Sparse representation of intricate natural image with multi-scale geometric dictionary
COMPUTER MODELLING & NEW TECHNOLOGIES 2014 18(12B) 623-628
1College of Electronic and Information Engineering, Yili Normal University, No.448,Jiefang West Road, Yining,China
2School of Electronic Science and Engineering, Nanjing University,No.163, Xianlin Dadao, Nanjing, China
Sparse representation of natural image is the fundamental problem of multi-scale geometric analysis, deep learning and K-SVD learning method. Traditional multi-scale geometric analysis is based on simple mathematical model which cannot express intricate natural images, and learning methods rely on prior knowledge. In this paper, a complex sparse representation mathematical model of natural images which have non-smooth area, non-smooth contours and intricate texture features is proposed. The model is established from the perspective of highly nonlinear approximation and according to the theories of wavelet, ridgelet, contourlet, and dictionaries such as wavelet dictionary and multi-scale ridgelet dictionary. The model can represent all natural images without any learning and priori knowledge. Simulation comparison experiments which established by a new multi-scale geometric dictionary show that this model greatly improves the sparse ratio and peak signal noise ratio and has the progressive optimal expression of intricate natural images.