  This paper aims at achieving a "good" estimator for the gradient of a
function on a high-dimensional space. Often such functions are not sensitive in
all coordinates and the gradient of the function is almost sparse. We propose a
method for gradient estimation that combines ideas from Spall's Simultaneous
Perturbation Stochastic Approximation with compressive sensing. The aim is to
obtain "good" estimator without too many function evaluations. Application to
estimating gradient outer product matrix as well as standard optimization
problems are illustrated via simulations.
