The Lagrange interpolation for He’s frequency formulation

Nonlinear oscillators arise everywhere in engineering, and though there are many analytical methods available, a fast and accurate estimation of the frequency–amplitude relationship is much needed in practical applications. He’s frequency formulation meets this requirement, but the local points are chosen randomly. In this paper, the Gaussian interpolation points are adopted, making He’s method more mathematically rigorous and physically reliable. The cubic-quintic Duffing equation is used for comparison, and an excellent result is obtained.

Modification of the Algorithm for Selecting a Variable Parameter of the Gaussian Interpolation Function

The paper presents an algorithm for selecting the optimal value of the variable parameter α of the Gaussian interpolation function to obtain the smallest possible error when interpolating the tabular data. The results of the algorithm are checked on a sample of elementary mathematical functions. For comparison, the interpolation data of the Lagrange polynomial are given. The paper presents the results of Gaussian interpolation at different α, conclusions are made about the need to applying the algorithm for selecting of its optimal value.

Optimized Wavelet Decomposition and Gaussian interpolation based Satellite Image Enhancement

Satellite images (SI) play a vital role in various remote sensing applications like geoscience, geographical studies, observing the earth's atmosphere, monitoring natural disasters, etc. The SI are used in these applications require high-resolution. The performance of the wavelet transforms based resolution enhancement methods depends on the type of the mother wavelet used and it varies with image to image. The novel robust SI resolution enhancement technique including Optimized wavelet transform based image decomposition and Gaussian interpolation is proposed in this paper. Optimized wavelet decomposition is obtained using the Stochastic Diffusion Search algorithm and the Gaussian distribution function is used for interpolation. The proposed method is compared with the Discrete wavelet decomposition and Gaussian interpolation resolution enhancement method and proved that the proposed method gives the best results for any image.

A generic interpolator for multi-label images

We present a generic interpolator for label images. The basic idea is to interpolate each label with an ordinary image interpolator, and return the label with the highest value. This is the idea used by the itk::LabelImageGaussianInterpolateImageFunction interpolator. Unfortunately, this class is currently limited to Gaussian interpolation. Using generic programming, our proposed interpolator extends this idea to any image interpolator. Combined with linear interpolation, this results in similar or better accuracy and much improved computation speeds on a test image.