Study On Image Compressed Sensing Reconstruction Algorithms

Compressed sensing is a novel sampling theory. This theory shows that a small number of random projections of a compressible signal contain enough information for exact reconstruction. It has gained much attention in the past few years due to its promising practical potentials. As one of the crucial issues, the reconstruction algorithm plays a key role in the application of compressed sensing and affects its practical usage. Since the compressed sensing theory was presented, how to design a reconstruction algorithm with low complexity and high reconstruction accuracy to reconstruct signal, especially the large scale image signal, has been a hot study. Under this background, the dissertation has deeply studied the compressed sensing reconstruction algorithms for image in order to find robust and effective reconstruction algorithms. The main contributions and innovations of the dissertation are as follows.1. The traditional class of matching pursuit algorithm is deeply studied and its atom selection strategy is analyzed. As the orthogonal matching pursuit algorithm can not select the best atom in each iteration, an optimized orthogonal matching pursuit algorithm for compressed sensing reconstruction is proposed. The theory analysis of its atom selection strategy is presented. The validity of the proposed algorithm is proved by the experiments under different measurement matrixes.2. In order to improve the reconstruction accuracy and efficiency of the directional pursuit algorithm, a compressed sensing reconstruction algorithm based on spectral projected gradient pursuit is proposed. Directional pursuit frame is adopted by this algorithm. The update direction and step length are computed by spectral projected gradient method. Local optimum point is avoided by adopting the nonmonotone line search strategy. The balance between reconstruction accuracy and efficiency of the algorithm can be achieved by setting an appropriate threshold parameter. The experimental results show that this algorithm has better reconstruction accuracy and efficiency.3. Most existing compressed sensing reconstruction algorithms are based on single measurement vector. When processing image signal, the efficiency of these algorithms is low and the quality of the reconstructed image is not good enough, because the image is treated as one dimension signal. A reconstruction algorithm based on multiple measurement vectors and sparse Bayesian learning is proposed. By using the multiple measurement vectors model that suits image processing in compressed sensing, the image can be reconstructed quickly because the weighting coefficient matrix can be got directly by processing each column of the measurement matrix simultaneously. The sparse Bayesian learning algorithm guarantees the sparsity of the weighting coefficient matrix. The experimental results show that the proposed algorithm has better reconstruction accuracy and the efficiency is improved obviously.4. According to the existing multiscale compressed sensing scheme, only a few of wavelet coefficients are sampled and the others are set to zero, which results in the coarse edges of the reconstruction images and low reconstruction accuracy. In order to overcome this conundrum, an improved multiscale compressed sensing scheme which interpolates the image reconstructed by multiscale compressed sensing scheme with contourlet transform is proposed. The reconstruction accuracy of the new scheme is improved by estimating the unsampled wavelet coefficients and keeping the sampled unchanged. The experimental results show that the proposed scheme overcomes the mosaic effect and has better reconstruction accuracy than the existing scheme.