Although both acquisitions are initiated at approximately the same time (close ticks, far left), the respiratory signal acquisition starts first (at , which is chosen as the time origin), and then the list-mode acquisition (at ). Then n respiratory marks are inserted in the list-mode file at time points , .
(a) The values of the respiratory curve are found at time points with increasing values for starting from 0 and being the trigger marks found in the list-mode files. The mean and standard deviation (SD) values of are computed. (b) When the form an approximately horizontal line over time crossing the axis at the user-defined triggering level, the SD is minimum and is found.
Results from one study. Average and standard deviation (SD) values of for ranging from 0 to with a increment. A unique minimum for the SD well below the baseline is found in this range. This minimum indicates the time , which allows us to determine . Note that when the SD is minimal, the average value is here approximately 0, which is the user-defined threshold that triggers signals for this case.
The first minutes of acquisition of the respiratory signal from the same study as presented in Fig. 2. The points (white squares) are all on an ascending part of the signal and form an approximately horizontal line crossing the -axis at the user-defined threshold (here ).
The standard deviation of the respiratory values for values ranging from 0 to . Left and right columns present the results for the studies acquired with the Philips and GE systems, respectively. The horizontal line represents the average value of each curve and is used as a baseline to which the minimum SD value can be compared. Studies 9 and 10 were obtained with the same patient.
The SD and triggering threshold values. The delay is presented in the last column.
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