Analytical considerations of photon attenuation and system response function in SPECT reconstruction

2005 ◽  
pp. 339-353
Author(s):  
Xiaochuan Pan ◽  
Chin-Tu Chen ◽  
John N. Aarsvold ◽  
Wing. H. Wong
Keyword(s):  
Response Function ◽  
System Response ◽  
Photon Attenuation ◽  
Spect Reconstruction

Power Spectra Density Replication Control Strategy for 2-Axis Hydraulic Shaker Based on HV Estimator

2014 ◽  
Vol 596 ◽  
pp. 610-615
Author(s):  
Yu Chen ◽  
Qiang Li Luan ◽  
Zhang Wei Chen ◽  
Hui Nong He
Keyword(s):  
Response Function ◽  
Control Algorithm ◽  
Power Spectra ◽  
Time History ◽  
Good Effect ◽  
System Response ◽  
Power Spectral ◽  
Iterative Correction ◽  
Replication Control ◽  
The Given

Hydraulic shaker, equipment of simulating laboratory vibration environment, can accurately replicate the given power spectral density (PSD) and time history with an appropriate control algorithm. By studying method Hv estimator of frequency response function (FRF) estimation, a FRF identification strategy based on the Hv estimator is designed to increase the convergence rapidity and improve the system response function specialty. The system amplitude-frequency characteristics in some frequency points or frequency bands have large fluctuation. To solve this issue, a step-varying and frequency-sectioning iterative correction control algorithm is proposed for the control of 2-axial exciter PSD replication tests and the results show that the algorithm has a good effect on the control of hydraulic shaker, and can achieve reliable and high-precision PSD replication.

The probe particle scattering cross-section off the many-fermion systems in the impulse approximation

2021 ◽  
Author(s):  
Yahya Younesizadeh ◽  
Fayzollah Younesizadeh
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Spectral Function ◽  
Cross Section ◽  
Response Function ◽  
Momentum Distribution ◽  
Impulse Approximation ◽  
System Response ◽  
Probe Particle ◽  
Momentum Distribution Function

In this work, we study the differential scattering cross-section (DSCS) in the first-order Born approximation. It is not difficult to show that the DSCS can be simplified in terms of the system response function. Also, the system response function has this property to be written in terms of the spectral function and the momentum distribution function in the impulse approximation (IA) scheme. Therefore, the DSCS in the IA scheme can be formulated in terms of the spectral function and the momentum distribution function. On the other hand, the DSCS for an electron off the [Formula: see text] and [Formula: see text] nuclei is calculated in the harmonic oscillator shell model. The obtained results are compared with the experimental data, too. The most important result derived from this study is that the calculated DSCS in terms of the spectral function has a high agreement with the experimental data at the low-energy transfer, while the obtained DSCS in terms of the momentum distribution function does not. Therefore, we conclude that the response of a many-fermion system to a probe particle in IA must be written in terms of the spectral function for getting accurate theoretical results in the field of collision. This is another important result of our study.

Statistical determination of geophysical well log response functions

Geophysics ◽  
1983 ◽  
Vol 48 (11) ◽  
pp. 1525-1535 ◽  
Author(s):  
Eugene A. Nosal
Keyword(s):  
Power Spectrum ◽  
Response Function ◽  
System Response ◽  
General Terms ◽  
Induction Logging ◽  
Conductivity Profile ◽  
Statistical Determination ◽  
The One

The vertical response function of induction logging tools is shown to be derivable from a power spectrum analysis of the measurement. The vertical response function is the one‐dimensional sequence of weights that characterizes how the tool combines the rock conductivities along the borehole to form an output called the apparent conductivity; it is the system impulse response. The value of knowing this function lies in the possible use of filter theory to aid in data processing and interpretation. Two general notions establish the framework for the analysis. The first is that logging is a linear, convolutional operation. Second, the earth’s conductivity profile forms a stochastic process. The probabilistic component is fleshed out by reasonably based assumptions about the occurrence of bed boundaries and nature of conductivity changes across them. Brought together, these tenets create a characterization of the conductivity sequence that is not a stationary process, but rather is intrinsic, as defined in the discipline of geostatistics. Such a process is described by a variogram, and it is increments of the process that are stationary. The connection between the power spectrum of the measurement and the system response function is made when the convolutional model is merged with the conductivity process. Some examples of induction log functions are shown using these ideas. The analysis is presented in general terms for possibly wider application.

