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Problems in signal detection and image recovery can sometimes be formulated as a convex feasibility problem (CFP) of finding a vector in the intersection of a finite family of closed convex sets. Algorithms for this purpose typically employ orthogonal or generalized projections onto the individual convex sets. The simultaneous multiprojection algorithm of… (More)

The recently presented sequential unconstrained minimization algorithm SUMMA is extended to provide a framework for the derivation of block-iterative, or partial-gradient, optimization methods. This BI-SUMMA includes, and is motivated by, block-iterative versions of the algebraic reconstruction technique (ART) and its multiplicative variant, the MART. The… (More)

The EM algorithm is not a single algorithm, but a framework for the design of iterative likelihood maximization methods for parameter estimation. Any algorithm based on the EM framework we refer to as an " EM algorithm ". Because there is no inclusive theory that applies to all EM algorithms, the subject is a work in progress, and we find it appropriate to… (More)

We obtain the following upper bounds for the eigenvalues of the matrix A † A. For any a in the interval [0, 2] let c aj =

The EM algorithm is not a single algorithm, but a template for the construction of iterative algorithms. While it is always presented in stochastic language, relying on conditional expectations to obtain a method for estimating parameters in statistics, the essence of the EM algorithm is not stochastic. The conventional formulation of the EM algorithm given… (More)

The most common image representation method for biomed-ical image reconstruction uses pixels, and the image is assumed to be constant throughout the pixel. Other methods have also been used. In many reconstruction problems, the measured data is approximated by line integrals through the object. This fact suggests a new class of model representation methods… (More)

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