A Two-Level Method for Image Denoising and Image Deblurring Models Using Mean Curvature Regularization

The mean curvature (MC)-based image denoising and image deblurring models are used to enhance the quality of the denoised images and deblurred images respectively. These models are very efficient in removing staircase effect, preserving edges and other nice properties. However, high order derivatives appear in the Euler–Lagrange equations of the MC-based models which create problems in developing an efficient numerical algorithm. To overcome this difficulty, we present a robust and efficient Two-Level method for MC-based image denoising and image deblurring models. The Two-Level method consists of solving one small problem and one large problem. The small problem is a nonlinear system, having high order derivative, on Level I (image having small number of pixels). The large problem is one less expensive system, having low order derivative, on Level II (image having large number of pixels). The derivation of the optimal regularization parameter of Level II is studied and formula is presented. Numerical experiments on digital images are presented to exhibit the performance of the Two-Level method

Thermoreversible hyaluronan-hydrogel and autologous nucleus pulposus cell delivery regenerates human intervertebral discs in an ex vivo, physiological organ culture model

Numerous studies show promise for cell-based tissue engineering strategies aiming to repair painful intervertebral disc (IVD) degeneration. However, clinical translation to human IVD repair is slow. In the present study, the regenerative potential of an autologous nucleus pulposus (NP)-cell-seeded thermoresponsive hyaluronic acid hydrogel in human lumbar IVDs was assessed under physiological conditions. First, agarose-encased in vitro constructs were developed, showing greater than 90 % NP cell viability and high proteoglycan deposition within HA-pNIPAM hydrogels following 3 weeks of dynamic loading. Second, a bovine-induced IVD degeneration model was used to optimise and validate T1ρ magnetic resonance imaging (MRI) for detection of changes in proteoglycan content in isolated intact IVDs. Finally, isolated intact human lumbar IVDs were pre-scanned using the established MRI sequence. Then, IVDs were injected with HA-pNIPAM hydrogel alone or autologous NP-cell-seeded. Next, the treated IVDs were cultured under cyclic dynamic loading for 5 weeks. Post-treatment T1ρ values were significantly higher as compared to pre-treatment scans within the same IVD and region of interest. Histological evaluation of treated human IVDs showed that the implanted hydrogel alone accumulated proteoglycans, while those that contained NP cells also displayed neo-matrix-surrounded cells within the gel. The study indicated a clinical potential for repairing early degenerative human IVDs using autologous cells/hydrogel suspensions. This unique IVD culture set-up, combined with the long-term physiological culture of intact human IVDs, allowed for a more clinically relevant evaluation of human tissue repair and regeneration, which otherwise could not be replicated using the available in vitro and in vivo models

A two-level finite-element discretization of the stream function form of the Navier-Stokes equations

We analyze a two-level method of discretizing the stream function form of the Navier-Stokes equations. This report presents the two-level algorithm and error analysis for the case of conforming elements. The two-level algorithm consists of solving a small nonlinear system on the coarse mesh, then solving a linear system on the fine mesh. The basic result states that the error between the coarse and fine meshes are related superlinearly via $|\psi- \psi^h|_2\le C\left\{ \inf_{w^h\in X^h}|\psi- w^h|_2+ |\ln h|^{1/2}\cdot|\psi- \psi^H|_1\right\}$. As an example, if the Clough-Tocher triangles or the Bogner-Fox-Schmit rectangles are used, then the coarse and fine meshes are related by $h= O(H^{3/2}|\ln H|^{1/4})$