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- Jian-Feng Cai, Emmanuel J. CandÃ¨s, Zuowei Shen
- SIAM Journal on Optimization
- 2010

This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convexâ€¦ (More)

- Jian-Feng Cai, Stanley Osher, Zuowei Shen
- Multiscale Modeling & Simulation
- 2009

Split Bregman methods introduced in [47] have been demonstrated to be efficient tools to solve total variation (TV) norm minimization problems, which arise from partial differential equation basedâ€¦ (More)

Image inpainting is a fundamental problem in image processing and has many applications. Motivated by the recent tight frame based methods on image restoration in either the image or the transformâ€¦ (More)

- Jian-Feng Cai, Raymond H. Chan, Mila Nikolova
- Journal of Mathematical Imaging and Vision
- 2009

In this paper, we propose a two-phase approach to restore images corrupted by blur and impulse noise. In the first phase, we identify the outlier candidatesâ€”the pixels that are likely to be corruptedâ€¦ (More)

The variational techniques (e.g., the total variation based method [1]) are well established and effective for image restoration, as well as many other applications, while wavelet frame basedâ€¦ (More)

- Jian-Feng Cai, Hui Ji, Zuowei Shen, Gui-Bo Ye
- 2013

Sparsity based regularization methods for image restoration assume that the underlying image has a good sparse approximation under a certain system. Such a system can be a basis, a frame, or aâ€¦ (More)

- Jian-Feng Cai, Hui Ji, Chaoqiang Liu, Zuowei Shen
- IEEE Transactions on Image Processing
- 2012

How to recover a clear image from a single motion-blurred image has long been a challenging open problem in digital imaging. In this paper, we focus on how to recover a motion-blurred image due toâ€¦ (More)

- Jian-Feng Cai, Hui Ji, Chaoqiang Liu, Zuowei Shen
- 2009 IEEE Conference on Computer Vision andâ€¦
- 2009

Restoring a clear image from a single motion-blurred image due to camera shake has long been a challenging problem in digital imaging. Existing blind deblurring techniques either only remove simpleâ€¦ (More)

The restoration of blurred images corrupted with impulse noise is a difficult problem which has been considered in a series of recent papers. These papers tackle the problem by using variationalâ€¦ (More)

- Jian-Feng Cai, Stanley Osher, Zuowei Shen
- Math. Comput.
- 2009

One of the key steps in compressed sensing is to solve the basis pursuit problem minuâˆˆRn{âˆ¥uâˆ¥1 : Au = f}. Bregman iteration was very successfully used to solve this problem in [40]. Also, a simple andâ€¦ (More)