Error Bounds for the Method of Alternating Projections.

Abstract

Given a collection of closed subspaces of a Hilbert space, the method of alternating projections produces a sequence which converges to the orthogonal projections onto the intersection of the subspaces. A large class of problems in medical and geophysical image reconstruction can be solved using this method. A sharp error bound will enable the user to accurately estimate the number of iterations necessary to achieve a desired relative error. The sharpest possible upper bound is obtained for the case of two subspaces, and the sharpest known upper bound for more than two subspaces. Keywords: Alternating projections; Error bounds; Image reconstruction.

Document Details

Document Type
Technical Report
Publication Date
Jan 27, 1987
Accession Number
ADA176770

Entities

People

  • Howard L. Weinert
  • Selahattin Kayalar

Organizations

  • Johns Hopkins University

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Banach Space
  • Hilbert Space
  • Image Reconstruction
  • Iterations
  • Mathematical Analysis
  • Mathematics
  • Sequences

Fields of Study

  • Engineering

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Computer Vision.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space
  • Space - Space Objects