A compressed sensing integrate-and-fire neuron concept for massively parallel recordings is presented which expands the fundamental idea of superimposing timely sparse signals for data compression to any kind of continuous-time signals. Merging compressed sensing and amplitude-to-spike conversion, the proposed approach increases the information density and reduces the channel load. Combining multiple data-compressive neurons as a sensing array, further compression can be achieved when the spikes from different recording sites are superimposed on a single transmission channel. Signal reconstruction quality and transmission channel load are investigated to provide a strategy for selecting the design parameters of the proposed system. A proof-of-concept is presented, where a load per recording channel of 1 % under a relative reconstruction error of 0.32 % (SNR = 25 dB) is achieved.