Optimising Spatial and Tonal Data for PDE-based Inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. We also give an extensive literature survey on PDE-based image compression methods

Golden needle mushroom:A culinary medicine with evidenced-based biological activities and health promoting properties

Flammulina velutipes (enoki, velvet shank, golden needle mushroom or winter mushroom), one of the main edible mushrooms on the market, has long been recognized for its nutritional value and delicious taste. In recent decades, research has expanded beyond detailing its nutritional composition and delved into the biological activities and potential health benefits of its constituents. Many bioactive constituents from a range of families have been isolated from different parts of the mushroom, including carbohydrates, protein, lipids, glycoproteins, phenols, and sesquiterpenes. These compounds have been demonstrated to exhibit various biological activities, such as antitumour and anticancer activities, anti-atherosclerotic and thrombosis inhibition activity, antihypertensive and cholesterol lowering effects, anti-aging and antioxidant properties, ability to aid with restoring memory and overcoming learning deficits, anti-inflammatory, immunomodulatory, anti-bacterial, ribosome inactivation and melanosis inhibition. This review aims to consolidate the information concerning the phytochemistry and biological activities of various compounds isolated from F. velutipes to demonstrate that this mushroom is not only a great source of nutrients but also possesses tremendous potential in pharmaceutical drug development

Golden needle mushroom: A culinary medicine with evidenced-based biological activities and health promoting properties

Flammulina velutipes (enoki, velvet shank, golden needle mushroom or winter mushroom), one of the main edible mushrooms on the market, has long been recognised for its nutritional value and delicious taste. In recent decades, research has expanded beyond detailing its nutritional composition and delved into the biological activities and potential health benefits of its constituents. Many bioactive constituents from a range of families have been isolated from different parts of the mushroom, including carbohydrates, protein, lipids, glycoproteins, phenols and sesquiterpenes. These compounds have been demonstrated to exhibit various biological activities, such as antitumour and anticancer activities, anti-atherosclerotic and thrombosis inhibition activity, antihypertensive and cholesterol lowering effects, anti-aging and antioxidant properties, ability to aid with restoring memory and overcoming learning deficits, anti-inflammatory, immunomodulatory, anti-bacterial, ribosome inactivation and melanosis inhibition. This review aims to consolidate the information concerning the phytochemistry and biological activities of various compounds isolated from Flammulina velutipes to demonstrate that this mushroom is not only a great source of nutrients but also possesses tremendous potential in pharmaceutical drug development