  This paper considers the problem of detecting the support (sparsity pattern)
of a sparse vector from random noisy measurements. Conditional power of a
component of the sparse vector is defined as the energy conditioned on the
component being nonzero. Analysis of a simplified version of orthogonal
matching pursuit (OMP) called sequential OMP (SequOMP) demonstrates the
importance of knowledge of the rankings of conditional powers. When the simple
SequOMP algorithm is applied to components in nonincreasing order of
conditional power, the detrimental effect of dynamic range on thresholding
performance is eliminated. Furthermore, under the most favorable conditional
powers, the performance of SequOMP approaches maximum likelihood performance at
high signal-to-noise ratio.
