Detection over multiresolution analysis subspaces

The binary detection problem of a known signal in Gaussian noise is transposed to multiple problems of detecting the signal's projection to Multiresolution subspaces. We observe that subspaces exist where detectability of the projected signal in projected noise is significantly higher than the detectability of the original signal. This leads to a divide-and-conquer approach that uses optimal detection methods in a numerically economic and stable fashion. The required eigenvalue decompositions, now translated to subspaces, pose new challenges to enable the computations in the children subspaces to be used to reduce the computational load in the parent subspaces. We develop the theoretical relationships of eigenvalue decompositions over subspaces and show empirically how Receiver Operating Characteristic (ROC) change over subspaces. We verify results using various test signals and simulated and real noise data.