Multiplicative iterative algorithms for convex programming
TLDR
Study of multiplicative iterative algorithms for the minimization of a differentiable, convex function defined on the positive orthant of R N and the convergence is nearly monotone in the sense of Kullback-Leibler divergence.About:
This article is published in Linear Algebra and its Applications.The article was published on 1990-03-01 and is currently open access. It has received 87 citations till now. The article focuses on the topics: Convex analysis & Convex function.read more
Citations
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A unified treatment of some iterative algorithms in signal processing and image reconstruction
TL;DR: The Krasnoselskii?Mann (KM) approach to finding fixed points of nonlinear continuous operators on a Hilbert space was introduced in this article, where a wide variety of iterative procedures used in signal processing and image reconstruction and elsewhere are special cases of the KM iterative procedure.
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A multiprojection algorithm using Bregman projections in a product space
Yair Censor,Tommy Elfving +1 more
TL;DR: Using an extension of Pierra's product space formalism, it is shown here that a multiprojection algorithm converges and is fully simultaneous, i.e., it uses in each iterative stepall sets of the convex feasibility problem.
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Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning
TL;DR: An overview of the majorization-minimization (MM) algorithmic framework, which can provide guidance in deriving problem-driven algorithms with low computational cost and is elaborated by a wide range of applications in signal processing, communications, and machine learning.
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Equilibrium programming using proximal-like algorithms
Sjur Didrik Flåm,Anatoly Antipin +1 more
TL;DR: Under a monotonicity hypothesis it is shown that equilibrium solutions can be found via iterative convex minimization via iteratives convex maximization.
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Iterative deblurring for CT metal artifact reduction
TL;DR: In experiments with synthetic noise-free and additive noisy projection data of dental phantoms, it is found that both simultaneous iterative algorithms produce superior image quality as compared to filtered backprojection after linearly fitting projection gaps.
References
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Maximum Likelihood Reconstruction for Emission Tomography
L. A. Shepp,Y. Vardi +1 more
TL;DR: In this paper, the authors proposed a more accurate general mathematical model for ET where an unknown emission density generates, and is to be reconstructed from, the number of counts n*(d) in each of D detector units d. Within the model, they gave an algorithm for determining an estimate? of? which maximizes the probability p(n*|?) of observing the actual detector count data n* over all possible densities?.
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Monotone Operators and the Proximal Point Algorithm
TL;DR: In this paper, the proximal point algorithm in exact form is investigated in a more general form where the requirement for exact minimization at each iteration is weakened, and the subdifferential $\partial f$ is replaced by an arbitrary maximal monotone operator T.
Book
Nonlinear Programming
TL;DR: It is shown that if A is closed for all k → x x, k → y y, where ( k A ∈ ) k y x , then ( ) A ∉ y x .
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A Statistical Model for Positron Emission Tomography
TL;DR: In this article, a mathematical model tailored to the physics of positron emissions is presented, and the model is used to describe the image reconstruction problem of PET as a standard problem in statistical estimation from incomplete data.