Algorithm model for penalty functions-type iterative procedures

An iterative deautoconvolution algorithm for nonnegative functions

Abstract. This paper considers the inverse problem of recovering a nonnegative function from its autoconvolution. We propose an algorithm that solves the problem by minimizing Csiszár’s I-divergence between the observed autoconvolution and an estimated autoconvolution. We call it a deautoconvolution algorithm. Various properties of the algorithm are discussed and proven. The effectiveness of th...

An Objective Penalty Functions Algorithm for Multiobjective Optimization Problem

By using the penalty function method with objective parameters, the paper presents an interactive algorithm to solve the inequality constrained multi-objective programming (MP). The MP is transformed into a single objective optimal problem (SOOP) with inequality constrains; and it is proved that, under some conditions, an optimal solution to SOOP is a Pareto efficient solution to MP. Then, an i...

Stability of Jungck-type iterative procedures

Let (X ,d) be a metric space and T : X → X . Several physical problems, expressed as a fixed point equation Tx = x, are solved by approximating a sequence {xn} ⊂ X generated by an iterative procedure f (T ,xn). Let the sequence {xn} converge to a fixed point of T . The iterative procedure f (T ,xn) is considered numerically stable if and only if a sequence {yn} ⊂ X approximatively close to {xn}...

Iterative reconstruction with segmentation penalty for PET.

Segmentation technique is widely accepted to reduce noise propagation from transmission scanning for positron emission tomography. The conventional routine is to sequentially perform reconstruction and segmentation. A smoothness penalty is also usually used to reduce noise, which can be imposed to both the ML and WLS estimators. In this paper we replace the smoothness penalty by a segmentation ...

Penalty Functions