L. Lucy, "An iterative technique for the rectification of observed distribution," The Astronomical Journal , pp. 745-- 754, 1974.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....be more efficient in overall computation time, but are more difficult to implement and may not generalize to different cost functions. Algorithms similar to ours where only one of the factors is adapted have previously been used for the deconvolution of emission tomography and astronomical images [9, 10, 11, 12]. At each iteration of our algorithms, the new value of W or H is found by multiplying the current value by some factor that depends on the quality of the approximation in Eq. 1) We prove that the quality of the approximation improves monotonically with the application of these multiplicative ....

Lucy, LB (1974). An iterative technique for the rectification of observed distributions. Astron. J. 74, 745--754.

.... [Foldiak, Olshausen] Analytically, the NMF algorithm can be derived from a probabilistic generative model that incorporates Poisson noise [Hinton] This model has previously been used in the deconvolution of astronomical images that have been blurred by the atmosphere and the telescope [Richardson, Lucy]. NMF may thus be considered a generalization of this technique to blind deconvolution. By maximizing the likelihood of this probabilistic model, the NMF learning rule for nonnegative matrix factorization is obtained [Dempster, Saul] Given a data matrix # , the matrix factors # and # are first ....

L. B. Lucy, An iterative technique for the rectification of observed distributions, Astronomical J. 74 (1974) 745.

....Other algorithms may possibly be more efficient in overall computation time, but can be considerably more difficult to implement. Algorithms similar to ours where only one of the factors is adapted have previously been used for the deconvolution of emission tomography and astronomical images [9, 10, 11]. At each iteration of our algorithms, the new value of W or H is found by multiplying the current value by some factor that depends on the quality of the approximation in Eq. 1) We prove that the quality of the approximation improves monotonically with the application of these multiplicative ....

Lucy, LB (1974). An iterative technique for the rectification of observed distributions. Astron. J. 74, 745--754.

....is the constrained optimization of some function measure of fit to the data. Among them is the constrained least squares estimation x = argmax x fky Gamma Axk 2 ; x 2 Cg: 5) Sometimes another scoring function is used, which imposes naturally some constraint, see for instance [41, 64], where a Kullback distance is used in the case C = IR ) K and A is a matrix with positive components. Such approaches either do not satisfy requirement A4 (how to characterize the reconstruction (5) or do not lead to a stable reconstruction, because they ultimately impose A x = y and ....

L. B. Lucy. An iterative technique for the rectification of observed distributions. The Astronomical Journal, 79(6):745--754, 1974.

....allowing the user to introduce a priori knowledge of objects of interest. Eq. 14 is always an ill posed problem. If the noise is modeled as a Gaussian or Poisson process, then an iterative approach for computing maximum likelihood estimates may be used. The Richardson Lucy method ( 34] [24]; see also [1] 18] uses such an iterative approach: O (n 1) Gamma O (n) I=I (n) P ] I (n) Gamma P O (n) 15) where P is the transpose of the PSF, and O (n) is the current estimate of the desired real image . 4.2 Noise Suppression based on the Wavelet Transform ....

L.B. Lucy, "An iterative technique for the rectification of observed distributions", Astronomical Journal, 79, 1974, 745--754. 16

....A variable kernel approximation scheme is derived, where the locations and widths of the components are obtained from the likelihood functions of the samples in an iterative procedure. Our algorithm can be considered as an improvement of the classical rectification method proposed by Lucy [7] using a wellknown regularization tool, Parzen s method. Visual P EDR is an implementation in parallel of the EDR algorithm with a graphical interface, used to show how the algorithm progressively converges within each iteration, and to supervise when the solution has reached a fixed (stable) ....

L.B. Lucy. An Iterative Technique for the Rectification of the Observed Distributions. The Astronomical Journal. Vol. 79, No. 6, pages 745-754, 1974.

....noise assigned to the ith footprint. The kth estimate of the image is computed by f (k) j = f (k Gamma1) j c j : 5) In practice when the footprint noise oe i is not easily estimated, an equal noise value for all footprints is assumed, and the MCM is identical to the Richardson Lucy algorithm [10, 8]. 5. Parallelization Detector data are stored in scanlines called legs, which contain individual footprints. Profiling a typical HIRES process showed that more than 95 of the total execution time was spent within the code which calculates the footprint and image correction factors. In the ....

L. B. Lucy, "An Iterative Technique for the Rectification of Observed Distributions," Astronomical Journal , Vol. 79, pp: 745--754, 1974.

