The Internet of Underwater Things (IoUT) is a typical energy-limited and bandwidth-limited system where the technical bottleneck is the asymmetry between the massive demand for information access and the limited communication bandwidth. Therefore, storing and transmitting high-quality underwater images is a challenging task. The data measured by cameras need to be effectively compressed before transmission to reduce storage and reconstruc-ted with minor errors, which is the best solution. Compressed sensing (CS) theory breaks through the Nyquist sampling theorem and has been widely used to reconstruct sparse signals accurately. For adaptive sampling underwater images and improving the reconstruction performance, we propose the ESPC-BCS-Net by combining the advantages of CS and Deep Learning. The ESPC-BCS-Net consists of three parts: Sampling-Net, ESPC-Net, and BCS-Net. The parameters (e.g. sampling matrix, sparse transforms, shrinkage thresholds, etc.) in ESPC-BCS-Net are learned end-to-end rather than hand-crafted. The Sampling-Net achieves adaptive sampling by replacing the sampling matrix with a convolutional layer. The ESPC-Net implements image upsampling, while the BCS-Net is used to image reconstruction. The efficient sub-pixel layer of ESPC-Net effectively avoids blocking artifacts. The visual and quantitative evaluation of the experimental results shows that the underwater image reconstruction still performs well when the CS ratio is 0.1 and the PSNR of the reconstructed underwater images is above 29.