Orthogonal Wavelets via Filter Banks: Theory and Applications

Wavelets are used in many applications, including image processing, signal analysis and seismology. The critical problem is the representation of a signal using a small number of computable functions, such that it is represented in a concise and computationally efficient form. It is shown that wavelets are closely related to filter banks (sub band filtering) and that there is a direct analogy between multiresolution analysis in continuous time and a filter bank in discrete time. This provides a clear physical interpretation of the approximation and detail spaces of multiresolution analysis in terms of the frequency bands of a signal. Only orthogonal wavelets, which are derived from orthogonal filter banks, are discussed. Several examples and applications are considered

Blind image deconvolution using the Sylvester resultant matrix

This paper uses techniques from computational algebraic geometry to perform blind image deconvolution, such that prior knowledge of the point spread function (PSF) is not required to compute a deblurred form of a given blurred image. In particular, it is shown that the Sylvester resultant matrix enables the PSF to be calculated by two approximate greatest common divisor computations. These computations, and not greatest common divisor computations, are required because of the noise that is present in the exact image and PSF. The computed PSF is then deconvolved from the blurred image in order to calculate the deblurred image. The experimental results show consistently good results for the deblurred image and PSF, and they are compared with the results from other methods for blind image deconvolution

An approximate factorisation of three bivariate Bernstein basis polynomials defined in a triangular domain

This paper considers an approximate factorisation of three bivariate Bernstein basis polynomials that are defined in a triangular domain. This problem is important for the computation of the intersection points of curves in computer-aided design systems, and it reduces to the determination of an approximate greatest common divisor (AGCD) d (y) of the polynomials. The Sylvester matrix and its subresultant matrices of these three polynomials are formed and it is shown that there are four forms of these matrices. The most difficult part of the computation is the determination of the degree of d (y) because it reduces to the determination of the rank loss of these matrices. This computation is made harder by the presence of trinomial terms in the Bernstein basis functions because they cause the entries of the matrices to span many orders of magnitude. The adverse numerical effects of this wide range of magnitudes of the entries of the four forms of the Sylvester matrix and its subresultant matrices are mitigated by processing the polynomials before these matrices are formed. It is shown that significantly improved results are obtained if the polynomials are processed before computations are performed on their Sylvester matrices and subresultant matrices

The Two Dimensional Kondo Model with Rashba Spin-Orbit Coupling

We investigate the effect that Rashba spin-orbit coupling has on the low energy behaviour of a two dimensional magnetic impurity system. It is shown that the Kondo effect, the screening of the magnetic impurity at temperatures T < T_K, is robust against such spin-orbit coupling, despite the fact that the spin of the conduction electrons is no longer a conserved quantity. A proposal is made for how the spin-orbit coupling may change the value of the Kondo temperature T_K in such systems and the prospects of measuring this change are discussed. We conclude that many of the assumptions made in our analysis invalidate our results as applied to recent experiments in semi-conductor quantum dots but may apply to measurements made with magnetic atoms placed on metallic surfaces.Comment: 22 pages, 1 figure; reference update

Centrifugal stretching from lifetime measurements in the 170Hf ground state band

Centrifugal stretching in the deformed rare-earth nucleus 170Hf is investigated using high-precision lifetime measurements, performed with the New Yale Plunger Device at Wright Nuclear Structure Laboratory, Yale University. Excited states were populated in the fusion-evaporation reaction 124Sn(50Ti,4n)170Hf at a beam energy of 195 MeV. Recoil distance doppler shift data were recorded for the ground state band through the J=16+ level. The measured B(E2) values and transition quadrupole moments improve on existing data and show increasing β deformation in the ground state band of 170Hf. The results are compared to descriptions by a rigid rotor and by the confined β-soft rotor model. © 2013 American Physical Society