Department of Mathematics
Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction
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. © 2010 IEEE.
Continuation methods, fast Fourier transform, image reconstruction, image restoration, nonconvex nonsmooth global minimization, nonconvex nonsmooth regularization, total variation
Source Publication Title
IEEE Transactions on Image Processing
Institute of Electrical and Electronics Engineers
Link to Publisher's Edition
Nikolova, Mila, Michael K. Ng, and Chi-Pan Tam. "Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction." IEEE Transactions on Image Processing 19.12 (2010): 3073-3088.