DTI Image Denoising Algorithm Based On Riemann Geometric Frame

Diffusion tensor imaging(DTI)is a new type of imaging technology.Compared with traditional magnetic resonance imaging,DTI is non-invasive and is widely used to study the diffusion process in the brain.As a non-invasive imaging method,DTI can not only display white matter fiber bundles in vivo,but also has attracted great attention in the theoretical research of brain function,brain development and other clinical applications such as diagnosis of white matter lesions.Due to the influence of noise in the imaging process,the shape and direction of the tensor to be destroyed,which reduces the quality of the image,thereby limiting the development of DTI in clinical applications.Therefore,the research on DTI denoising algorithm is of great significance to the clinical application of related diseases.From a visual point of view,DTI image denoising has two goals: one is to obtain a high-quality DTI image;the other is to obtain a uniformly arranged tensor field.High-quality images can obtain clear brain tissue structure,and evenly arranged tensor fields effectively retain the image edge texture structure to better guide medical staff to perform brain surgery.Of course,if the second goal is achieved,the first goal is often achieved at the same time.Therefore,this article focuses on the second goal,which is to better retain the nonlinear structure of the diffusion tensor while denoising.Through in-depth research on Riemann geometry,this paper combines sparse Bayesian learning theory and non-local similarity theory,and proposes two new DTI denoising algorithms,and validates the proposed denoising methods on simulated and real data.The main research work of this paper is as follows:(1)Riemann Geometric Properties of Diffusion TensorThe diffusion tensor in DTI can be regarded as a symmetric positive definite matrix of 3×3 on the Riemannian manifold,and the existing denoising algorithms do not fully consider the symmetric positive definiteness of the diffusion tensor,but only the characteristic information of the tensor(especially main feature information)for regularization.Therefore,this paper studies the properties of the diffusion tensor on the Riemannian manifold,and studies the affine-invariant Riemannian metric,and describes the distance between any two points on the manifold with the geodesic distance on the manifold.The distance between any two points on the tensor field under the Riemannian manifold and the spatial gradient of the tensor field are derived.Through experimental comparison,the Riemann gradient can better describe the characteristics of the tensor than the Euclidean gradient.(2)DTI denoising based on Riemann geometric frame and sparse Bayesian learningIn order to better remove the Rician noise in DTI,and to better preserve the geometry of the diffusion tensor,this paper proposes a DTI denoising algorithm based on the Riemann geometry frame and sparse Bayesian learning.In order to protect the structure of the tensor,the algorithm maps the DTI tensor to the Riemannian manifold,and then uses the sparse Bayesian learning method to denoise it with sparse representation.Finally,the denoised image can be obtained by reconstructing the image.The algorithm fully considers the sparseness of the image and the symmetric positive definiteness of the tensor,which can not only better remove the noise,but also better retain the structural information of the tensor image.(3)DTI denoising based on Riemann nonlocal similarityIn order to make full use of the prior information of the image,this paper proposes a DTI denoising algorithm based on Riemann non-local similarity.First,the DTI tensor is mapped onto the Riemannian manifold according to its structural properties,and the Riemann similarity measure is used to search for non-locally similar blocks to form similar block groups.Second,the Gaussian mixture model is used to learn the prior distribution of the block groups.Finally,it is denoised by Bayesian inference,and the denoised blocks are recombined to obtain the final image.The algorithm fully considers the non-local similarity of the images,and has better effects in terms of noise removal and edge texture information retention.