The propagation of quasi-detonations in porous media is depended on interaction of distinct ignition mechanisms being responsible for sustaining the supersonic combustion mode under filtration conditions [1-3]. These are in the broad sense the local shock adiabatic compression resulting in auto-ignitions of the mixture [4] and reaction of unburnt products at elevated thermodynamic conditions in surroundings of the burnt material, usually referred as turbulent mixing mechanism [5]. In the case of adiabatic compression, hot spots in porous media can be formed via single or multiple reflections of the leading shock front, shock wave diffractions resulting in focusing phenomena inside a porous matrix, and interactions of shock headed transient gas jets from the adjacent pores. From experimental and theoretical point of view it is interesting to elucidate the dominating ignition mechanisms of quasi-detonation at different velocity ranges. This work presents experimental studies of the relative influence of normal shock wave reflections on ignition and propagation of quasi-detonations near the limit. Quasi-detonation transmissions are also accompanied by the flow acceleration and formation of a leading shock wave, which is strongly coupled with a flame front. The interaction and propagation of transverse shock waves caused by individual hot jets across the random flow field downstream of a porous bed can create hot spots in a fresh mixture by means of shock wave focusing and diffraction on flow inhomogeneities. In addition, transverse waves enhance the mixing and deforms the turbulent interface between reacted and unreacted products, thus increasing local reaction rates. Both mechanisms can lead to the formation of localized explosions in unburnt materials, which are capable of sustaining the leading shock during its expansion into a large volume, and can significantly promote the transition or re-initiation of a detonation wave [6, 7]. The aim of these studies was to establish the critical conditions required for detonation re-initiations and elaborates the tools for their estimations.