Research On Image Compressed Sensing In Fractional Fourier Domain

With the rapid development of society, people’s requirement in information transmission rate is kept increasing. As signal bandwidth gets wider, signal processing framework requires higher sampling rate and higher signal processing speed. And how to handle the wideband signal is an urgent problem. Candes, Donoho, and Tao founded the non-Nyquist signal sampling and processing system—compressed sensing (CS) theory attempts to solve the above problems. The theory caused great concern of the signal processing community.As a generalization of the traditional Fourier transform(FT), the fractional Fourier transform (FrFT) which adds a degree of freedom paramete-rotation angle and retains all the features of the classical Fourier and novel advantages moreover, can describes the time domain and frequence domain information of the signal at the same time. It is very propitious for processing of the non-stationary signals and widely used in scientific research and engineering in all aspects.This paper use image processing as the entry point, combines compressed sensing theory with fractional Fourier transform to exert their advantages. Made a preliminary exploration in the field of image reconstruction and facial expression recognition. The main research work are as follows:1. First expounded the development process, theoretical framework and theoretical significance of compressed sensing theory, summarize the direction of the latest applications. Describes the definition, nature and discrete algorithm of fractional Fourier transform. Focus on the nature of the image in the fractional Fourier domain. Discusses the feasibility of the program.2. A image sub-frequency compressed sensing algorithm based on fractional Fourier transform is proposed. Smooth low frequency accounted for the vast majority of a natural image. So overall transformation of the image with a single order is difficult to play the advantages of fractional Fourier transform. This new algorithm uses the wavelet transform to separated different frequency components of image and different frequencies corresponding to the optimal transform order, which embodies the advantages of fractional Fourier transform. The experiments show that the algorithm is effective.3. A novel expression recognition method via SRC in Fractional Fourier Domain is proposed. In particular, the human expression recognition task is fitted into the SRC framework. Due to the FRFT and the excellent theory of SRC, the proposed algorithm gives better results when comparing with the state-of-art SRC human expression recognition method. Experiments conducted on publicly human expression database verify the accuracy and efficiency of our algorithm.