An accurate knowledge of the sound field distribution inside a room is required to identify and optimally locate corrective measures for room acoustics. However, the spatial recovery of the sound field would result in an impractically high number of microphones in the room. Fortunately, at low frequencies, the possibility to rely on a sparse description of sound fields can help reduce the total number of measurement points without affecting the accuracy of the reconstruction. In this paper, the use of Greedy algorithm and Global curve-fitting techniques are proposed, in order to first recover the modal parameters of the room, and then to reconstruct the entire enclosed sound field at low frequencies, using a reasonably low set of measurements. First, numerical investigations are conducted on a non-rectangular room configuration, with different acoustic properties, in order to analyze various aspects of the reconstruction frameworks such as accuracy and robustness. The model is then validated with an experimental study in an actual reverberation chamber. The study yields promising results in which the enclosed sound field can be faithfully reconstructed using a practically feasible number of microphones, even in complex-shaped and damped rooms.