Inconsistent signal feasibility problems: least-squares solutions in a product space
- 1 January 1994
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing
- Vol. 42 (11) , 2955-2966
- https://doi.org/10.1109/78.330356
Abstract
In this paper, we present parallel projection methods to find least-squares solutions to inconsistent convex set theoretic signal synthesis problems. The problem of finding a signal that minimizes a weighted average of the squares of the distances to constraint sets is reformulated in a product space, where it is equivalent to that of finding a point that lies in a particular subspace and at minimum distance from the Cartesian product of the original sets. A solution is obtained in the product space via methods of alternating projections which naturally lead to methods of parallel projections in the original space. The convergence properties of the proposed methods are analyzed and signal synthesis applications are demonstrated.Keywords
This publication has 27 references indexed in Scilit:
- Signal recovery by best feasible approximationIEEE Transactions on Image Processing, 1993
- On the Convergence of the Products of Firmly Nonexpansive MappingsSIAM Journal on Optimization, 1992
- Comments on "Design of a class of time-constrained FIR digital filters by successive projectionsIEEE Transactions on Circuits and Systems, 1990
- Extensions of a result on the synthesis of signals in the presence of inconsistent constraintsIEEE Transactions on Circuits and Systems, 1986
- Nonlinear Functional Analysis and its ApplicationsPublished by Springer Nature ,1986
- Nonlinear Functional Analysis and its ApplicationsPublished by Springer Nature ,1985
- The feasible solution in signal restorationIEEE Transactions on Acoustics, Speech, and Signal Processing, 1984
- Image restoration by convex projections in the presence of noiseApplied Optics, 1983
- Image Restoration by the Method of Convex Projections: Part 1ߞTheoryIEEE Transactions on Medical Imaging, 1982
- Projections on Convex Sets in Hilbert Space and Spectral Theory: Part I. Projections on Convex Sets: Part II. Spectral TheoryPublished by Elsevier ,1971