Research Of Image Reconstruction And Applications To Digital Watermarking Based On Compressed Sensing Theory

With the development of information technology, the demand for information is increasing dramatically. The conventional Nyquist sampling theory requires that sampling rate can’t be lower than two times the maximum frequency of singal, which put forward higher requirements to the system’s processing capacity and posed a great challenge to the design of the hardware devices. Therefore, the search for a new signal acquisition and data processing method is known as an inevitable. Compressed Sensing, which indicates that the sparsity prior of the signals or images can accurately reconstruct original signals or images from a small quantity of measurements, becomes a new research direction in the field of digital signal processing, medical imaging, pattern recognition, optical and radar imaging. The paper mainly researches on image reconstruction and application on digital watermarking.SAMP algorithm is one of the matching pursuit algorithms. It can restrict signal accurately when signal sparsity is unknown. This paper made improvements for SAMP algorithms against to the enough and over-estimated the accuracy of fixed step size. Experiments show good performances and faster reconstruction speed.In connection with the characteristic of wavelet tree structure and advantages of dual tree complex wavelet(DTCWT), such as shift invariance, directional selectivity and a lower computational complexity, the paper proposes an algorithm that one can reconstruct images based on CS and layer DTCWT transform, which use the sparse prior in the dual tree complex wavelet domain. The experiment results show the validity of the algorithm.In this paper, by making full use of the characteristics of CS, we complemented digital watermarking process in CS domain. The measurement matrix for CS acts as the key for extraction of watermark. Since there are a lot of methods for constructing a measurement matrix and the size of matrix is warious, it is difficult to extract the watermark from the given image without the key. Simulation results show that the proposed method is robust to most of attacks.