Previously, we proposed a method to achieve high-precision measurement systems to record 3D sound-space information. This enables the transmission of spatial sound to distant places, and enables its preservation. Our method, named Symmetrical object with ENchased ZIllion microphones (SENZI), was implemented using a spherical microphone array with 252 microphones. It was applied to the recording of 3D sound-space information. The microphone positions follow an icosahedral pattern. Reproducing a 3D sound space recorded with the SENZI implementation requires transmission of all the microphone signals. However, the necessarily large number of channels produce vast amounts of data. Therefore, it is important to compress these data without markedly reducing the accuracy of the reproduced 3D sound-space. In this paper, we propose a multi-channel sound signal compression technique for recordings done with a SENZI microphone array. Inter-channel correlation in the SENZI system is extremely high because the microphones are arranged densely on the sphere. Our proposed method exploits this correlation to predict some microphone signals from those recorded by microphones that are aligned with the vertices of the underlying icosahedron. The possibility of recovering some microphone signals from those of their neighbors is verified through computer simulations of a SENZI array.