A primal-dual iterative algorithm for a maximum likelihood estimation problem

Alfredo N. Iusem, Marc Teboulle*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The duality between maximum likelihood and entropy maximization problems is used to provide a primal-dual method for solving a maximum likelihood estimation problem arising from Positron Emission Tomography. We prove convergence of our algorithm from the fact that the sequence it generates can be seen as the dual sequence produced by the hybrid version of Bregman's method when applied to a linearly constrained convex program with a Burg's entropy type objective function. This algorithm is shown to be closely connected to the so called Expectation Maximization (EM) algorithm.

Original languageEnglish
Pages (from-to)443-456
Number of pages14
JournalComputational Statistics and Data Analysis
Issue number4
StatePublished - Nov 1992
Externally publishedYes


FundersFunder number
National Science FoundationECS-88-0239
Air Force Office of Scientific Research0218-88
Conselho Nacional de Desenvolvimento Científico e Tecnológico301280/86


    • Bregman's Algorithm
    • Convex programming
    • Duality
    • EM algorithm
    • Entropy
    • Maximum likelihood
    • Statistical estimation


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