Multidimensional signal detection in the presence of correlated noise with application to brain imaging

When testing for the presence and location of a signal in a 2D or 3D image, standard hypothesis testing methods that control the False Discovery Rate (FDR) exhibit low power and poor interpretability in the presence of correlated noise. This problem is complicated by the multiple comparisons problem for very large images. This is the setting when testing for the presence of a signal in Functional Magnetic Resonance Imaging (fMRI) experimental data. One strategy for avoiding many of the problems associated with correlated noise is to perform analyses in the wavelet domain. Several powerful wavelet-based methods have been developed for fMRI analysis taking advantage of the decorrelating property of the wavelet transformation. The power and FDR control of these methods can be further improved in several ways.;Wavelet coefficient estimation assuming a sparse signal provides an effective shrinkage step in the wavelet denoising algorithm. Extension of current wavelet-based methods to a full 3D wavelet analysis avoids potential inconsistencies among slice-by-slice 2D wavelet analyses. The sparse signal assumption and the use of 3D wavelets are demonstrated to provide better results than previous methods that assume a dense underlying signal and use 2D wavelets. Furthermore, it is shown that the widely used dependence assumption between a wavelet coefficient and its "parent" is unnecessary in the current research. Spatial inference on wavelet-denoised data sets is improved by estimating the spatial regression function and performing voxel-wise nonparametric tests for significance. Simulation studies are used to evaluate the proposed methods and compare them to existing methodology.