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Superresolution capabilities of the Gerchberg method in the band‐pass case: An eigenvalue analysis
Author(s) -
Salerno Emanuele
Publication year - 1998
Publication title -
international journal of imaging systems and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.359
H-Index - 47
eISSN - 1098-1098
pISSN - 0899-9457
DOI - 10.1002/(sici)1098-1098(1998)9:2/3<181::aid-ima15>3.0.co;2-#
Subject(s) - extrapolation , eigenfunction , eigenvalues and eigenvectors , operator (biology) , algorithm , spectrum (functional analysis) , computer science , component (thermodynamics) , image (mathematics) , feature (linguistics) , object (grammar) , mathematics , artificial intelligence , computer vision , optics , mathematical analysis , physics , quantum mechanics , biochemistry , chemistry , linguistics , philosophy , repressor , transcription factor , gene , thermodynamics
This article first provides a general introduction to the Gerchberg superresolution algorithm. Some specific properties of this algorithm, when applied to 2D band‐pass images, are then studied by means of an eigenvalue analysis of the imaging operator. The main feature derived is the capability to recover the dc component of the unknown object that has to be reconstructed from the noisy image available. This aspect is important with band‐pass images of strictly positive objects, in that recovering the low‐frequency and dc components in this case is tantamount to suppressing intolerable artifacts. A set of eigenpairs of the imaging operator was calculated numerically. From the dominant eigenvalues, the spectrum extrapolation capabilities of the method can be derived. From the behavior of the eigenfunctions, the capability of the method to recover the dc component of the original object can be evaluated. Some of the calculated eigenfunctions are shown as examples. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 181–188, 1998