We investigate the ultraslow structural relaxation of ageing foams with rheologically-tunable continuous phases. We probe the bubble dynamics associated with pressure-driven foam coarsening using differential dynamic microscopy, which allows characterizing the sample dynamics in the reciprocal space with imaging experiments. Similar to other out-of-equilibrium jammed soft systems, these foams exhibit compressed exponential relaxations, with a ballistic-like linear dependency of the relaxation rate on the scattering wavevector. By tuning the rheology of the continuous phase we observe changes in the relaxation shape, where stiffer matrices yield larger compressing exponents. Our results corroborate recent real-space observations obtained with bubble tracking, providing a comprehensive overview of structural relaxation in these complex systems, both in direct and reciprocal space.