Study On Low Rank Two-dimensional CZT And Wavelet Tree Compound Sparse Constrained MRI Reconstruction

Magnetic resonance imaging（MRI）is a non-invasive technique for observing tissue changes in patients.It is a medical imaging method that can make clear images of living organs and tissues.It is widely applicable to people and diseases.In recent years,how to reduce the reconstruction time without reducing the imaging quality has become a research hotspot.Because part of K-space reconstruction does not need to improve the hardware,it only needs to improve the K-space reconstruction algorithm to achieve the goal of improving the imaging speed,which attracts much attention.The application of compressed sensing in MRI has brought new development to MRI.Discrete Fourier transform（DFT）is the classical sparse constrained basis of compressed sensing,and CZT can be regarded as an extension of Fourier transform and can refine local spectrum.Can CZT be used to reconstruct and improve the overall or local image quality by Compressed Sensing-Magnetic Resonance Imaging（CS-MRI）?Based on this idea,the following aspects are studied in this paper:Firstly,in order to improve the ability of displaying local details of magnetic resonance images,the application of two-dimensional CZT in MRI reconstruction is studied in this paper.Through a lot of simulation experiments,the effects of initial sampling point radius₀A,phase angle of initial sampling point?₀,angle between two sampling points₀?and spiral stretch ratio₀W on image K-space and reconstructed image are discussed.Moreover,the discrete Fourier transform and wavelet transform are studied and the reconstructed image is compared with the CZT reconstructed image to analyze the advantages and disadvantages of different algorithms.Secondly,the complex Sparse constraint MRI reconstruction model Compound Sparse Constraints of CZT Transform and Wavelet Tree,（CW）is proposed.At the same time,it is compared with the reconstructed image quality of wavelet tree sparse transform and CZT to analyze the advantages and disadvantages of different algorithms.Finally,a two-dimensional CZT and wavelet tree sparse constrained MRI reconstruction model based on low rank（LRCW）is proposed,in which smooth pixels and edge pixels are matched separately,similar blocks are searched along the edge direction,and image block mean nodes are introduced into the non-local sparse structure of the image,which shortens the running time and improves the noise resistance.The simulation results under the same conditions and different sampling rates show that compared with other algorithms,the edge details of the image reconstructed by the proposed algorithm are more prominent,and the effect of local image reconstruction is clearer.