The Quest for the Ideal Scintillator for Hybrid Phototubes

In this paper we present the results of extensive studies of scintillators for hybrid phototubes with luminescent screens. The results of the developments of such phototubes with a variety of scintillators are presented. New scintillator materials for such kind of application are discussed. The requirements for scintillators to use in such hybrid phototubes are formulated. It is shown that very fast and highly efficient inorganic scintillators like ZnO:Ga will be ideal scintillators for such kind of application.Comment: 5 pages, 6 figures and 1 table. Submitted to the proceedings of SCINT2007 Conference, Winston-Salem, NC USA, June 4-8, 200

A Fixed Point Framework for Recovering Signals from Nonlinear Transformations

We consider the problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information. Standard feasibility and optimization methods are ill-suited to tackle this problem due to the nonlinearities. We show that, in many common applications, the transformation model can be associated with fixed point equations involving firmly nonexpansive operators. In turn, the recovery problem is reduced to a tractable common fixed point formulation, which is solved efficiently by a provably convergent, block-iterative algorithm. Applications to signal and image recovery are demonstrated. Inconsistent problems are also addressed.Comment: 5 page

Stochastic forward-backward and primal-dual approximation algorithms with application to online image restoration

Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily smooth. Our framework can handle stochastic approximations of the gradient of the smooth function and allows for stochastic errors in the evaluation of the proximity operator of the nonsmooth function. The almost sure convergence of the iterates generated by the algorithm to a minimizer is established under relatively mild assumptions. We also propose a stochastic version of a popular primal-dual proximal splitting algorithm, establish its convergence, and apply it to an online image restoration problem.Comment: 5 Figure

Quasinonexpansive Iterations on the Affine Hull of Orbits: From Mann's Mean Value Algorithm to Inertial Methods

Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms. We study a new iterative scheme in which the update is obtained by applying a composition of quasinonexpansive operators to a point in the affine hull of the orbit generated up to the current iterate. This investigation unifies several algorithmic constructs, including Mann's mean value method, inertial methods, and multi-layer memoryless methods. It also provides a framework for the development of new algorithms, such as those we propose for solving monotone inclusion and minimization problems

Variable Metric Forward-Backward Splitting with Applications to Monotone Inclusions in Duality

We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in duality. Some of these algorithms are new even when specialized to the fixed metric case. Various applications are discussed