T1 - Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction
AU - Nikolova, Mila
AU - NG, Kwok Po
AU - Tam, Chi Pan
N1 - Funding Information:
Manuscript received September 03, 2009; revised January 07, 2010 and May 09, 2010; accepted May 18, 2010. Date of publication June 10, 2010; date of current version November 17, 2010. The work of M. Nikolova was supported by the French Agence Nationale de la Recherche (ANR), under Grant FREEDOM (ANR07-JCJC-0048-01). The work of M. K. Ng was supported in part by Hong Kong Research Grants Council Grants and HKBU FRGs.The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Minh N. Do.
PY - 2010/12
Y1 - 2010/12
N2 - Nonconvex nonsmooth regularization has advantages over convex regularization for restoring images with neat edges. However, its practical interest used to be limited by the difficulty of the computational stage which requires a nonconvex nonsmooth minimization. In this paper, we deal with nonconvex nonsmooth minimization methods for image restoration and reconstruction. Our theoretical results show that the solution of the nonconvex nonsmooth minimization problem is composed of constant regions surrounded by closed contours and neat edges. The main goal of this paper is to develop fast minimization algorithms to solve the nonconvex nonsmooth minimization problem. Our experimental results show that the effectiveness and efficiency of the proposed algorithms.
AB - Nonconvex nonsmooth regularization has advantages over convex regularization for restoring images with neat edges. However, its practical interest used to be limited by the difficulty of the computational stage which requires a nonconvex nonsmooth minimization. In this paper, we deal with nonconvex nonsmooth minimization methods for image restoration and reconstruction. Our theoretical results show that the solution of the nonconvex nonsmooth minimization problem is composed of constant regions surrounded by closed contours and neat edges. The main goal of this paper is to develop fast minimization algorithms to solve the nonconvex nonsmooth minimization problem. Our experimental results show that the effectiveness and efficiency of the proposed algorithms.
KW - Continuation methods
KW - fast Fourier transform
KW - image reconstruction
KW - image restoration
KW - nonconvex nonsmooth global minimization
KW - nonconvex nonsmooth regularization
KW - total variation
UR - http://www.scopus.com/inward/record.url?scp=78649252763&partnerID=8YFLogxK
U2 - 10.1109/TIP.2010.2052275
DO - 10.1109/TIP.2010.2052275
M3 - Journal article
C2 - 20542766
AN - SCOPUS:78649252763
SN - 1057-7149
VL - 19
SP - 3073
EP - 3088
JO - IEEE Transactions on Image Processing
JF - IEEE Transactions on Image Processing
IS - 12
M1 - 5483167
ER -