3D Denoising Sample Clauses

3D Denoising. The Beltrami regularization for image denoising and enhancement was introduced for 2D natural images by Xxxxxx, Kimmel and Xxxxxxx (79) and proposed for 2D MRI myocardial T1 mapping denoising by Xxxxxx et al (61). The potential of the Beltrami regularization framework lies in the general definition of the space-feature manifold and the choice of its metric. In particular, the regularization can be chosen such that the energy of the unknown image corresponds to an arbitrary interpolation between quadratic or total variation gradient penalties. In this work, the Beltrami denoising framework is applied to 3D T1 mapping by exploiting the 3D spatial and T1 recovery dimension redundant information. This approach thus exploits the 3D spatial gradients of each T1-weighted image and the common edge information between T1-weighted images with varying contrast. A coupling between the T1-weighted images is performed as described by Xxxxxx et al (61), to enforce common edge information across the 3D images in the T1 encoding direction. With this approach, common structures/edges in different T1-weighted images are preserved, while local intensity variations specific to each T1-weighted image are treated as noise, and thus reduced. Therefore, edges/details in the images will be better enhanced if they are present in multiple T1-weighted images. Following the derivation in (8), the 3D Beltrami denoising framework for 3D T1 mapping can be expressed as the following optimization problem: ̂ = {‖ − ‖2 + √1 + 2 ∑ |∇|2} [22] =1 =1 where{̂} are the denoised 3D T1-weighted images for the contrasts = 1, … , , =1 {} are the corresponding 3D T1-weighted images before denoising, is the regularization parameter that controls the trade off between the fidelity to the original acquired data and the Beltrami regularization term, is the Beltrami constant that allows selection of any arbitrary interpolation between quadratic or total variation gradient =1 penalties and{∇} are the 3D weighted-gradient transformation applied to the 3D T1-weighted images with varying contrast. The weighted-gradient functions penalise the gradients depending on their local orientation in order to decrease local smoothing in the directions where sharp transitions are observed, with () = iteration of the optimization and ℎ a smoothing parameter. −(∇) ℎ2 updated at each The optimization problem described above was solved using an efficient and simple primal-dual hybrid gradient algorithm (12,13). The parameters ...