  We pose the problem of the optimal approximation of a given nonnegative
signal $y_t$ with the scalar autoconvolution $(x*x)_t$ of a nonnegative signal
$x_t$, where $x_t$ and $y_t$ are signals of equal length. The
$\mathcal{I}$-divergence has been adopted as optimality criterion, being well
suited to incorporate nonnegativity constraints. To find a minimizer we derive
an iterative descent algorithm of the alternating minimization type. The
algorithm is based on the lifting of the original problem to a larger space, a
relaxation technique developed by Csisz\'ar and Tusn\'ady in [Statistics \&
Decisions (S1) (1984), 205--237] which, in the present context, requires the
solution of a hard partial minimization problem. We study the asymptotic
behavior of the algorithm exploiting the optimality properties of the partial
minimization problems and prove, among other results, that its limit points are
Kuhn-Tucker points of the original minimization problem. Numerical experiments
illustrate the results.
