Magnetic resonance (MR) data reconstruction can be computationally a challenging task. The signal-to-noise ratio might also present complications, especially with high-resolution images. In this sense, data compression can be useful not only for reducing the complexity and memory requirements, but also to reduce noise, even to allow eliminate spurious components.This article proposes the use of a system based on singular value decomposition of low order for noise reconstruction and reduction in MR imaging system. The proposed method is evaluated using in vivo MRI data. Rebuilt images with less than 20 of the original data and with similar quality in terms of visual inspection are presented. Also a quantitative evaluation of the method is presented.
KEYWORDS: Wavelet transforms, Image compression, Detection and tracking algorithms, Sensors, Data storage, Synthetic aperture radar, Image processing, Digital imaging, Software development, 3D optical data storage
Computer Algebra Software, especially Maple and its Image Tools package, is used to develop image compression using
the Weibull distribution, Wavelet transform application and Singular Value Decomposition (SVD). For prototyping of
the image compression process, Maple packages, Linear Algebra, Array Tools and Discrete Transform are used
simultaneously with Image Tools image processing package. The image compression process implies the realization of
matrix computing with high dimension matrices, and Maple software develops those operations easily and efficiently.
Some image compression experiments are done, and the matrix dimension for minimum information needed to store an
image is shown clearly, also the matrix dimension of redundant information. Implementation of algorithms for image
compression in other computer algebra systems such as Mathematica and Maxima is proposed as future investigation
path. Also it is proposed the use of curvelet transform as a tool for image compression,
We simulate the immune compatibility using the Install Problem: The idea is to define a Boolean variable for each
antibody. This variable is true if the antibody must be in the immune system. The Install Problem refers to the
incompatibility that some programs may have with an specific operative system making it impossible to be installed. The
analysis was implemented using SMT-solvers, specifically Z3, and the code was wrote using the commands
“DependsOn”, “Conflict” and “Compatibility_check”, making it possible to check the antibody compatibility. The
programming languages used to build up the code were Z3-Python and Z3-SMT-Lib. The results can be used in systems
biology and in the analysis of immunological therapies. As future line of research it could be developed a more complex
algorithm to verify the immunological compatibility.
Transdermal patches are used in medicine to deliver a specific amount of medication through the skin and into the
bloodstream, and then to the injury that will be treated. The diffusion process involved in this method was modeled using
cartesian coordinates and it was solved using Laplace transformation, Bromwich integral and the residue theorem. The
solution obtained in cartesian coordinates was given in terms of Fourier series. The cumulative amount of drug released
at time t was calculated and it is represented as an infinite series of decreasing exponentials. It’s expected that the
analytic results obtained will be useful for pharmaceutical engineering.