Constrained Sampling: Optimum Reconstruction in Subspace With Minimax Regret Constraint

This paper considers the problem of optimum reconstruction in generalized sampling-reconstruction processes (GSRPs). We propose constrained GSRP, a novel framework that minimizes the reconstruction error for inputs in a subspace, subject to a constraint on the maximum regret-error for any other sign...

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Bibliographic Details
Published inIEEE transactions on signal processing Vol. 67; no. 16; pp. 4218 - 4230
Main Authors Sadeghi, Bashir, Runyi Yu, Boddeti, Vishnu Naresh
Format Journal Article
LanguageEnglish
Published New York IEEE 15.08.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Aerospace electronics
Computer science
Consistent sampling
constrained optimization
Constraints
Decision theory
Error analysis
generalized sampling-reconstruction processes
Generators
Hilbert space
Image reconstruction
minimax regret sampling
Minimax technique
oblique projection
Optimization
orthogonal projection
Reconstruction
reconstruction error
Sampling
Signal processing
subspace sampling
Subspaces
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Summary:This paper considers the problem of optimum reconstruction in generalized sampling-reconstruction processes (GSRPs). We propose constrained GSRP, a novel framework that minimizes the reconstruction error for inputs in a subspace, subject to a constraint on the maximum regret-error for any other signal in the entire signal space. This framework addresses the primary limitation of existing GSRPs (consistent, subspace, and minimax regret), namely, the assumption that the a priori subspace is either fully known or fully ignored. We formulate constrained GSRP as a constrained optimization problem, the solution to which turns out to be a convex combination of the subspace and the minimax regret samplings. Detailed theoretical analysis on the reconstruction error shows that constrained sampling achieves a reconstruction that is, 1) (sub)optimal for signals in the input subspace, 2) robust for signals around the input subspace, and 3) reasonably bounded for any other signals with a simple choice of the constraint parameter. Experimental results on sampling-reconstruction of a Gaussian signal and a speech signal demonstrate the effectiveness of the proposed scheme.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2019.2925608