.... to overcome the difficulty [3] 13] While tackling the ringing problem in IRAS (Infrared Astronomical Satellite, 2] image reconstruction, it was found using the image space reconstruction algorithm (ISRA, 5] gives more severe ringing than the Richardson Lucy algorithm ( 14] [12]; known as EM in medical imaging, 16] 11] EM will be used hereafter) In light of the fact that ISRA and EM can be integrated into the same mathematical framework [7] it is natural to ask whether there is an iterative scheme in the same family, which gives even less ringing than EM. The ....

L. B. Lucy, "An iterative technique for the rectification of observed distributions," Astron. J., vol. 79, pp. 745--754, 1974.

....cut off frequency, the solution is clearly unstable, meaning that it leads to an uncontrolled amplification of the noise. Similarly, the ML solution with photon noise (minimization of J poisson (o) P r (h o) r) Gamma i(r) ln[ h o) r) is also unstable. Note, that the Richardson Lucy[17, 18] algorithm [RL] is nothing but an iterative process which minimizes J poisson . As an illustration, we apply RL to the first of Vesta s images shown in Fig. 3. The PSF is assumed to be the image of 63 Ceti acquired shortly after (first image of Fig. 1) The ML estimate is obtained for an infinite ....

L. B. Lucy, "An iterative technique for rectification of observed distributions," Astrophys. J. 79, 745--754 (1974).

....A statistical measure of the information given by a probability distribution is its entropy. The Jaynes principle of maximum entropy [9] then allows one to select an a priori probability distribution. These two points are introduced in subsection 2.2. In section 3, following references [12] and [19] we reinterpret the direct Bayesian method as a maximum likelihood method. We then examine the original motivations and actual properties of the so called maximum entropy image reconstruction methods. Section 4 is devoted to a unified approach of the maximum entropy method, called ....

....on the n th pixel. The parameters [ p 1 ; p N ] are proportions of flux passing through the n th pixel. In the sequel, we present two approaches, which use this model, and apply statistical techniques to derive a reconstructed image, namely the direct Bayesian method, see Lucy, 1974 [12]) and the maximum entropy methods [16] 3.1 Bayesian direct deconvolution method This method consists in an iterative refinement of the dirty map d = A y. We first assume (as in Ref. 19] that the dirty map does not contain regions of negative intensity. This map is regarded as a realization ....

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L. B. Lucy, "An iterative technique for the rectification of observed distributions," The Astronomical Journal, 79, pp. 745-754 (1974).

....stream of gas that is thought to be a jet. Restoration of HST imagery and spectra is an active subject due to the flaw in the primary mirror; see, e.g. 22] and the collection of papers in [23] One popular method is Lucy Richardson iteration, a modification of maximum likelihood (see [24] [25], 26] to which we compare our method in x5. The accuracy of the Saturn restoration is confirmed by Voyager data, which has higher resolution; in particular, the ring is indeed almost two dimensional. Our restoration of the jet image is the basis of a separate article ( 27] For a similar ....

....are repeated with sufficient frequency. After being cut to 512 2 256 and routinely despiked, the preprocessed data are displayed on the left of Figure 1. On the right of that figure is the result of our algorithm, with = 0:1. In order to compare our approach with that of Lucy Richardson ([25], 26] which is popular in astronomy, and to compare different orders of smoothing, we have enlarged one 32232 piece of the Saturn image. Due to the limitations of the display resolution, these differences are otherwise difficult to see. The Lucy Richardson method is an iterative procedure ....

L. B. Lucy, "An iterative technique for the rectification of observed distribution," Astronomical Journal, vol. 79, p. 745, June 1974.

....et al. 1992) are not practicable as convergence is achieved extremely slowly. A suitable alternative procedure is the Expectation Maximisation (EM) algorithm (Dempster et al. 1977) which generalised a number of other procedures emerging from specific applications (for example Richardson 1972; Lucy 1974). The algorithm was introduced as a general approach to the iterative computation of maximum likelihood estimates when the observations can be viewed as incomplete data . Certain data are deemed to be missing because they are inferred only indirectly via the observed data y. The algorithm can ....

Lucy, L.B. (1974). An iterative technique for the rectification of observed distributions.

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L. Lucy, "An iterative technique for the rectification of observed distribution," The Astronomical Journal , pp. 745-- 754, 1974.

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Lucy, L.B. "An Iterative Technique for the Rectification of the Observed Distributions". The Astronomical Journal. Vol. 79, No. 6, pp. 745-754, 1974.

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L.B. Lucy, An iterative technique for the rectification of the observed distributions, Astron. J. 79 (6) (1974) 745--754.

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: L. B. Lucy, "An iterative technique for the rectification of observed distributions," Astron. J., vol. 79, no. 6, June 1974, 745-59.

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