Research On Compressive Sensing Reconstruction Algorithm Based On The Constraint Of Sparse Combination

The compressive sensing(CS)theory is an emerging theory in the field of image processing.It breaks the limitation of the sampling frequency indicated in the traditional Nyquist sampling law,and allows the image signal to be reconstructed accurately just from small amount of samples.The theory reduces the pressure of data transmission and storage greatly,and saves a lot of space and time resources at the same time,so it has great significance in the field of processing.The theory has attracted the attention of the majority of scholars since it was proposed,and it has also been rapidly developed and applied.The compressive sensing theory mainly includes sparse representation,linear projection and reconstruction algorithm.The sparse representation of signals is to seek proper basis for the accurate reconstruction of signals.At present,most reconstruction algorithms are based on single sparse transform,however single sparse transform is only effective for a particular feature of the image,and it is easy to lose other feature information of the image,resulting in poor reconstruction effect.Therefore,this thesis uses multiple joint sparse transforms as the sparse constraints to represent different features of the image and focuses on the sparse constraints and reconstruction algorithms of the CS theory.Major topics are as follows:For the insufficiency of the detailed information such as the contour and edge of the image reconstructed by the discrete wavelet transform and the total variation sparse combination reconstruction algorithm,a reconstruction algorithm based on the combination of contourlet transform and total variation sparse is proposed to improve the reconstruction of image detail information.However,the contourlet transform has the disadvantage of aliasing in the frequency domain and can not represent the image details well.In order to solve this problem,an iterative weighted reconstruction algorithm based on sharp frequency localized contourlet transform and total variation sparse combination is further proposed.The algorithm can adaptively adjust the weights of sparse regular terms,eliminate the frequency domain aliasing of the original contourlet transform and have a better reconstruction effect.The experimental results show that compared with the algorithm based on the discrete wavelet transform and the total variation sparse combination and the algotithm based on the contourlet and total variation sparse combination,the image reconstructed by the proposed method is 7.54 dB and 2.13 dB higher than the one based on the peak signal-to-noise ratio(PSNR)respectively,and the reconstructed images have stronger detail expression and better subjective visual effects.In the magnetic resonance imaging research based on CS theory,for the problem of the loss of the image structure and detailed information brought about by the reconstruction algorithm using local and global sparse constraints alone,the local and global sparsity of the image is studied in this thesis.In order to capture the local detail and the overall structural information of the MR images simultaneously and improve the reconstruction effect of the image detail information such as outline,edge and textures,a new model based on the global and local sparse constraints for the sparse representation of the magnetic resonance(MR)images is proposed.This model uses a new sparse composition constraint to force the image become sparse,and replaces the wavelet transform by the sharp frequency localized contourlet transform with the total variation and adaptive dictionary to sparsely represent the image,which has a better sparse representation effect.It uses the alternating direction multiplier method to reconstruct the image.Experimental results show that compared with the MR image reconstruction algorithm based on dictionary learning and the original model,the images reconstructed by this algorithm have an improvement in the subjective visual effect and the peak signal to noise ratio(PSNR),and the PSNR is improved by 4.8dB and 0.7dB on average respectively.