https://www2.econ.iastate.edu/tesfatsi/DeepLearningInNeuralNetworksOverview.JSchmidhuber2015.pdf

Deep learning in neural networks

Basics of qualitative research: Grounded theory procedures and techniques

New, efficient reconstruction procedures are proposed for sensitivity encoding (SENSE) with arbitrary k-space trajectories. The presented methods combine gridding principles with so-called conjugate-gradient iteration. In this fashion, the bulk of the work of reconstruction can be performed by fast Fourier transform (FFT), reducing the complexity of data processing to the same order of magnitude as in conventional gridding reconstruction. Using the proposed method, SENSE becomes practical with nonstandard k-space trajectories, enabling considerable scan time reduction with respect to mere gradient encoding. This is illustrated by imaging simulations with spiral, radial, and random k-space patterns. Simulations were also used for investigating the convergence behavior of the proposed algorithm and its dependence on the factor by which gradient encoding is reduced. The in vivo feasibility of non-Cartesian SENSE imaging with iterative reconstruction is demonstrated by examples of brain and cardiac imaging using spiral trajectories. In brain imaging with six receiver coils, the number of spiral interleaves was reduced by factors ranging from 2 to 6. In cardiac real-time imaging with four coils, spiral SENSE permitted reducing the scan time per image from 112 ms to 56 ms, thus doubling the frame-rate. Magn Reson Med 46:638–651, 2001. © 2001 Wiley-Liss, Inc.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/mrm.1241

Advances in sensitivity encoding with arbitrary k-space trajectories.

Barycentric interpolation is a variant of Lagrange polynomial interpolation that is fast and stable. It deserves to be known as the standard method of polynomial interpolation.

/pdf/barycentric-lagrange-interpolation-4t9rmsagmj.pdf

Barycentric Lagrange Interpolation

The completion of interrupted lines or the enhancement of flow-like structures is a challenging task in computer vision, human vision, and image processing. We address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so-called interest operator (second-moment matrix, structure tensor). An m-dimensional formulation of this method is analysed with respect to its well-posedness and scale-space properties. An efficient scheme is presented which uses a stabilization by a semi-implicit additive operator splitting (AOS), and the scale-space behaviour of this method is illustrated by applying it to both 2-D and 3-D images.

Coherence-Enhancing Diffusion Filtering

Numerische Mathematik. I

/pdf/numerical-analysis-in-modern-scientific-computing-dam2t0xzuz.pdf

Numerical Analysis in Modern Scientific Computing

From the Publisher:
This text will appeal to undergraduate and graduate students as well as researchers in mathematics, computer science, science, and engineering. At the same time, it is addressed to practical computational scientists who, via self-study, wish to become acquainted with modern concepts of numerical analysis and scientific computing on an elementary level. The sole prerequisite is undergraduate knowledge in linear algebra and calculus.

Numerical Analysis in Modern Scientific Computing: An Introduction

The purpose of the paper is to demonstrate that the performance of an elite female swimmer in the finals of the 200-m backstroke at the Olympic Games 2000 in Sydney can be predicted by means of the nonlinear mathematical method of artificial neural networks (Multi-Layer Perceptrons). The data consisted of the performance output of 19 competitions (200-m backstroke) prior to the Olympics and the training input data of the last 4 weeks prior to each competition. Multi-Layer Perceptrons with 10 input neurons, 2 hidden neuron, and 1 output neuron were used. Since the data of 19 competitions are insufficient to train such networks, the training input and competition data of another athlete were used in the training processes of the neural networks to pre-train the neural networks. The neural models were validated by the “leave-one-out” method, then the neural models were used to predict the Olympic competitive performance. The results show that the modeling was very precise; the error of the prediction was only 0.05 s, with a total swim time of 2:12.64 min:s.

Andreas Hohmann

Papers

Numerische Mathematik. I

Numerical Analysis in Modern Scientific Computing

Numerical Analysis in Modern Scientific Computing: An Introduction

Modeling and Prediction of Competitive Performance in Swimming Upon Neural Networks

Numerische Mathematik 1: Eine algorithmisch orientierte Einführung