Traditional detectors for spectrum sensing in cognitive radio networks always become disabled when noise uncertainty is severe. Shannon entropy-based detection methods have aroused widespread attention in recent years due to the characteristics of effective anti-noise uncertainty. However, in existing entropy-based sensing schemes, the uniform quantization method cannot guarantee the maximum entropy distribution when primary users do not exist, and cannot effectively distinguish between two hypotheses, which severely limits the promotion of detection performance. Moreover, the Shannon entropy-based sensing schemes are prone to misconvergence occurring when estimating entropy values, thus causing failure detection, which leads to system detection inefficiency and resource waste. These are the two major serious defects in Shannon entropy-based detectors, which restrict the performance improvement. In this paper, a novel non-uniform quantized exponential entropy-based (NQEE) detector is proposed for local sensing to deal with the problems of maximum entropy distribution and detection failure. To further improve the reliability of the detection, a collaborative spectrum sensing algorithm based on an NQEE detector with multiple fusion rules is presented. Simulation results verify that the detection performance of the improved local entropy-based detector is superior to the existing Shannon entropy-based detectors and is proved to be robust to noise power uncertainty. In addition, the novel collaborative detection algorithm outperforms the traditional collaborative spectrum detection method to a great degree.