Optical Holonomic Quantum Computer

In this paper the idea of holonomic quantum computation is realized within quantum optics. In a non-linear Kerr medium the degenerate states of laser beams are interpreted as qubits. Displacing devices, squeezing devices and interferometers provide the classical control parameter space where the adiabatic loops are performed. This results into logical gates acting on the states of the combined degenerate subspaces of the lasers, producing any one qubit rotations and interactions between any two qubits. Issues such as universality, complexity and scalability are addressed and several steps are taken towards the physical implementation of this model.Comment: 16 pages, 3 figures, REVTE

Removal of blur in images based on least squares solutions

We propose an image restoration method. The method generalizes image restoration algorithms that are based on the Moore–Penrose solution of certain matrix equations that define the linear motion blur. Our approach is based on the usage of least squares solutions of these matrix equations, wherein an arbitrary matrix of appropriate dimensions is included besides the Moore–Penrose inverse. In addition, the method is a useful tool for improving results obtained by other image restoration methods. Toward that direction, we investigate the case where the arbitrary matrix is replaced by the matrix obtained by the Haar basis reconstructed image. The method has been tested by reconstructing an image after the removal of blur caused by the uniform linear motion and filtering the noise that is corrupted with the image pixels. The quality of the restoration is observable by a human eye. Benefits of using the method are illustrated by the values of the improvement in signal-to-noise ratio and in the values of peak signal-to-noise ratio

Image deblurring process based on separable restoration methods

This paper proposes a method for reconstruction of blurred images damaged by a separable motion blur. The method can be used after the application of currently developed image restoration algorithms. Our approach is based on the usage of least squares solutions of certain matrix equations which define the separable motion blur. The method uses appropriately selected matrices besides the Moore–Penrose inverse. The method is tested by reconstructing a set of images after the removal of blur caused by uniform and separable motion. The quality of the restoration is observable by a human eye. The measurements such as the Improvement in Signal to Noise Ratio and the Peak in Signal to Noise Ratio have been increased significantly in comparison with the classical image restoration methods as well as the image restoration proposals based on the usage of the Moore–Penrose inverse

On Removing Blur in Images Using Least Squares Solutions

The further investigation of the image restoration method introduced in [17, 18] is presented in this paper. Continuing investigations in that area, two additional applications of the method are investigated. More precisely, we consider the possibility to replace the available matrix in the method by the restoration obtained applying the Tikhonov regularization method or the Truncated Singular Value decomposition method. Additionally, statistical analysis of numerical results generated by applying the proposed improvement of image restoration methods is presented. Previously performed numerical experiments as well as new numerical results and the statistical analysis confirm that the least squares approach can be used as a useful tool for improving restored images obtained by other image restoration methods

Digital Image Reconstruction in the Spectral Domain Utilizing the Moore-Penrose Inverse

The field of image restoration has seen a tremendous growth in interest over the last two decades. The recovery of an original image from degraded observations is a crucial method and finds application in several scientific areas including medical imaging and diagnosis, military surveillance, satellite and astronomical imaging, and remote sensing. The proposed approach presented in this work employs Fourier coefficients for moment-based image analysis. The main contributions of the presented technique, are that the image is first analyzed in orthogonal basis matrix formulation increasing the selectivity on image components, and then transmitted in the spectral domain. After the transmission has taken place, at the receiving end the image is transformed back and reconstructed from a set of its geometrical moments. The calculation of the Moore-Penrose inverse of × matrices provides the computation framework of the method. The method has been tested by reconstructing an image represented by an × matrix after the removal of blur caused by uniform linear motions. The noise during the transmission process is another issue that is considered in the current work

Applications of the Moore-Penrose Inverse in Digital Image Restoration

This paper presents a fast computational method that finds application in a broad scientific field such as digital image restoration. The proposed method provides a new approach to the problem of image reconstruction by using the Moore-Penrose inverse. The resolution of the reconstructed image remains at a very high level but the main advantage of the method was found on the computational load that has been decreased considerably compared to the classic techniques