Implementing the combustion strategy of lean premixed (LPM), gas turbines can significantly reduce regulated emissions from the combustion process but are susceptible to thermoacoustic instabilities. With the use of time-resolved PLIF and dynamic pressure transducers, the coupling between the flame structure and pressure was used to characterize the instability. Without the porous insert, the pressure measurements revealed a strong dominate frequency at 340 Hz, which was identical to the oscillation frequency of the OH intensity at different locations are indicating a global instability. The pressure and OH* signal oscillation are coupled with a consistent phase shift. With the addition of the porous insert, the pressure oscillation amplitude was reduced by an order of magnitude with minor peaks observed in the OH spectra indicating a reduction in the thermoacoustic instability while removing the phase relationship previously seen. To verify the importance of the porous structure, a comparison between a solid and porous insert, having identical geometries, was tested. Two regions were produced, one where the inserts have near identical performance, driven by insert geometry, and a second where the porous insert mitigates an instability seen with the solid insert demonstrating the requirement of the porous structure. To verify the ability of a single porous design to be effective over a wide operating range, different thermoacoustic instability modes are produced by adjusting equivalence ratio. For multiple conditions where the porous exhibited external flamelet stabilization the insert is effective at mitigating the thermoacoustic instability, but when the flamelets subside into the insert a thermoacoustic instability was seen. With the requirement of external stabilization meet, distinct instability modes were eliminated thus giving evidence a single porous insert design mitigates thermoacoustic instabilities across a range of inlet conditions. Finally a potential relationship between expansion ratio and total SPL is investigated for a lean direct injection (LDI) system. With a combustor diameter of 50 mm, the LDI system demonstrates cyclic flame structures indicating its susceptibility of thermoacoustic instability. Further the dominating frequencies observed in dynamic pressure and OH* signal are identical signifying a coupling between the flame intensity and pressure oscillations.