RICHARDSON, W. 1972. Bayesian-based iterative method of image restoration. J. Opt. Soc. of Am. 62, 1 (January), 55--59.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....tool and is routinely applied in scientific and clinical practice. In most cases the MLE must be computed numerically, and the most common method for this purpose is the expectation maximization (EM) algorithm [4 6] also known as the Richardson Lucy algorithm in the context of Poisson data [7]) EM algorithms have been widely studied and applied and provide a very simple means to compute the MLE. However the maximum likelihood criterion is not always useful. For example, in PET and SPECT the resulting system of equations is very ill posed and often the MLE is extremely noisy (highly ....

W. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. of Am., vol. 62, pp. 55--59, 1972.

....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 ....

Richardson, WH (1972). Bayesian-based iterative method of image restoration. J. Opt. Soc. Am. 62, 55--59.

....tool and is routinely applied in scientific and clinical practice. In most cases the MLE must be computed numerically, and the most common method for this purpose is the expectation maximization (EM) algorithm [21, 36, 37] also known as the Richardson Lucy algorithm in the context of Poisson data [38]) EM algorithms have been widely studied and applied and provide a very simple means to compute the MLE. However, the maximum likelihood criterion is not always useful. For example, in PET and SPECT the resulting system of equations is very ill posed, and often the MLE is extremely noisy (highly ....

W. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. of Am., vol. 62, pp. 55--59, 1972.

....tool and is routinely applied in scientific and clinical practice. In most cases the MLE must be computed numerically, and the most common method for this purpose is the expectation maximization (EM) algorithm [4 6] also known as the Richardson Lucy algorithm in the context of Poisson data [7]) EM algorithms have been widely studied and applied and provide a very simple means to compute the MLE. However the maximum likelihood criterion is not always useful. For example, in PET and SPECT the resulting system of equations is very ill posed and often the MLE is extremely noisy (highly ....

W. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. of Am., vol. 62, pp. 55--59, 1972.

....D. P. O LEARY 4.1.2. Comparison with Other Blind Deconvolution Methods. We compare RSTLN with two other blind deconvolution methods: blind Lucy Richardson, and the APEX SECB method of Carasso. The blind Lucy Richardson algorithm is an extension of the well known original Lucy Richardson method [13, 21]. The original iterative method was derived from Bayes Theorem and assumes that the blurred image, the original image, and the PSF are (possibly non normalized) probability density functions. The most common and ecient implementation makes use of the FFT to compute convolutions. This implicitly ....

W. H. Richardson, Bayesian-based iterative method of image restoration, J. Opt. Soc. Am. A, 62, (1972), pp. 55-59.

....f 0 is used. Furthermore the likelihood of each iteration of the EM algorithm will strictly increase to a global maximum [12] The EM algorithm for finding the maximum likelihood estimator of a translated Poisson process (often referred to as EM MLE) is identical to the RichardsonLucy algorithm [18]. The Richardson Lucy algorithm is a constrained but unregularized iterative image restoration algorithm. The ICTM and Carrington algorithms, however, incorporate Tikhonov regularization to suppress undesired solutions. Conchello has derived an algorithm that incorporates Tikhonov regularization ....

W. H. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. of Am., vol. 62, pp. 55-59, 1972.

.... [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 ....

W. H. Richardson, Bayesian-based iterative method of image restoration,J.Opt.Soc.Am. 62 (1972) 55--59.

....that the unknown function is nonnegative. Snyder et al. 28] obtained a similar algorithm as a solution to a general Fredholm integral equation of the first kind. They derive the formula by minimizing Csisz ar s I divergence, which is closely related to the concept of likelihood. Richardson [26], Kennett et al. 14, 15, 16] and Di Ges u et al. 4] obtained the same result from a more intuitive Bayesian point of view, and term it as Bayesian deconvolution . All of these methods could be 2 0 50 100 150 200 250 300 350 400 450 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure 1: A segment ....

W. H. Richardson. Bayesian--based iterative method of image restoration. J. Opt. Soc. Am., 62(1):55--59, 1972.

....Lee [40] and Vardi [39] found this algorithm is applicable to a wide class of linear inverse problem with positive constraints. Snyder et al. 35] obtained the algorithm as a solution to a general Fredholm integral equation of the first type, and their derivation used the E M algorithm. Richardson [33], Kennett et al. 16, 17, 18] and Di Ges u et al. 7] obtained the formula from an intuitive Bayesian point of view, and termed it Bayesian deconvolution . It is worth mentioning that the 2 D image data studied by Shepp and Vardi [34] Vardi, et al. 41] Snyder et al. 35] are quite distinct ....

W. H. Richardson. Bayesian--based iterative method of image restoration. J. Opt. Soc. Am., 62(1):55--59, 1972.

....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 ....

Richardson, WH (1972). Bayesian-based iterative method of image restoration. J. Opt. Soc. Am. 62, 55--59.

....framework, 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 ....

W.H. Richardson, "Bayesian-based iterative method of image restoration", Journal of the Optical Society of America, 62, 1972, 55--59.

....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 ....

W. H. Richardson, "Bayesian-Based Iterative Method of Image Restoration," Journal of the Optical Society of America, Vol. 62, pp: 55-59, 1972.

.... reconstruction 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. ....

W. H. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. Am., vol. 62, pp. 55--59, 1972.

....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 ....

W. H. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. Am. 62, 55--59 (1972).

....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 approach ....

....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 which ....

W. Richardson, "Bayesian-based iterative methods of image restoration," J. Opt. Soc. Am., vol. 62, pp. 55--59, 1972.

....(Press 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 ....

Richardson, W.H. (1972). Bayesian-based iterative method of image restoration. J. Optical Soc. America. 62, 55-59.

No context found.

RICHARDSON, W. 1972. Bayesian-based iterative method of image restoration. J. Opt. Soc. of Am. 62, 1 (January), 55--59.

No context found.

W. Richardson, "Bayesian-based iterative method of image restoration," Journal of the Optical Society of America , pp. 55--59, 1972.

No context found.

Richardson, W. H. (1972), "Bayesian-based iterative method of image restoration," J. Opt. Soc. Am., vol. 62, p. 55-59

No context found.

W. H. Richardson. Bayesian--based iterative method of image restoration. J. Opt. Soc. Am., 62(1):55--59, 1972.

No context found.

: W. H. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. Am. A, Vol. 62, No. 1, Jan. 1972, 55-59.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC