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With the development of ubiquitous computing, many small, inexpensive, networked processing devices, such as wireless sensor and mobile terminal, have become more and more popular and performed a critical function in environmental protection, transportation, health and other fields. For example, in a wireless sensor network (Estrin, Govindan, Heidemann, & Kumar, 1999), sensor nodes usually function as an information collector to sense, capture, process and monitor a variety of monitoring information, and provide a wealth of detailed data. Nevertheless, since their computational capability and information processing capability are poor, and they are vulnerable to the problem of insufficient processing power. The contradictions are even worse for multimedia data, such as image.
How to cope with a huge amount of data when using resource-constrained devices becomes a primary issue for us to consider. Compressed sensing (CS) (Donoho, 2006) can sample the signal at a much lower sampling frequency than Nyquist theory. The CS sampling process of signal 
, is done by matrix multiplication, i.e. 
, where 
is a measurement matrix with the size of m x n and 
is the measurement vector and m<<n CS compresses data while sampling to reduce transmission bandwidth consumption and save energy, which provides a new idea for solving the problem of resource limitation of information acquisition device. On the other hand, CS can be regarded as a symmetric encryption system. When using CS for sample compression, protecting confidentiality can be achieved without additional cost or minimal cost. The application of CS can greatly improve the efficiency of sensor information collection and transmission. However, since the process of CS reconstruction is relatively complicated (Karmarkar, 1984), many related studies cannot be directly applied to the situation where the receiving end resource is limited.
Cloud is a hosting technology for computing, storing, processing and sharing data. Cloud has huge storage space and strong information processing capability. In order to store and manage large amounts of image data more efficiently, a good choice is to outsource the storage and processing of these data to cloud. In many cloud applications, the data that the user needs to use is not uploaded by the user himself, but is provided by the sampling end or other users, namely the data holder. In this case, the data in cloud will be uploaded by the data holder, and be downloaded and used by the legal user only.
By combining CS with cloud, CS is utilized to collect data while the storage and calculation of data are managed by the cloud. It can not only fully reflect the advantages of both compressed sensing and cloud, but also make up for the shortcomings of each other. And thus, the burden of data holder and user can be greatly reduced. However, since the cloud is an open platform, how to ensure the security of data uploaded to the cloud will be a crucial issue. At the same time, since digital products are particularly vulnerable to plagiarism and illegal copying during transmission and exchange, copyright protection is also desirable.