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In this paper, two robust perception-based haptic data reduction and transmission techniques are presented to reduce data traffic in telehaptic systems. A prediction approach that relies on the least-squares method and median filtering is exploited in order to reduce the number of packets transmitted, and efficiently reconstruct unsuccessfully received data samples. Knowledge from human haptic perception is also used and incorporated into the general data reduction architecture. The techniques are initially evaluated in a basic experimental setting in order to validate their performance. Their application in a haptic-enabled telementoring surgery simulation is also demonstrated. The experimental results prove the proposed approach's effectiveness as haptic data packets can be reduced by as much as 96% in normal network conditions and up to 93% in the presence of significant communication delay and packet loss, while preserving the overall quality of the telehaptic environment.