In this work, the growth regime of combustion instability was studied by analyzing 10 kHz OH planar laser-induced fluorescence (PLIF) images through a combination of dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD) methods. Combustion instabilities were induced in a mesoscale burner array through an external speaker at an imposed perturbation frequency of 210 Hz. During the transient growth phase of combustion instability, 10 kHz OH PLIF imaging was employed to capture spatially and temporally resolved flame dynamics. Increased acoustic perturbations prevented flame reignition in the central recirculation zone and eventually led to the flame being extinguished inward from the outer burner array elements. Coherent modes and their growth rates were obtained from DMD spectral analyses of high-speed OH PLIF images. Positive growth rates were observed at the forcing frequency during the growth regime. Coherent structures, closely associated with thermoacoustic instability, were extracted using an appropriate SPOD filter operation to identify mode structures that correlate to physical phenomena such as shear layer instability and flame response to longitudinal acoustic forcing. Overall, a combination of DMD and SPOD was shown to be effective at analyzing the onset and propagation of combustion instabilities, particularly under transient burner operations.