Digital Image Representation by Atomic Functions: The Compression and Protection of Data for Edge Computing in IoT Systems

Digital images are used in various technological, financial, economic, and social processes. Huge datasets of high-resolution images require protected storage and low resource-intensive processing, especially when applying edge computing (EC) for designing Internet of Things (IoT) systems for industrial domains such as autonomous transport systems. For this reason, the problem of the development of image representation, which provides compression and protection features in combination with the ability to perform low complexity analysis, is relevant for EC-based systems. Security and privacy issues are important for image processing considering IoT and cloud architectures as well. To solve this problem, we propose to apply discrete atomic transform (DAT) that is based on a special class of atomic functions generalizing the well-known up-function of V.A. Rvachev. A lossless image compression algorithm based on DAT is developed, and its performance is studied for different structures of DAT. This algorithm, which combines low computational complexity, efficient lossless compression, and reliable protection features with convenient image representation, is the main contribution of the paper. It is shown that a sufficient reduction of memory expenses can be obtained. Additionally, a dependence of compression efficiency measured by compression ratio (CR) on the structure of DAT applied is investigated. It is established that the variation of DAT structure produces a minor variation of CR. A possibility to apply this feature to data protection and security assurance is grounded and discussed. In addition, a structure or file for storing the compressed and protected data is proposed, and its properties are considered. Multi-level structure for the application of atomic functions in image processing and protection for EC in IoT systems is suggested and analyzed.