In the study of compressed sensing (CS), the two main challenges are the design of sampling matrix and the development of reconstruction method. On the one hand, the usually used random sampling matrices (e.g. GRM) are signal independent, which ignore the characteristics of the signal. On the other hand, the state-of-the-art image CS methods (e.g. GSR and MH) achieve quite good performance, however with much higher computational complexity. To deal with the two challenges, we propose an image CS framework using convolutional neural network (dubbed CSNet) that includes a sampling network and a reconstruction network, which are optimized jointly. The sampling network adaptively learns the sampling matrix from the training images, which makes the CS measurements retain more image structural information for better reconstruction. Specifically, three types of sampling matrices are learned, i.e. floating-point matrix, {0,1}-binary matrix, and {-1,+1}-bipolar matrix. The last two matrices are specially designed for easy storage and hardware implementation. The reconstruction network, which contains a linear initial reconstruction network and a non-linear deep reconstruction network, learns an end-to-end mapping between the CS measurements and the reconstructed images. Experimental results demonstrate that CSNet offers state-of-the-art reconstruction quality, while achieving fast running speed. In addition, CSNet with {0,1}-binary matrix, and {-1,+1}-bipolar matrix gets comparable performance with the existing deep learning based CS methods, and outperforms the traditional CS methods. What’s more, the experimental results further suggest that the learned sampling matrices can improve the traditional image CS reconstruction methods significantly.

Deep learning, e.g., convolutional neural networks (CNNs), has achieved great success in image processing and computer vision especially in high-level vision applications, such as recognition and understanding. However, it is rarely used to solve low-level vision problems such as image compression studied in this paper. Here, we move forward a step and propose a novel compression framework based on CNNs. To achieve high-quality image compression at low bit rates, two CNNs are seamlessly integrated into an end-to-end compression framework. The first CNN, named compact convolutional neural network (ComCNN), learns an optimal compact representation from an input image, which preserves the structural information and is then encoded using an image codec (e.g., JPEG, JPEG2000, or BPG). The second CNN, named reconstruction convolutional neural network (RecCNN), is used to reconstruct the decoded image with high quality in the decoding end. To make two CNNs effectively collaborate, we develop a unified end-to-end learning algorithm to simultaneously learn ComCNN and RecCNN, which facilitates the accurate reconstruction of the decoded image using RecCNN. Such a design also makes the proposed compression framework compatible with existing image coding standards. Experimental results validate that the proposed compression framework greatly outperforms several compression frameworks that use existing image coding standards with the state-of-the-art deblocking or denoising post-processing methods.