Efficient absorbers are important to create a pleasant acoustic environment, or to meet certain technical specifications. Standard solutions make use of open-pore foams or thin resonating plates. The first option requires a thick layer to be efficient at low frequencies, reducing the available space. Plate absorbers, on the other hand, can be thin constructions, but they have a very narrow absorption band. Wideband high absorption levels at low frequencies can be achieved by careful design of the porosity and pore connectivity of a foam. If the matrix material is sufficiently rigid, the acoustic absorption can be predicted in two steps. First, a finite element model of a representative volume element (RVE) yields a set of non-acoustic parameters: flow resistivity, thermal and viscous length, tortuosity, and thermal permeability. In the second step, these values lead to equivalent homogenized fluid properties, as formalized in the Johnson-Champoux-Allard- Lafarge (JCAL) model. Gypsum foams are rigid, closed-cell materials with a narrow, controllable, pore size and wall thickness distribution. The inherent acoustic absorption is weak due to the closed cells. We investigated how a rectangular array of sub-millimeter perforations of the foam results in a high acoustic absorption coefficient. JCAL model predictions based on a Kelvin cell RVE are validated by impedance tube measurements for a variety of perforation diameters. The results show that a suitable combination of pore geometry and perforation pattern leads to a perfect absorption peak below 1 kHz for foam layers as thin as several centimeters. An optimal design of the perforated foams, e.g. using random perforation patterns or graded pore sizes, can lead to the engineering of a desired absorption curve.