  We consider minimax signal detection in the sequence model. Working with
certain ellipsoids in the space of square-summable sequences of real numbers,
with a ball of positive radius removed, we obtain upper and lower bounds for
the minimax separation radius in the non-asymptotic framework, i.e., for a
fixed value of the involved noise level. We use very weak assumptions on the
noise (i.e., fourth moments are assumed to be uniformly bounded). In
particular, we do not use any kind of Gaussianity or independence assumption on
the noise. It is shown that the established minimax separation rates are not
faster than the ones obtained in the classical sequence model (i.e.,
independent standard Gaussian noise) but, surprisingly, are of the same order
as the minimax estimation rates in the classical setting. Under an additional
condition on the noise, the classical minimax separation rates are also
retrieved in benchmark well-posed and ill-posed inverse problems.
