Wotao Yin

A New Alternating Minimization Algorithm for Total Variation Image Reconstruction

We propose, analyze, and test an alternating minimization algorithm for recovering images from blurry and noisy observations with total variation (TV) regularization. This algorithm arises from a new half-quadratic model applicable to not only the anisotropic but also the isotropic forms of TV discretizations. The per-iteration computational complexity of the algorithm is three fast Fourier transforms. We establish strong convergence properties for the algorithm including finite convergence for some variables and relatively fast exponential (or

An Iterative Regularization Method for Total Variation-Based Image Restoration

q

Bregman Iterative Algorithms for

-linear in optimization terminology) convergence for the others. Furthermore, we propose a continuation scheme to accelerate the practical convergence of the algorithm. Extensive numerical results show that our algorithm performs favorably in comparison to several state-of-the-art algorithms. In particular, it runs orders of magnitude faster than the lagged diffusivity algorithm for TV-based deblurring. Some extensions of our algorithm are also discussed.

\ell_1

We introduce a new iterative regularization procedure for inverse problems based on the use of Bregman distances, with particular focus on problems arising in image processing. We are motivated by the problem of restoring noisy and blurry images via variational methods by using total variation regularization. We obtain rigorous convergence results and effective stopping criteria for the general procedure. The numerical results for denoising appear to give significant improvement over standard models, and preliminary results for deblurring/denoising are very encouraging.

-Minimization with Applications to Compressed Sensing

We propose simple and extremely efficient methods for solving the basis pursuit problem

Iteratively reweighted algorithms for compressive sensing

\min\{\|u\|_1 : Au = f, u\in\mathbb{R}^n\},

Fixed-Point Continuation for

which is used in compressed sensing. Our methods are based on Bregman iterative regularization, and they give a very accurate solution after solving only a very small number of instances of the unconstrained problem

\ell_1

\min_{u\in\mathbb{R}^n} \mu\|u\|_1+\frac{1}{2}\|Au-f^k\|_2^2

-Minimization: Methodology and Convergence

for given matrix

Total variation models for variable lighting face recognition

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