Estimation of semi-sparse radar range profiles

We study the use of semi-sparse models, i.e., models having a few coefficients that are significantly larger than the rest, for estimation of range profiles in radar and other active sensing applications. The estimation of such range profiles is equivalent to estimation of a vector of regression coefficients in an underdetermined linear system. Each coefficient corresponds to a certain range bin in the illuminated area. If a range bin contains a target the reflections from that bin will, in some applications, result in a value of the corresponding coefficient which is significantly larger than the value corresponding to a target-free range bin. Under the assumption of a mixture of semi-sparse linear Gaussian models, we derive the minimum mean square error (MMSE) estimate of the range profile. We then find computationally efficient approximations of this MMSE estimate. As a by-product we also obtain a maximum a posteriori (MAP) target detector that does not require the choice of any detection threshold. The performances of our methods are illustrated via numerical examples.