Deconvolution Analysis of FMRI Time Series Data - Waisman ...

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Note that, since there is only one input stimulus function, the Partial R^2 and Partial Fvalues (listed under Stimulus: f) are identical to the Full Model R^2 and F-stat, respectively.Also, note that the estimated full model parameter vector is now:b t = 95:97 1:30 0:28 6:45 10:15 5:53 3:81Due to the measurement noise, the estimated full model parameter vector is not exactlyequal to the \true" parameter vector.Example 1.4.2.3 Estimation of IRF from Overlapping Responses No MeasurementNoiseIn the previous Examples, the input impulses were spaced suciently far apart in timethat the system responses to the individual stimuli did not overlap. What happens whenthe system responses do overlap? Consider the following stimulus function:g(t) = 1 1 0 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 0 0Save g(t) as a single column of numbers in le g.1D. The stimulus function g(t) contains10 impulses. Assuming that the system is linear, the response to the sequence of impulsesshould be equal to the sum of the responses to the individual impulses. Thus, the systemresponse y(t) =g(t) h(t) can be calculated by adding up the individual impulse responsefunctions:y(t) =0 5 10 5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 5 10 5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 5 10 5 2 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 5 10 5 2 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 5 10 5 2 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 5 10 5 2 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 5 10 5 2 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 10 5 2 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 10 5 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 10 5{ { { { { { { { { { { { { { { { { { { {0 5 15 15 7 7 15 20 17 7 7 10 5 7 10 10 17 20 17 7Now, model the measured data as a constant (100) plus slope (1) plus the system response,e.g.:w(t) = b 0 + b 1 t + y(t) = 100 + 1 t + y(t)=f 100 106 117 118 111 112 121 127 125 116117 121 117 120 124 125 133 137 135 126 gand store this as a single column of numbers into le w.1D. You can plot the \data" usingthe command: 1dplot w.1D. Looking at the plot, can you visualize the shape of the IRF?Execute the following script, which uses the g(t) stimulus function, and the w(t) \data".32
Program 3dDeconvolve Command Line for Example 1.4.2.33dDeconvolve n-input1D w.1D -num stimts 1 n-stim file 1 g.1D -stim label 1 ''g'' -stim maxlag 1 4Since no noise is present, the program output should agree with the \true" parametervector:b t = 100:00 1:00 0:00 5:00 10:00 5:00 2:00Example 1.4.2.4 Estimation of IRF from Overlapping Responses AdditiveNoiseAgain simulate the eect of measurement error, by adding white Gaussian noise to theabove data. So, adding random values (say from a table of N( 2 ) = N(0 4) randomvariates (see Ref.[3])) to the above w(t), you obtain something that looks like:wn(t) =w(t)+"(t)= f 99:78 105:46 116:30 123:51 108:60 111:01 120:84 126:42 123:11 116:85114:55 118:18 117:58 118:93 125:01 126:21 135:23 140:22 138:75 127:28 gSave your \response+noise" data into le wn.1D. You can plot the \data" using thecommand: 1dplot wn.1D. Looking at the plot, can you visualize the shape of the IRF?Now, execute the script from the previous Example, except replace -input1D w.1D with-input1D wn.1D. The program output, for the above data,isasshown below:Program 3dDeconvolve Screen Output for Example 1.4.2.4Program:3dDeconvolveAuthor:B. Douglas WardInitial Release: 02 Sept 1998Latest Revision: 27 July 2000Baseline:t^0 coef = 92.6567 t^0 t-st = 77.2499t^1 coef = 1.3345 t^1 t-st = 23.6341Stimulus: gh[0] coef = 1.9530 h[0] t-st = 3.5183h[1] coef = 6.0968 h[1] t-st = 11.2205h[2] coef = 11.5062 h[2] t-st = 19.8937h[3] coef = 6.6768 h[3] t-st = 11.9295h[4] coef = 2.6870 h[4] t-st = 4.7401R^2 = 0.9835 F[5,9] = 107.3899 p-value = 9.6139e-0833
Page 1: Deconvolution Analysis of FMRI Time
Page 7 and 8: Since the system is linear, the ope
Page 9: the above equation can be written:Z
Page 13 and 14: where s(h k ) is the square root of
Page 15 and 16: Here, SSE(F )isthe error sum of squ
Page 17 and 18: concatenated runs, this is not the
Page 19: This equation relates the output y
Page 22 and 23: value is pnum = 1 (corresponding to
Page 24 and 25: model parameters, and P columns, ea
Page 26 and 27: Program 3dDeconvolve Command Line f
Page 28 and 29: f(t) = f 0 0 1 1 1 0 1 1 0 0 1 0 1
Page 30 and 31: If we model the measured response b
Page 34 and 35: Full Model:MSE = 0.9618R^2 = 0.9835
Page 36 and 37: that are not of inherent interest,
Page 40 and 41: Now, model the measured data as a c
Page 42 and 43: -stim label 1 Random -stim label 2
Page 44 and 45: Note: This example is for illustrat
Page 46 and 47: The output is the same as for Examp
Page 48 and 49: After program 3dDeconvolve has nish
Page 52 and 53: Program:3dDeconvolveAuthor:B. Dougl
Page 54 and 55: cat y.1D y.1D > ycat.1DBe sure to r
Page 56 and 57: Recall that in Example 1.4.4.6, we
Page 58 and 59: and the noisy measurement data:wp(t
Page 60 and 61: The model that we will use for the
Page 62 and 63: Program 3dConvolve Command Line for
Page 64 and 65: 2 Program plug deconvolve2.1 Purpos
Page 66 and 67: voxels indicated by the crosshairs,
Page 68 and 69: Deconvolution Plugin Screen Output
Page 70 and 71: The following Random Permutation an
Page 72 and 73: Shuffled array:0 5 6 1 3 5 0 2 1 1
Page 74 and 75: Program RSFgen Command Line for Exa
Page 76 and 77: Example 3.3.3.1 Initial Random Bloc
Page 78 and 79: Compare the output for this example
Page 80 and 81: Markov chain time series:0 0 1 5 0
Page 82 and 83:
(X'X) inverse matrix::065 ;:000 ;:0
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Program 3dDeconvolve Screen Output
Page 86 and 87:
then the standard deviation for the
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4 Program 3dConvolve4.1 PurposeAs t
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-input1DThe -input1D command specie
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-stim minlag k m-stim maxlag k n-st
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parameters b 0 and b 1 , and impuls
Page 96 and 97:
Program 3dConvolve Command Line for
Page 98 and 99:
Example 4.4.6 Single Stimulus No No
Page 100:
5 References[1 ]F.Stremler, Fourier
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