Noise robustness

A Preliminary Study of Compression Efficiency and Noise Robustness of Orthogonal Moments on Medical X-Ray Images... 

Keywords— Orthogonal moments, Legendre, Tchebichef, compression, noise robustness. 

It is important to understand that this material will not be presented in a theoretical vacuum. Instead, it will be presented in a particular context, consistent with the majority of the author s experience, namely the development of calibrations in an industrial setting. We will focus on working with the types of data, noise, nonlinearities, and other sources of error, as well as the requirements for accuracy, reliability, and robustness typically encountered in industrial analytical laboratories and process analyzers. Since some of the advantages, tradeoffs, and limitations of these methods can be data and/or application dependent, the guidance In this book may sometimes differ from the guidance offered in the general literature. 

Whether this tendency of PLS to reject nonlinearities by pushing them onto the later factors which are usually discarded as noise factors will improve or degrade the prediction accuracy and robustness of a PLS calibration as compared to the same calibration generated by PCR depends very much upon the specifics of the data and the application. If the nonlinearities are poorly correlated to the properties which we are trying to predict, rejecting them can improve the accuracy. On the other hand, if the rejected nonlinearities contain information that has predictive value, then the PLS calibration may not perform as well as the corresponding PCR calibration that retains more of the nonlinearities and therefore is able to exploit the information they contain. In short, the only sure way to determine if PLS or PCR is better for a given calibration is to try both of them and compare the results. 

If the exact statistics of the noise is unknown, assuming stationary Gaussian noise is however more robust than Poissonian (Lane, 1996). 

We have seen that minimizing the likelihood penalty ml(x) enforces agreement with the data. Exact expression of ml(x) should depends on the known statistics of the noise. However, if the statistics of the noise is not known, using a least-squares penalty is more robust (Lane, 1996). In the following, and for sake of simplicity, we will assume Gaussian stationary noise ... 

Testing the robustness of a (best) model (and second-best contenders) by evaluating sets of statistically similar data created with program SIMILAR if the derived decisions remain unaffected by measurement noise, the model is adequate. 

In this work, therefore we aim to combine the stochastic observer to input/output prediction model so that it can be robust against the influence of noise. We employ the modified I/O data-based prediction model [3] as a linear part of Wimra" model to design the WMPC and these controllers are applied to a continuous mefihyl methacrylate (MMA) solution polymerization reactor to examine the performance of controller. 

Robustness. The relative ordering of the triangular episodes in a trend is invariant to scaling of both the time axis and the function value. It is also invariant to any linear transformation (e.g., rotation, translation). Finally it is quite robust to uncertainties in the real value of the signal (e.g., noise), provided that the extent of a maximal episode is much larger than the period of noise. 

Filters are designed to remove unwanted information, but do not address the fact that processes involve few events monitored by many measurements. Many chemical processes are well instrumented and are capable of producing many process measurements. However, there are far fewer independent physical phenomena occurring than there are measured variables. This means that many of the process variables must be highly correlated because they are reflections of a limited number of physical events. Eliminating this redundancy in the measured variables decreases the contribution of noise and reduces the dimensionality of the data. Model robustness and predictive performance also require that the dimensionality of the data be reduced. 

The stability of scarred states to external noise and other environmental disturbances was the next natural issue that was raised and partially addressed earlier (L. Sirko, et.al., 1993 R. Scharf, et.al., 1994). The main conclusion was that scarred states are quite robust to reasonable levels of noise. This question took on added relevance with the coming of age of mesoscopic systems where, be it spontaneous emission in atom optics or leads or scattering and other forms of dissipation in heterostructures, the open nature of the system must be accounted for. These new experiments also provided non-ideal realizations of simple theoretical paradigms such as stadium billiards and the kicked rotor, with additional issues that had to be accounted for in the theory. 

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