By using spline polynomials with free nodal points, the propagation of a flame front and its velocity in a long pipe is reconstructed from incomplete and only relative data produced by optical sensors. The proposed method of reconstruction is illustrated by processing of results obtained for a stoichiometric hydrogen-air mixture (1 bar, ambient temperature) ignited by a single hot wire in a smooth-walled detonation tube (diameter D = 110 mm; length 21 m). The optimum nodal points of the splines (15D, 85D and 100D) divide the piping into four physically different parts. A stationary detonation velocity 2028 ± 7 m s −1 from position 100D and a maximum velocity about 2590 m s −1 at 85D are observed. (A neglect of the predetonation excess velocity provides only a misleading mean detonation speed 2098 ± 9 m s −1 from 67D.) Using the theory of experimental design, the minimum number (11) and optimum positions of monitoring sensors within the characteristic regions of the whole pipe are calculated. With respect to the complexity of the deflagration-to-detonation transition, also the optimum distribution of 16 sensors is discussed.