On the Applications of the Special Class of Atomic Functions: Practical Aspects and Perspectives

Makarichev, Viktor; Brysina, Iryna

doi:10.1007/978-3-030-66717-7_4

Cited by 10 publications

(22 citation statements)

References 13 publications

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“…Generally, the problem is to develop such a transformation of an image matrix that provides its further efficient compression, protection, and representation, which is convenient for recognition. Different ways to apply atomic functions (1) are discussed in [ 47 ]. It was shown that atomic wavelets, constructed using

, are the most appropriate tool for discrete data processing, in particular, matrices.…”

Section: Formulation Of the Problem And An Approachmentioning

confidence: 99%

“…Discrete atomic transform (DAT), which is the wavelet transform based on atomic functions

, constitutes a core of the DAC algorithm. In [ 47 ], it was proved that DAT has linear time complexity, i.e.,

where N is the size of the data processed (in the case of matrix processing, N is a number of pixels). Moreover, it requires insignificant additional memory overhead.…”

Section: Formulation Of the Problem And An Approachmentioning

confidence: 99%

“…DAT is based on atomic wavelets that provide a decomposition of data given by an array into orthogonal components (see Figure 5 ). The number of orthogonal layers obtained is called a depth of transform [ 47 ]. Depending on how one-dimensional DAT is applied to blocks of a matrix, results of the different structures are obtained.…”

Section: Dac Based Solutionsmentioning

confidence: 99%

“…In the current paper, the possibility of solving this problem using atomic functions [ 46 , 47 ] is considered. Atomic functions were introduced in the early 1970s of the 20th century.…”

Section: Introductionmentioning

confidence: 99%

“…Atomic functions

have several useful features, which are important in the context of the problem stated above. Indeed, they have good approximation properties and provide fast data decomposition [ 46 , 47 ]. Their application to the development of image representation, which combines the features described, is promising.…”

Section: Introductionmentioning

confidence: 99%

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

Makarichev

Illiashenko

Kharchenko

2022

Sensors

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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.

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, are the most appropriate tool for discrete data processing, in particular, matrices.…”

Section: Formulation Of the Problem And An Approachmentioning

confidence: 99%

“…Discrete atomic transform (DAT), which is the wavelet transform based on atomic functions

, constitutes a core of the DAC algorithm. In [ 47 ], it was proved that DAT has linear time complexity, i.e.,

where N is the size of the data processed (in the case of matrix processing, N is a number of pixels). Moreover, it requires insignificant additional memory overhead.…”

Section: Formulation Of the Problem And An Approachmentioning

confidence: 99%

Section: Dac Based Solutionsmentioning

confidence: 99%

“…In the current paper, the possibility of solving this problem using atomic functions [ 46 , 47 ] is considered. Atomic functions were introduced in the early 1970s of the 20th century.…”

Section: Introductionmentioning

confidence: 99%

“…Atomic functions

Section: Introductionmentioning

confidence: 99%

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