Noise parametric

System (A8.2)-(A8.4) defines completely the time variation of orientation and angular velocity for every path X(t). One can easily see that (A8.2)-(A8.4) describe the system with parametrical modulation, as the X(t) variation is an input noise and does not depend on behaviour of the solution of (Q(t), co(r). In other words, the back reaction of the rotator to the collective motion of the closest neighbourhood is neglected. Since the spectrum of fluctuations X(t) does not possess a carrying frequency, in principle, for the rotator the conditions of parametrical resonance and excitation (unrestricted heating of rotational degrees of freedom) are always fulfilled. In reality the thermal equilibrium is provided by dissipation of rotational energy from the rotator to the environment and... 

Wiener inverse-filter however yields, possibly, unphysical solution with negative values and ripples around sharp features (e.g. bright stars) as can be seen in Fig. 3b. Another drawback of Wiener inverse-filter is that spectral densities of noise and signal are usually unknown and must be guessed from the data. For instance, for white noise and assuming that the spectral density of object brightness distribution follows a simple parametric law, e.g. a power law, then ... 

An extensive series of studies is conducted to investigate the effects of various weighting factors associated with the mechanical energy of the oscillatory field ((/), actuation energy (r), plant disturbance (a), and sensor noise (/ ) on the robustness and performance of the controller. Also included in the parametric investigation are the affordable bound of system dynamics uncertainty (I/7) and the maximum time delay of the distributed combustion of control fuel 5t). Results indicate that... 

Standard examples of noise-suppression rules include the so-called Wienei6 suppression rule, the power-subtraction (see Figure 4.16), the spectral subtraction [Boll, 1979, Lim and Oppenheim, 1979, McAulay and Malpass, 1980, Vary, 1985], as well as several families of parametric suppression curves [Lim and Oppenheim, 1979, Moorer and Berger, 1986, Etter and Moschytz, 1994],... 

This chapter presents, in a natural order, the different steps for obtaining an exploitable parametric map i.e., the modeling of acquired data in terms of noise and signal (Section 2), the optimization of the measurement protocol parameters (Section 3) and the actual methods of reconstruction that lead from the acquisition space to the parametric space (Section 4). The last part looks at certain applications and the current limits of these approaches (Section 5). 

Segmenting background (noise-alone regions) from object (mixture of signal and noise), which is useful to avoid degrading the parametric map with aberrant values in the background. 

Obtaining parametric maps necessarily requires estimating the vector of the parameter 0 from K-noised samples. The general theory of estimation59,60 provides solutions that can be applied in the domain of quantitative MRI. In practice, the ML approach is the most commonly used, because it concerns the estimation of non-random parameters, unlike the Bayesian approach, which is mostly applied to segment the images.61 The LS approaches defined by... 

If the accuracy of both parametric tests was not so different in the benchmark set, the situation changes dramatically towards PIT performance. This might be explained by, what can be termed lack of noise in the real data. In fact, for a time series to be considered stationary by the F-like test, it must have some level of noise. Cao Rhinehart (1995) recommend the introduction of a white noise before analyzing data. 

The exact operator expansions presented in the previous section indicated that the parametric approximation fails for sufficiently long evolution times, and, moreover, the quantum character of the pump mode introduces corrections to the field evolution coming from the quantum noise. Since the two parts of the Hamiltonian Hq and /// given by Eq. (55) are constants of motion, again we can split the Hilbert space into orthogonal sectors, as before, and introduce for a given number n of the pump mode at frequency 2co the states... 

In partial order ranking - in contrast to standard multidimensional statistical analysis - neither assumptions about linearity nor any assumptions about distribution properties are made. In this way the partial order ranking can be considered as a non-parametric method. Thus, there is no preference among the descriptors. However, due to the simple mathematics outlined above, it is obvious that the method a priori is rather sensitive to noise, since even minor fluctuations in the descriptor values may lead to non-comparability or reversed ordering. An approach how to handle loss of information by using an ordinal in stead of a matrix can also be found in the chapter by Pavan et al., see p. 181). 

Using this model, adaptive posi-cast controllers were designed, and detailed numerical simulation studies were carried out. These studies consisted of (i) the closed-loop performance of the adaptive controller, (ii) comparison of the adaptive controller with an empirical phase-shift controller, (iii) robustness with respect to parametric uncertainties, (w) robustness with respect to unmodeled dynamics and uncertain delays, (i/) performance in the presence of noise. 

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