Prior Information Based Compressed Sensing Image Restoration Algorithm

Compressed Sensing(CS)theory is a new sampling technology different from the Nyquist sampling theorem.It indicates that as long as the signal is compressible or sparse in some transform domain,an observation matrix that is not related to sparse basis can be used for linear observation,and an optimization algorithm is utilized to recover the original signal.Specially,the CS reconstruction is an ill-conditioned or ill-posed inverse problem,so it is necessary to introduce the sparse prior information of signal into the CS reconstruction system to obtain the only exact solution.Therefore,it is of great significance for signal reconstruction to employ prior information of signal and take advantage of them in CS theory.For the content-rich image signal,its inherent local and non-local properties can reflect internal structural features,which provide an idea for the research of image CS reconstruction.In this thesis,a CS reconstruction algorithm based on non-local low rank prior and gradient sparse prior of image is focused,and the main innovations are shown as follows:1.In order to reconstruct natural image from CS measurements accurately and effectively,a CS image reconstruction algorithm based on non-local low rank and weighted total variation is proposed.The proposed algorithm considers the non-local self-similarity and local smoothness in the image and improves the traditional TV model,in which only the weights of image's high-frequency components are set and constructed with a differential curvature edge detection operator.In addition,the optimization model of the proposed algorithm is built with constraints of the improved TV and the non-local low rank model,and then a non-convex smooth function and soft thresholding function are utilized to solve low rank and TV optimization problems respectively.By taking advantage of them,the proposed method makes full use of the property of image,and therefore conserves the details of image and is more robust and adaptable.Experimental results show that,the proposed algorithm can effectively recover the texture and preserve edge of image at low sampling rate,while possessing a better robustness.2.Due to the low accuracy of similar image patches matching and ringing artifacts caused by enforcing local similarity in non-repetitive in the traditional construction ofnon-local low rank model,a CS image reconstruction algorithm based on adaptive non-local low rank and weighted total variation is proposed.In order to adaptively construct a similar matrices of different size,the proposed algorithm sets different number of similar image patches in structures and textures of image.Meanwhile,to measure the similarity between image patches more accurately,a new patch matching method based on Mahalanobis distance is introduced to improve the quality of reconstructed image.Experimental results show that,the proposed scheme gets better reconstruction results compared to the old non-local low rank model with the same sampling rate.