Large amount of data is one of the most obvious features in satellite based remote sensing systems, which is also a burden for data processing and transmission. The theory of compressive sensing(CS) has been proposed for almost a decade, and massive experiments show that CS has favorable performance in data compression and recovery, so we apply CS theory to remote sensing images acquisition. In CS, the construction of classical sensing matrix for all sparse signals has to satisfy the Restricted Isometry Property (RIP) strictly, which limits applying CS in practical in image compression. While for remote sensing images, we know some inherent characteristics such as non-negative, smoothness and etc.. Therefore, the goal of this paper is to present a novel measurement matrix that breaks RIP. The new sensing matrix consists of two parts: the standard Nyquist sampling matrix for thumbnails and the conventional CS sampling matrix. Since most of sun-synchronous based satellites fly around the earth 90 minutes and the revisit cycle is also short, lots of previously captured remote sensing images of the same place are available in advance. This drives us to reconstruct remote sensing images through a deep learning approach with those measurements from the new framework. Therefore, we propose a novel deep convolutional neural network (CNN) architecture which takes in undersampsing measurements as input and outputs an intermediate reconstruction image. It is well known that the training procedure to the network costs long time, luckily, the training step can be done only once, which makes the approach attractive for a host of sparse recovery problems.