Fractal compressed sensing imaging with sparse difference based on fractal and entropy recognition

Abstract

Compressed sensing (CS) is a topic of great interest in many research fields, especially image processing. However, in the traditional CS framework, one disadvantage is that the computational cost of sparse representation (SR) is too high to meet basic application requirements. Another is that l₁-norm minimisation, as the object function of CS recovery, is unsuitable for the approximation of image details. Therefore, this paper presents a novel fractal CS (FCS) framework for digital imaging. The FCS framework is basically as follows: first, the sparse difference (SD) is used to solve the hard problem of sparse representation; then, acquisition of SD is based on the results of classification under a combined fractal and entropy feature space; finally, fractal minimisation is used instead of l₁-norm minimisation as the object function to realise high-quality CS recovery of image details. Several experiments show the feasibility and dependability of the FCS imaging framework.

Keywords:

• Compressed sensing
• Image processing
• Sparse representation
• l₁-normminimisation
• Fractal
• Entropy

Acknowledgements

This work was supported by the China National Natural Science Funds (Grant Nos. 61302156, 61401220 and 61471206), the Provincial Natural Science Foundation of Science and Technology Bureau of Jiangsu Province (Grant Nos. BK20140884 and BK20141428), the University Natural Science Research Project of Jiangsu province (Grant Nos. 13KJB510021 and 14KJB510022), and the Scientific Research Foundation of Nanjing University of Posts and Telecommunications (Grant No. NY213109).