Further Analyses

Because the algorithm constructs the indicator functions as orthogonal P-dimensional vectors, one can project the original data into this signal subspace spanned by the indicator functions. If we define the projection matrix  as
 

$$\mathbf{P}_{s}=\Phi \Phi ^{\mathrm{T}}$$

then the original data projected into the signal subspace is,
 

$$\mathbf{F}\mathbf{P}_{s}=\mathbf{F}\Phi \Phi ^{\mathrm{T}}=\mathbf{R}\Phi ^{\mathrm{T}}.$$

Therefore the KT x P matrix, , can be considered as the ``cleaned data'', after all noise contributions have been removed. At this point, one can apply any standard analysis procedures, like averaging among all images under each experimental condition, etc.