Minimax nonparametric testing in a problem related to the Radon   transform
  We consider the detection problem of a two-dimensional function from noisy observations of its integrals over lines. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, the derived tests are non-adaptive. We also construct a minimax rate-optimal adaptive test of rather simple structure. 
Yuri I. Ingster, Theofanis Sapatinas, Irina A. Suslina
math.ST stat.TH