The Effects of Errors on the Convergence of an Iterative Deconvolution Method

1975 ◽  
Vol 19 ◽  
pp. 657-671 ◽  
Author(s):  
H. H. Madden ◽  
J. E. Houston
Keyword(s):  
Response Function ◽  
Random Noise ◽  
System Response ◽  
Smoothing Function ◽  
Deconvolution Method ◽  
X Ray ◽  
Truncation Errors ◽  
Large Fluctuations ◽  
Peak Location ◽  
Iterative Deconvolution

Calculations carried out to investigate the van Cittert iterative deconvolution method and the effects of random noise and truncation errors on its convergence behavior are presented. Gaussian functions are used for "both the true function W and the system, response function A. The model "observed" function S is generated from W and A. Both rms differences between the result of n iterations Wn and the true function, and between Wn*A and S are used to measure convergence. The effects of introducing errors can be measured against standards set by the convergence without such errors. These "no-error" calculations make use of true functions with widths from 2.0 to 0.67 times the response function width. The effects of random noise are investigated by adding noise to W*A before deconvolution. A small amount of random noise initially added builds up rapidly in amplitude during the iterative process and eventually dominates the rms difference calculations. To suppress the effects of random noise build-up; smoothing techniques are applied, the best of which involved smoothing both the noisy observed function, S, and the system response function, A, before deconvolution. The smoothing operation is thus taken as part of the measurement and. the divergence resulting from, the noise build-up is avoided. The results depend strongly upon, the -width of the smoothing function. Uhsymmetric system response functions, similar' to those encountered in soft x-ray appearance potential spectroscopy and in x-ray continuum, isochromat measurements, are used in investigations of truncation errors. Abrupt cut-offs of the model S and A functions before deconvolution result in the build-up of large fluctuations in W . These truncation errors become increasingly localized with continued iterations and make only minor contributions to the errors in Wn in the vicinity of the real peak if the truncations are made sufficiently far from the peak location. Alternatively, the truncation errors can be avoided by analytical continuation.

Reinforcing the Driving Quality of Soccer Playing Robots by Anticipation (Verbesserung der Fahreigenschaften von fußballspielenden Robotern durch Antizipation)

2005 ◽  
Vol 47 (5) ◽  
Author(s):  
Alexander Gloye ◽  
Fabian Wiesel ◽  
Oliver Tenchio ◽  
Mark Simon
Keyword(s):  
Neural Network ◽  
Response Function ◽  
Black Box ◽  
System Response ◽  
Control Software ◽  
Ideal Behavior ◽  
Straight Path ◽  
Control Computer ◽  
The Ideal

SummaryThis paper shows how an omnidirectional robot can learn to correct inaccuracies when driving, or even learn to use corrective motor commands when a motor fails, whether partially or completely. Driving inaccuracies are unavoidable, since not all wheels have the same grip on the surface, or not all motors can provide exactly the same power. When a robot starts driving, the real system response differs from the ideal behavior assumed by the control software. Also, malfunctioning motors are a fact of life that we have to take into account. Our approach is to let the control software learn how the robot reacts to instructions sent from the control computer. We use a neural network, or a linear model for learning the robot's response to the commands. The model can be used to predict deviations from the desired path, and take corrective action in advance, thus increasing the driving accuracy of the robot. The model can also be used to monitor the robot and assess if it is performing according to its learned response function. If it is not, the new response function of the malfunctioning robot can be learned and updated. We show, that even if a robot loses power from a motor, the system can re-learn to drive the robot in a straight path, even if the robot is a black-box and we are not aware of how the commands are applied internally.

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