Activation detection in functional MRI using subspace modeling and maximumlikelihood estimation

A statistical method for detecting activated pixels in functional MRI (fMRI ) data is presented. In this method, the fMRI time series measured at each pixel is modeled as the sum of a response signal which arises due to the ex perimentally controlled activation-baseline pattern, a nuisance component r epresenting effects of no interest, and Gaussian white noise. For periodic activation-baseline patterns, the response signal is modeled by a truncated Fourier series with a known fundamental frequency but unknown Fourier coef ficients. The nuisance subspace is assumed to be unknown. A maximum likelih ood estimate is derived for the component of the nuisance subspace which is orthogonal to the response signal subspace, An estimate for the order of t he nuisance subspace is obtained from an information theoretic criterion. A statistical test is derived and shown to be the uniformly most powerful (U MP) test invariant to a group of transformations which are natural to the h ypothesis testing problem. The maximal invariant statistic used in this tes t has an F distribution. The theoretical F distribution under the null hypo thesis strongly concurred with the experimental frequency distribution obta ined by performing null experiments in which the subjects did not perform a ny activation task. Application of the theory to motor activation and visua l stimulation fMRI studies is presented.