Controlling False Discovery Rate in Signal Space for Transformation-Invariant Thresholding of… – Europe PMC Article – Europe PMC

Either your web browser doesn't support Javascript or it is currently turned off. In the latter case, please turn on Javascript support in your web browser and reload this page. where q is the user specified FDR level, p(k) is the k-th smallest voxel p-value, and N is the number of voxels. This step-up procedure is able to handle positive dependence among tests, as Benjamini and Yekutieli discussed in [4]. For more general dependence among tests, please refer to [4]. If an image is spatially transformed, some voxels will expand and some will shrink, so does the volumetric measure of the positive and false positive regions. The weighted FDR provides us a way to exploit the signal space volumetric measure for transformation invariance. The normalized residual image u = f(x) (where x is a point and u is a normalized residual vector) defines a mapping from to (where D is the image’s dimension). Instead of defining |Rpos| and |Rtru| in , we define them in the unit space: where R stands for either Rpos or Rtru, and J(x) is the Jacobian matrix of the mapping at x. For voxel-based FDR implementation, we can assign each voxel i a weight wi=J⊤J and then apply the weighted step-up procedure (2). For the calculation of J(x), instead of directly taking linear difference between a center u and its neighboring voxel value u†, we first map u† to u’s tangent plane: Source.

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