Compressed sensing magnetic resonance imaging (CS-MRI) has made great progress in speeding up MRI imaging. The existing non-local self-similarity (NSS) prior based CS-MRI models mainly take similar image patches as the processing objects, this patch-level non-local sparse representation method can not make full use of the self-similarity among pixels in the image, so it can not recover the weak edge information in the undersampled MRI image well and there will still be some artifacts. In this paper, a pixel-level non-local method based compressed sensing undersampled MRI image reconstruction method is introduced. First, zero filling is performed on the undersampled k-space data to obtain a full-size 2D signal, and IFFT is performed to obtain a preliminary reconstructed MRI image. Block-matching and row-matching are successively performed on the reconstructed image in turn to obtain similar pixel groups, so as to establish a better sparse representation under the non-local self-similarity (NSS) prior. The separable Haar transform is performed on similar pixel groups, and the hard threshold of the transform coefficients and Wiener filtering can effectively remove the artifacts introduced in the undersampled reconstructed MRI images. The proposed pixel-level non-local iterative thinning model based on compressed sensing theory can ensure the removal of artifacts and better restore the details in the image. The qualitative and quantitative results under different undersampling modes and undersampling rates prove the advantages of the proposed method in subjective visual quality and objective evaluation (peak signal to noise ratio and structure similarity index). The performance of this method is not only superior to the existing traditional CS-MRI methods, but also competitive with the existing deep neural network (DNN) based models. The code will be released at https://github.com/HaoHou-98/PNCS.
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