Denoising Algorithm Development For Magnetic Resonance Images Based On Tensor Decomposition

Magnetic resonance imaging（MRI）is a non-invasive high-resolution imaging technology which plays an important role in clinical diagnosis,treatment and scientific research for its capability of revealing three-dimensional structural information with internal details of human tissues and organs.However,MR images are often corrupted by noise due to the inherent physical limitations of imaging during acquisition,conversion and transmission,resulting accuracy reduction of clinical diagnosis and treatment.In addition,degraded images can also affect the performance of subsequent computer-aided diagnostic analysis such as image segmentation,registration and classification.Therefore,considering the advantage of tensor decomposition in structural preservation for multidimensional data,this study involves the techniques of low-rank tensors approximation,non-local self-similarity and image gradient L₀ norm regularization techniques to develop novel 3D MR image denoising methods.The main researches are as follows:（1）A MR image denoising algorithm based on adaptive multi-linear tensor rank is proposed.The high-order singular value decomposition（HOSVD）with hard threshold truncation scheme that utilized in traditional MR denoising algorithm often cause unnecessary loss of details that distributed over smaller coefficients.In this study,we propose an adaptive multi-linear tensor rank denoising framework with parameterized non-convex logarithmic function regularization.Considering non-local self-similarity in3D MR images,the restoration of noise fourth-order tensors composed of similar block matching groups can be transformed into low-rank tensor approximation model.The rank of the fourth-order tensors along different modes is adaptively estimated by the low-rank method with parameterized non-convex logarithmic function regularization,and the corresponding core tensors and dictionary matrices are obtained.The restored low-rank tensors are obtained by HOSVD.Experiments are performed based on simulation and clinical data and the results are compared with tradition methods.The performance of the proposed method outstands the existing state-of-art methods in protect the details distributed on small singular values.（2）A novel MR image denoising algorithm based on non-local enhanced low-rank tensor is proposed.As the HOSVD used in traditional MR image denoising method is a constrained Tucker decomposition,we develop a low-rank tensor approximation framework with logarithm-sum regularization to further explore the application of generalized Tucker decomposition mode in 3D MR image denoising.With the consideration that different singular values represent different physical meanings,the proposed method can assign small weights to large singular to retain the potential component information and large weights to tinny singular values for detail protection.In addition,non-local self-similarity prior is introduced according to the self-similarity property of 3D MR images to further enhance the global low-rank feature of image for performance improvement.Experimental results show that the proposed method can remove the Rician noise while preserving the structural details of the image better compare to several existing classical methods.（3）A denoising algorithm for MR images based on non-convex tensor train rank approximation is proposed.Considering the well-balanced matricization scheme in tensor train decomposition,the weighted Schatten-p norm is introduced into tensor train decomposition.Therefore,a denoising framework based on tensor train rank which can fully describe the correlation across dimensions in multi-dimensional image is developed.The Schatten-p norm theoretically may improve the accuracy of signal recovery comparing to the traditional nuclear norm under weak restricted isometry property,while the weights assignment can further preserve the main potential information in image.In addition,the non-local self-similarity prior is also introduced.Experimental comparative analysis demonstrates higher quality of denoising images using the proposed method.（4）An edge-enhanced low-rank tensor algorithm for MR image denoising is proposed.3D MR images not only exhibit global low-rank sparse characteristics,but also have local structural smoothness.However,traditional low-rank tensor approximation denoising methods only take the global low-rank sparse feature characteristics into consideration,which ignore the local piecewise smoothing structure information.Therefore,an edge-enhanced low-rank tensor denoising algorithm is designed.The image gradient L₀ norm regularization that describes the local structure information is incorporated into the low-rank tensor approximation model.In addition,the weights assignment can further preserve the potentially useful information distributed on the core tensor coefficients.Experiments results based on simulation and clinical data illustrate that the proposed method can effectively remove noise while retaining structure information.To summary,this dissertation focuses on the denoising algorithm development for3D MR images based on tensor decomposition.According to non-convex penalty functions and image gradient L₀ norm regularization,this study has successfully constructed denoising algorithms involving the adaptive multi-linear tensor rank,the non-local enhanced low-rank tensor,the non-convex tensor train rank approximation and the edge enhanced tensor low-rank frameworksfor noise removal in MR images.The effectiveness of the proposed methods are verified by simulation and clinical image data.