Journal ArticleDOI
Restoration, Resolution, and Noise
C. K. Rushforth,R. W. Harris +1 more
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TLDR
A general conclusion is that the reconstruction technique described here is most useful when the smoothing is severe and when a modest improvement of resolution may be worthwhile.Abstract:
This paper treats the problem of restoring the detail to an optical image which has been degraded by diffraction and noise. The particular contribution of the paper is a more complete analysis of the effects of various types of noise on system performance than has been given previously. Background noise, measurement noise, and computer roundoff error are considered, and the errors in the reconstructed image caused by these noise processes are evaluated. Numerical results for the special case of a perfect one-dimensional slit aperture are obtained. A general conclusion is that the reconstruction technique described here is most useful when the smoothing is severe and when a modest improvement of resolution may be worthwhile.read more
Citations
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Journal ArticleDOI
Spectrum estimation and harmonic analysis
TL;DR: In this article, a local eigenexpansion is proposed to estimate the spectrum of a stationary time series from a finite sample of the process, which is equivalent to using the weishted average of a series of direct-spectrum estimates based on orthogonal data windows to treat both bias and smoothing problems.
Image processing
TL;DR: Parts of image processing are discussed--specifically: the mathematical operations one is likely to encounter, and ways of implementing them by optics and on digital computers; image description; and image quality evaluation.
Journal ArticleDOI
Super-resolution through Error Energy Reduction
TL;DR: A computational procedure is devised which must reduce a defined ‘error energy’ which is implicit in the truncated spectrum and it is demonstrated that by so doing, resolution well beyond the diffraction limit is attained.
Picture processing by computer
TL;DR: The field of picture processing by computer is reviewed from a technique-oriented standpoint and the processing of given pictures (as opposed to computer-synthesized pictures) is considered.
Book ChapterDOI
The Stability of Inverse Problems
TL;DR: Many inverse problems arising in optics and other fields like geophysics, medical diagnostics and remote sensing, present numerical instability: the noise affecting the data may produce arbitrarily large errors in the solutions.
References
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Journal ArticleDOI
Prolate spheroidal wave functions, fourier analysis and uncertainty — II
David Slepian,H. O. Pollak +1 more
TL;DR: In this paper, the authors apply the theory developed in the preceding paper to a number of questions about timelimited and bandlimited signals, and find the signals which do the best job of simultaneous time and frequency concentration.
Journal ArticleDOI
Reconstructed Wavefronts and Communication Theory
Emmett N. Leith,Juris Upatnieks +1 more
TL;DR: In this paper, a two-step imaging process is described from a communication-theory viewpoint, which consists of three well-known operations: a modulation, a frequency dispersion, and a square-law detection.
Journal ArticleDOI
Diffraction and Resolving Power
TL;DR: It is shown that two distinctly different objects of finite size cannot have identical images, so that no ambiguous image exists for such objects and diffraction limits resolving power in the sense of only the lack of precision of image measurement imposed by the system noise.
Journal ArticleDOI
Eigenvalues associated with prolate spheroidal wave functions of zero order
TL;DR: In this paper, a table of values of X n and λ n, quantities defined by the eigenvalue problems (1-x^2) is presented, along with some approximations for these quantities.
Journal ArticleDOI
Object Restoration in a Diffraction-Limited Imaging System
TL;DR: If the illumination in the object space is confined to a finite region, then the imaging equation can be solved for the object in terms of the image, and the solution can be expressed as a series expansion on the eigenfunctions of the imaging operator.