  We study the performance of estimators of a sparse nonrandom vector based on
an observation which is linearly transformed and corrupted by additive white
Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive
a new lower bound on the estimator variance for a given differentiable bias
function (including the unbiased case) and an almost arbitrary transformation
matrix (including the underdetermined case considered in compressed sensing
theory). For the special case of a sparse vector corrupted by white Gaussian
noise-i.e., without a linear transformation-and unbiased estimation, our lower
bound improves on previously proposed bounds.
