Noise reduction filters

Use sharpening, edge detection, or noise reduction filters globally across the... 

Problems will arise if the capture principle is not matched to the process or through the process itself (e.g., clogging of floor capture openings, clogging of filters). The structure of the booth could also be used for purposes of noise reduction. 

This filter is not an inverse filter of the type that we seek, being intended only for noise reduction. It does not undo any spreading introduced by s(x). It is, however, an optimum filter in the sense that no better linear filter can be found for noise reduction alone, provided that we are restricted to the knowledge that the noise is additive and Gaussian distributed. 

Certainly the most popular methods for noise reduction in audio signals to date are based upon short-time Fourier processing. These methods, which can be derived from non-stationary adaptations to the frequency-domain Wiener filter, are discussed fully in section 4.5.1. 

How can this be solved Clearly there are limits to the amount of peak sharpening that is practicable, but the filter function can be improved so that noise reduction and resolution enhancement are applied simultaneously. One common method is to multiply... 

One of the earliest applications of the Fourier transform in spectroscopy was in filtering and noise reduction. This technique is still extensively employed. 

Figure 4.10. Comparison of filtered backprojection (FBP) and iterative (OSEM) methods with attenuation correction, (a) Lungs, (b) Normal Liver, (c) Liver with tumor, (d) Breast. FBP images with attenuation corrections are noisier than OSEM images with attenuation correction. (Reprinted by permission of Society of Nuclear Medicine from Riddell C et al (2001) Noise reduction in oncology FDG PET images by iterative reconstructions a quantitative assessment. J Nucl Med 42 1316)...

Figure 3.3-2 shows typical results. The simple first-order averaging filter, panel (c) in Fig. 3.3-2, is most effective in reducing the noise, but also introduces the largest distortion, visible even on the broadest peaks. This is always a trade-off noise reduction is gained at the cost of distortion. The same can be seen especially with the narrower peaks, where the higher-order filters distort less, but also filter out less noise. In section 10.9 we will describe a more sophisticated filter, due to Barak, which for each point determines the optimal polynomial order to be used, and thereby achieves a better compromise between noise reduction and distortion. 

In such situations, Fourier transforms can provide a means for performing the differentiation, as well as digital filtering or other apodizations for noise reduction (see preceding section). A flow chart showing the interrelations between a function and its integral or derivative is shown in Figure 11. 

Figure 8.19 Three noise reduction approaches. Left grounded patient. Middle floating patient with instrumentational amplifier. Right ground-clamping circuit. Vp is typical patient AC voltage with respect to ground. Vp is in practice nonsinusoidal. Because of the high-pass filtering effects, the harmonics of the mains supply are expanded.

The processing errors are due to various factors as the orientation and number of views that influence the quality of the approximation. A reduced number of views decrease the amount of errors but increase image composition distortions at the edges of each image. The filtering processes and the noise reduction of digitized geometries have influence in the subsequent approximations. 

Figure 2.28 Simulation of a three-state single-molecule protein folding experiment in which the FRET value changes abruptly between 0.3, 0.5 and 0.7. The overall count rate is 1000 Hz. (a) Simulated data, acceptor in black and donor in gray, (b) Simulated data after filtration with the filter, (c) FRET efficiency calculated from a. (d) FRET efficiency calculated from b. (e) Histogram of the FRET efficiency values of c. (f) Histogram of the FRET efficiency values of (d).(Reprinted from Haran, G, Noise reduction in single-molecule Fluorescence trajectories of folding proteins. Chemical Physics 307 (2004) 137-145. (Copyright (2004) with permission from Elsevier.))...

The basic biopotential amplifier described above, along with the specific design considerations for each biopotential, can yield a signal acquisition of acceptable quality in most laboratory settings. In practice, however, further enhancements are always necessary to achieve acceptable clinical performance in novel applications. These enhancements include circuits for reducing electric interference, filtering noise, reduction of artifacts, electrical isolation of the amplifier, and electrical protection of the circuit against defibrillation shocks [9]. 

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