New Artificial Neural Network Models for Bio Medical Image Compression

This article presents an image compression method using feed-forward back-propagation neural networks (NNs). Marked progress has been made in the area of image compression in the last decade. Image compression removing redundant information in image data is a solution for storage and data transmission problems for huge amounts of data. NNs offer the potential for providing a novel solution to the problem of image compression by its ability to generate an internal data representation. A comparison among various feed-forward back-propagation training algorithms was presented with different compression ratios and different block sizes. The learning methods, the Levenberg Marquardt (LM) algorithm and the Gradient Descent (GD) have been used to perform the training of the network architecture and finally, the performance is evaluated in terms of MSE and PSNR using medical images. The decompressed results obtained using these two algorithms are computed in terms of PSNR and MSE along with performance plots and regression plots from which it can be observed that the LM algorithm gives more accurate results than the GD algorithm.

OSCILLATION PROPERTIES FOR NON-CLASSICAL STURM-LIOUVILLE PROBLEMS WITH ADDITIONAL TRANSMISSION CONDITIONS

This work is aimed at studying some comparison and oscillation properties of boundary value problems (BVP’s) of a new type, which differ from classical problems in that they are defined on two disjoint intervals and include additional transfer conditions that describe the interaction between the left and right intervals. This type of problems we call boundary value-transmission problems (BVTP’s). The main difficulty arises when studying the distribution of zeros of eigenfunctions, since it is unclear how to apply the classical methods of Sturm’s theory to problems of this type. We established new criteria for comparison and oscillation properties and new approaches used to obtain these criteria. The obtained results extend and generalizes the Sturm’s classical theorems on comparison and oscillation.

Fast solver for quasi-periodic 2D-Helmholtz scattering in layered media

We present a fast spectral Galerkin scheme for the discretization of boundary integral equations arising from two-dimensional Helmholtz transmission problems in multi-layered periodic structures or gratings. Employing suitably parametrized Fourier basis and excluding cut-off frequen- cies (also known as Rayleigh-Wood frequencies), we rigorously establish the well-posedness of both continuous and discrete problems, and prove super-algebraic error convergence rates for the proposed scheme. Through several numerical examples, we confirm our findings and show performances competitive to those attained via Nystr\"om methods.

A generalized finite element method for problems with sign-changing coefficients

Problems with sign-changing coefficients occur, for instance, in the study of transmission problems with metamaterials. In this work, we present and analyze a generalized finite element method in the spirit of the Localized Orthogonal Decomposition, that is especially efficient when the negative and positive materials exhibit multiscale features. We derive optimal linear convergence in the energy norm independently of the potentially low regularity of the exact solution. Numerical experiments illustrate the theoretical convergence rates and show the applicability of the method for a large class of sign-changing diffusion problems.