Surveillance with multiple cameras and microphones is promising to trace activities of suspicious persons for security purposes. When these sensors are connected to the Internet, they might also jeopardize innocent people's privacy because, as a result of human error, signals from sensors might allow eavesdropping by malicious persons. This paper presents a proposal for exploiting super-resolution to address this problem. Super-resolution is a signal processing technique by which a high-resolution version of a signal can be reproduced from a low-resolution version of the same signal source. Because of this property, an intelligible speech signal is reconstructed from multiple sensor signals, each of which is completely unintelligible because of its sufficiently low sampling rate. A method based on Bayesian linear regression is proposed in comparison with one based on maximum likelihood. Computer simulations using a simple sinusoidal input demonstrate that the methods restore the original signal from those which are actually measured. Moreover, results show that the method based on Bayesian linear regression is more robust than maximum likelihood under various microphone configurations in noisy environments and that this advantage is remarkable when the number of microphones enrolled in the process is as small as the minimum required. Finally, listening tests using speech signals confirmed that mean opinion score (MOS) of the reconstructed signal reach 3, while those of the original signal captured at each single microphone are almost 1.