Research On Image Recovery And Fusion Based On Compressed Sensing

In the rapid development of information technology era, the traditional Nyquist samplingtheory is unable to meet the demand for practical application. Recently Donoho and Candesetc. propose the new compressed sensing theory which points out that when the signal iscompressible or sparse in a transform domain, a few random projections contain the enoughinformation of the signal to be recovered. The signal finally can be reconstructed from theseprojections by solving an optimization problem at the high probability. This new theory has afeature of directly sampling information. The sampling rate, which is far lower than Nyquistsampling rate, depends on the information structure and content of the signal and can measureand code the signal. Applications that benefit from the new theory conclude image processing,radar and so on.This paper mainly brings the compressed sensing theory in the image recovery andfusion. The main contributions can be summarized as follows:(1) The modified subspace pursuit algorithm is proposed to recover the image. Thesubspace pursuit must have the prior knowledge of the sparsity, but in fact the sparsity ofimages is unknown. The proposed algorithm adaptively estimates the sparsity of signals,which estimates the sparsity at the given step factor in the iterative process. When thereconstruction error is less than the threshold, the new algorithm stops the iteration andrealizes the accurate recovery of sparse signals. The simulation results show that comparedwith other algorithms, the proposed algorithm has advantages of the computation time and theaccuracy of the reconstruction.(2) A new algorithm based on NSCT transform is proposed to fuse the images. Thewavelet transform multi-directionally mines the images so that it cann’t sparsely represent theimages very well. In this paper, the NSCT transform is chosen to sparsely represent the images and the new compressed sensing theory is introduced to measure the high-frequencycoefficients. Meanwhile the rules, maximizing the mean of adjacent grades and maximizingthe mean of absolute variance, are adopted to fuse the images by the high-frequencymeasurements and low-frequency coefficients respectively. Simulation results show thatcompared with other fusion algorithm, the proposed algorithm achieves a good effect of theimage fusion at the low rate of transmission and storage.