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Image reconstruction/synthesis from nonuniform data and zero/threshold crossings

Park, Yongwan and Soumekh, Mehrdad (1994) Image reconstruction/synthesis from nonuniform data and zero/threshold crossings. Optical Engineering, 33 (10). pp. 3290-3301. ISSN 0091-3286. https://resolver.caltech.edu/CaltechAUTHORS:20170809-112810664

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Abstract

We address the problem of reconstructing functions from their nonuniform data and zero/threshold crossings. We introduce a deterministic process via the Gram-Schmidt orthonormalization procedure to reconstruct functions from their nonuniform data and zero/threshold crossings. This is achieved by first introducing the nonorthogonal basis functions in a chosen 2-D domain (e.g., for a band-limited signal, a possible choice is the 2-D Fourier domain of the image) that span the signal subspace of the nonuniform data. We then use the Gram-Schmidt procedure to construct a set of orthogonal basis functions that span the linear signal subspace defined by the nonorthogonal basis functions. Next, we project the N-dimensional measurement vector (N is the number of nonuniform data or threshold crossings) onto the newly constructed orthogonal basis functions. Finally, the function at any point can be reconstructed by projecting the representation with respect to the newly constructed orthonormal basis functions onto the reconstruction basis functions that span the signal subspace of the evenly spaced sampled data. The reconstructed signal gives the minimum mean square error estimate of the original signal. This procedure gives error-free reconstruction provided that the nonorthogonal basis functions that span the signal subspace of the nonuniform data form a complete set in the signal subspace of the original band-limited signal. We apply this algorithm to reconstruct functions from their unevenly spaced sampled data and zero crossings and also apply it to solve the problem of synthesis of a 2-D band-limited function with the prescribed level crossings.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1117/12.182339DOIArticle
http://opticalengineering.spiedigitallibrary.org/article.aspx?articleid=1073366PublisherArticle
Additional Information:© 1994 The International Society for Optical Engineering. Paper DIR-09 received Nov. 18, 1993; revised manuscript received July 10, 1994; accepted for publication July 25, 1994.
Subject Keywords:digital image recovery and synthesis, nonharmonic Fourier function; image reconstruction; nonuniform sampling; Gram-Schmidt orthogonalization; zero crossings; band-limited functions
Issue or Number:10
Record Number:CaltechAUTHORS:20170809-112810664
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170809-112810664
Official Citation:Yongwan Park and Mehrdad Soumekh "Image reconstruction/synthesis from nonuniform data and zero/threshold crossings", Opt. Eng. 33(10), 3290-3301 (Oct 01, 1994). ; http://dx.doi.org/10.1117/12.182339
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80018
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Aug 2017 18:36
Last Modified:03 Oct 2019 18:26

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