An optimal factor analysis approach to improve the wavelet-based image resolution enhancement techniques

The existing wavelet-based image resolution enhancement techniques have many assumptions, such as limitation of the way to generate low-resolution images and the selection of wavelet functions, which limits their applications in different fields. This paper initially identifies the factors that effectively affect the performance of these techniques and quantitatively evaluates the impact of the existing assumptions. An approach called Optimal Factor Analysis employing the genetic algorithm is then introduced to increase the applicability and fidelity of the existing methods. Moreover, a new Figure of Merit is proposed to assist the selection of parameters and better measure the overall performance. The experimental results show that the proposed approach improves the performance of the selected image resolution enhancement methods and has potential to be extended to other methods

Satellite image resolution enhancement using discrete wavelet transform and new edge-directed interpolation

An image resolution enhancement approach based on discrete wavelet transform (DWT) and new edge-directed interpolation (NEDI) for degraded satellite images by geometric distortion to correct the errors in image geometry and recover the edge details of directional high-frequency subbands is proposed. The observed image is decomposed into four frequency subbands through DWT, and then the three high-frequency subbands and the observed image are processed with NEDI. To better preserve the edges and remove potential noise in the estimated high-frequency subbands, an adaptive threshold is applied to process the estimated wavelet coefficients. Finally, the enhanced image is reconstructed by applying inverse DWT. Four criteria are introduced, aiming to better assess the overall performance of the proposed approach for different types of satellite images. A public satellite images data set is selected for the validation purpose. The visual and quantitative results show the superiority of the proposed approach over the conventional and state-of-the-art image resolution enhancement

Global motion based video super-resolution reconstruction using discrete wavelet transform

Different from the existing super-resolution (SR) reconstruction approaches working under either the frequency-domain or the spatial- domain, this paper proposes an improved video SR approach based on both frequency and spatial-domains to improve the spatial resolution and recover the noiseless high-frequency components of the observed noisy low-resolution video sequences with global motion. An iterative planar motion estimation algorithm followed by a structure-adaptive normalised convolution reconstruction method are applied to produce the estimated low-frequency sub-band. The discrete wavelet transform process is employed to decompose the input low-resolution reference frame into four sub-bands, and then the new edge-directed interpolation method is used to interpolate each of the high-frequency sub-bands. The novelty of this algorithm is the introduction and integration of a nonlinear soft thresholding process to filter the estimated high-frequency sub-bands in order to better preserve the edges and remove potential noise. Another novelty of this algorithm is to provide flexibility with various motion levels, noise levels, wavelet functions, and the number of used low-resolution frames. The performance of the proposed method has been tested on three well-known videos. Both visual and quantitative results demonstrate the high performance and improved flexibility of the proposed technique over the conventional interpolation and the state-of-the-art video SR techniques in the wavelet- domain

Study of a class of non-polynomial oscillator potentials

We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in (-infinity,\infinity), g>0. The variational bounds are compared with results previously obtained in the literature. An infinite set of exact solutions is also obtained and used as a source of comparison eigenvalues.Comment: 16 page

Eigenvalues from power--series expansions: an alternative approach

An appropriate rational approximation to the eigenfunction of the Schr\"{o}dinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of Hankel determinants. The convergence rate of this approach is greater than that for a well--established method based on a power--series expansions weighted by a Gaussian factor with an adjustable parameter (the so--called Hill--determinant method)