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We generalize the primal-dual hybrid gradient (PDHG) algorithm proposed by Zhu draw connections to similar methods and discuss convergence of several special cases and modifications. In particular, we point out a convergence result for a modified version of PDHG that has a similarly good empirical convergence rate for total variation (TV) minimization(More)
We generalize the primal-dual hybrid gradient (PDHG) algorithm proposed by Zhu to a broader class of convex optimization problems. In addition, we survey several closely related methods and explain the connections to PDHG. We point out convergence results for a modified version of PDHG that has a similarly good empirical convergence rate for total variation(More)
The Primal-Dual hybrid gradient (PDHG) method is a powerful optimization scheme that breaks complex problems into simple sub-steps. Unfortunately, PDHG methods require the user to choose stepsize parameters, and the speed of convergence is highly sensitive to this choice. We introduce new adaptive PDHG schemes that automatically tune the stepsize parameters(More)
A collaborative convex framework for factoring a data matrix <i>X</i> into a nonnegative product <i>AS</i> , with a sparse coefficient matrix <i>S</i>, is proposed. We restrict the columns of the dictionary matrix <i>A</i> to coincide with certain columns of the data matrix <i>X</i>, thereby guaranteeing a physically meaningful dictionary and dimensionality(More)
• General framework for a class of primal-dual algorithms • Convergence of modified PDHG by connection to split inexact Uzawa (Sec. 3.4.2.3) • Operator splitting techniques for extending application to a large class of convex models (Sec. 2.1 and 3.6.1) • Clarification of dual interpretations and general shrinkage formulas (Sec. 2.4.2) • Proposed convex(More)
A collaborative convex framework for factoring a data matrix X into a non-negative product AS, with a sparse coefficient matrix S, is introduced. We restrict the columns of the dictionary matrix A to coincide with certain columns of X, thereby guaranteeing a physically meaningful dictionary and dimensionality reduction. As an example, we show applications(More)
This paper addresses the nonstationary out-of-focus (OOF) blur removal in the application of barcode reconstruction. We propose a partially blind deblurring method when partial knowledge of the clean barcode is available. In particular, we consider an image formation model based on geometrical optics, which involves the point-spread function (PSF) for the(More)