A method for reconstructing a pressure field at the surface of a radiating body or source is presented using recording data of a microphone array. The radiation is assumed to consist of many spherical radiators, as microphone positions are present in the array. These monopoles are weighted using a parameter α, which broadens or narrows the overall radiation directivity as an effective and highly intuitive parameter of the radiation characteristics. A radiation matrix is built out of these weighted monopole radiators, and for different assumed values of α, a linear equation solver reconstructs the pressure field at the body’s surface. It appears that from these many arbitrary reconstructions, the correct one minimizes the reconstruction energy. The method is tested, localizing the radiation points of a Balinese suling flute, reconstructing complex radiation from a duff frame drum, and determining the radiation directivity for the first seven modes of an Usbek tambourine. Stability in terms of measurement noise is demonstrated for the plain method, and additional highly effective algorithm is added for a noise level up to 0 dB. The stability of α in terms of minimal reconstruction energy is shown over the whole range of possible values for α. Additionally, the treatment of unwanted room reflections is discussed, still leading to satisfactory results in many cases.