The innovative concept of Compressed Sensing (CS) presents a breakthrough that enables the acquisition of sparse signals at much lower sampling rates compared to the conventional Nyquist rate. The scope of CS is not limited only to sparse signal but it is also applicable to compressible signals, such as multimedia signals including audio signals. Representing the random samples from CS process using finite-precision is a crucial problem in communication systems. In this paper, we focus on 1-bit quantized CS. We propose to take into account the perceptual CS model for audio compression, where the perceptual properties are taken into account. We propose two models, the first applies perceptual effect at the transmitter side. In the other model, a modified Binary Iterative Hard Thresholding (BIHT) is proposed to improve the performance of 1-bit compressed sensing by taking the perceptual properties of the received audio signal into account. The Mean Opinion Score (MOS) is used to compare the perceptual quality of the received signal for the proposed 1-bit perceptual CS algorithms. Simulation results show that a better performance is achieved using the proposed algorithms.