Compressive Sensing (CS) has proved to be an effective theory in the field of image acquisition. However, in order to distinguish the difference between the measurement matrices, the CS imaging system needs to have a higher signal sampling accuracy. At the same time, affected by the noise of the light path and the circuit, the measurements finally obtained are noisy, which directly affects the imaging quality. We propose a dual-optical imaging system that uses the bidirectional reflection characteristics of digital micromirror devices (DMD) to simultaneously acquire CS measurements and images under the same viewing angle. Since deep neural networks have powerful modeling capabilities, we trained the filter network and the reconstruction network separately. The filter network is used to filter the noise in the measurements, and the reconstruction network is used to reconstruct the CS image. Experiments have proved that the method we proposed can filter the noise in the sampling process of the CS system, and can significantly improve the quality of image reconstruction under a variety of algorithms.