Variable metric techniques for forward–backward methods in imaging

On Variable - Metric Methods for Sparse Hessians

The relationship between variable-metric methods derived by norm minimization and those derived by symmetrization of rank-one updates for sparse systems is studied, and an analogue of Dennis's nonsparse symmetrization formula derived. A new method of using norm minimization to produce a sparse analogue of any nonsparse variable-metric method is proposed. The sparse BFGS generated by this method...

Variable Metric Conjugate Gradient Methods

Imaging techniques in dermatology

Since the discovery of X-rays, the use of imaging technology has continued to play an important role in medicine. Technological advancements have led to the development of various imaging modalities, most of which have been used to image organs deep within the human body. More recently, attention has focused on the application of imaging technology for evaluation of the skin. A variety of techn...

A family of variable metric proximal methods

We consider conceptual optimization methods combining two ideas: the Moreau-Yosida regularization in convex analysis, and quasi-Newton approximations of smooth functions. We outline several approaches based on this combination, and establish their global convergence. Then we study theoretically the local convergence properties of one of these approaches, which uses quasi-Newton updates of the o...

Limited-memory projective variable metric methods for unconstrained minimization

A new family of limited-memory variable metric or quasi-Newton methods for unconstrained minimization is given. The methods are based on a positive definite inverse Hessian approximation in the form of the sum of identity matrix and two low rank matrices, obtained by the standard scaled Broyden class update. To reduce the rank of matrices, various projections are used. Numerical experience is e...