Research On Image Reconstruction Algorithms Based On Compressed Sensing

The traditional Nyquist sampling theory states that, the sampling frequency must be at least twice of the highest frequency of signal, so that after sampling, the digital signal could retain the whole information of the original signal. However, in many case, the sampling frequency can’t reach twice the highest frequency of the signal. With the rapid development of the modern science and technology, recently Donoho and Candès have proposed a new theory, called Compressed Sensing, short for CS. CS theory has broken through the limit of the Nyquist sampling theory, which performs compressed processing while signal sampling. CS theory applies the sparsity prior of the signals or images and reconstruct the original signals or images accurately by few measurements via an appropriate recovery algorithms. We research the application of compressed sensing to image reconstruction and propose some improvement of these existing recovery algorithms, major research of this paper are as follows:Those traditional compressed sensing reconstruction algorithms are all based on the whole image, which leads to the mass waste of storage space in the process of sampling and the slow speed of the reconstruction. Focusing on these problems, we research the block compressed sensing. Moreover, we research the Contourlet transform, which performs well on detail and contour. Then we put forward a improved Contourlet transform, and apply smooth projected Landweber iteration algorithm go with different sparse transforms to image reconstruction. The experimental results show that this proposed algorithm improve the quality of image construction effectively compared with other sparse transforms, especially in the aspect of detail processing.At present, most reconstruction algorithms are based on single sparse representation, so we research dual tree complex wavelet transform and Contourlet transform and propose an algorithm based on the sparse representation of image on dual tree complex wavelet transform and Contourlet transform, then we apply linearized Bregman iteration to the image reconstruction process. What’s more, this algorithm regulates the total variation and soft thresholding after every iteration. The experimental results express that image reconstructed by this algorithm is of high quality compared with the algorithm based on single sparse transform.Lastly, we research the total variation. Total variation method is of good robustness, and reconstruct image accurately. However, TV method reconstructs the image slowly. Considering those problem, we propose an image reconstruction algorithm which is based on total variation and block compressed sensing. Cause this algorithm will bring strong blocking artifacts, we put forward an improvement method of gradient calculation process that based on the whole image, this method takes advantage of the boundary pixel information of the reconstructed blocks which can eliminate the block artifacts effectively. The results of experiment show that this algorithm can improve the quality of image reconstruction and save the time of reconstruction process. The algorithm that we proposed is especially suitable for low sampling rate.