2003
DOI: 10.1088/0305-4470/36/43/024
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Non-monotonic behaviour in relaxation dynamics of image restoration

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Cited by 4 publications
(5 citation statements)
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“…From this panel, we find that some 'non-monotonic' behaviour is observed at the initial stage of the dynamics when we fail to set the amplitude to its optimal value (Γ ∼ 0.6). Similar behaviour was reported in the Bayesian image restoration via thermal (classical) fluctuation [38]. In the Bayesian framework, it is desired for us to obtain the estimate of each pixel and hyper-parameters simultaneously.…”
Section: Disordered Systems: An Application For Statistical-mechanica...supporting
confidence: 63%
“…From this panel, we find that some 'non-monotonic' behaviour is observed at the initial stage of the dynamics when we fail to set the amplitude to its optimal value (Γ ∼ 0.6). Similar behaviour was reported in the Bayesian image restoration via thermal (classical) fluctuation [38]. In the Bayesian framework, it is desired for us to obtain the estimate of each pixel and hyper-parameters simultaneously.…”
Section: Disordered Systems: An Application For Statistical-mechanica...supporting
confidence: 63%
“…In this case, we find that the minimum value of the square error is obtained in smaller number of time steps than the case of T m ¼ 0:9 (¼ T s ): the time evolution of the square error is minimum at t ¼ 2. This result corresponds to the one by Ozeki and Okada [7]. We show time evolution dðtÞ of the square error for T m ¼ 0:1, T m ¼ 0:9 (¼ T s ) and T m ¼ 2:0 when mð0Þ ¼ 1:0 in Fig.…”
Section: A Systemsupporting
confidence: 82%
“…On the other hand, Ozeki and Okada pointed out that a good restoration is achieved for a binary pattern by stopping a restoration during a relaxation process when a temperature is lower than that of an original pattern [7]. It is interesting to investigate whether the conclusion by Ozeki and Okada is still hold or not for gray-scale patterns.…”
Section: Introductionmentioning
confidence: 99%
“…Figure 2 shows the time dependent behavior of the overlap M with decoding temperatures, T = 0.3, T = 0.4, and T = 0.5. Compared to the case of image restoration, 7) we cannot observe the difference between the decoding temperatures. However, the most significant difference is that the overlap does not take a maximum value in the middle of decoding processes at the low temperature.…”
Section: Dynamics Of Sourlas Codecontrasting
confidence: 57%
“…However, it is unclear whether the Nishimori temperature is optimal in the decoding processes. 7) In this paper, the decoding processes of Sourlas code are investigated by means of statistical mechanics. In §2, we describe the Sourlas code within a Bayesian inference framework and its equilibrium properties.…”
Section: §1 Introductionmentioning
confidence: 99%