7.2. Deconvolution Analysis of FMRI Time Series Data

These are notes by B. Douglas Ward, written in the Good Ol’ Days, and subsequently updated by Gang Chen.

7.2.1. Abstract

Program 3dDeconvolve was developed to provide deconvolution analysis of FMRI time series data. This has two primary applications: (1) estimation of the system impulse response function, and (2) multiple linear regression analysis of time series data. Given the input stimulus function(s), and the measured FMRI signal data, program 3dDeconvolve first estimates the impulse response time series to yield the estimated response. Various statistics are calculated to indicate the “goodness” of the fit.

The capability of fitting multiple stimulus (or reference) waveforms differentiates program 3dDeconvolve from the cross-correlation analysis programs (such as AFNI’s fim and 3dfim). Another way that program 3dDeconvolve differs from the cross-correlation analysis programs is in the model for the output waveform. The cross-correlation programs model the system response as a scaled version of a fixed waveform (such as a square wave or a sine wave). Program 3dDeconvolve uses a sum of scaled and time-delayed versions of the stimulus time series. The data itself determines (within limits) teh functional form of the estimated response. In fact, the shape of the fitted waveform can vary from voxel to voxel. Program 3dDeconvolve is described in Section 1.

Program RSFgen is a simple program for generating random stimulus functions. This capability may be useful for experimental design, and the evaluation fo experimental designs. This program is described in Section 3.

The program 3dConvolve, as the name implies, performs the inverse operation of program 3dDeconvolve. That is, program 3dConvolve convolves the input stimulus functions with the given system impulse response functions, in order to predict the output measured response. This program is described in Section 4.

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7.2.2. ... Full Enlightenment

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