Abstract-We introduce a local image statistic for identifying noise pixels in images corrupted with impulse noise of random values. The statistical values quantify how different in intensity the particular pixels are from their most similar neighbors. We continue to demonstrate how this statistic may be incorporated into a filter designed to remove additive Gaussian noise. The result is a new filter capable of reducing both Gaussian and impulse noises from noisy images effectively, which performs remarkably well, both in terms of quantitative measures of signal restoration and qualitative judgements of image quality. Our approach is extended to automatically remove any mix of Gaussian and impulse noise.

The notion of vanishing-moment recovery (VMR) functions is introduced in this paper for the construction of compactly supported tight frames with two generators having the maximum order of vanishing moments as determined by the given refinable function, such as the mth order cardinal B-spline N m. Tight frames are also extended to "sibling frames" to allow additional properties, such as symmetry (or antisymmetry), minimum support, "shift-invariance," and inter-orthogonality. For N m , it turns out that symmetry can be achieved for even m and antisymmetry for odd m, that minimum support and shift-invariance can be attained by considering the frame generators with twoscale symbols 2 −m (1 − z) m and 2 −m z(1 − z) m , and that inter-orthogonality is always achievable, but sometimes at the sacrifice of symmetry. The results in this paper are valid for all compactly supported refinable functions that are reasonably smooth, such as piecewise Lip α for some α > 0, as long as the corresponding two-scale Laurent polynomial symbols vanish at z = −1. Furthermore, the methods developed here can be extended to the more general setting, such as arbitrary integer scaling factors, multi-wavelets, and certainly biframes (i.e., allowing the dual frames to be associated with a different refinable function).

Abstract-It is well known that in applied and computational mathematics, cardinal B-splines play an important role in geometric modeling (in computeraided geometric design), statistical data representation (or modeling), solution of differential equations (in numerical analysis), and so forth. More recently, in the development of wavelet analysis, cardinal B-splines also serve as a canonical example of scaling functions that generate multiresolution analyses of L 2 (−∞, ∞). However, although cardinal B-splines have compact support, their corresponding orthonormal wavelets (of Battle and Lemarie) have infinite duration. To preserve such properties as self-duality while requiring compact support, the notion of tight frames is probably the only replacement of that of orthonormal wavelets. In this paper, we study compactly supported tight frames = {ψ 1 , . . . , ψ N } for L 2 (−∞, ∞) that correspond to some refinable functions with compact support, give a precise existence criterion of in terms of an inequality condition on the Laurent polynomial symbols of the refinable functions, show that this condition is not always satisfied (implying the nonexistence of tight frames via the matrix extension approach), and give a constructive proof that when does exist, two functions with compact support are sufficient to constitute , while three guarantee symmetry/anti-symmetry, when the given refinable function is symmetric.

We report electric-field control of magnetism of (Co/Pt) multilayers involving perpendicular magnetic anisotropy with different Co-layer thicknesses grown on Pb(Mg,Nb)O-PbTiO (PMN-PT) FE substrates. For the first time, electric-field control of the interface magnetic anisotropy, which results in the spin reorientation transition, was demonstrated. The electric-field-induced changes of the bulk and interface magnetic anisotropies can be understood by considering the strain-induced change of magnetoelastic energy and weakening of Pt 5d-Co 3d hybridization, respectively. We also demonstrate the role of competition between the applied magnetic field and the electric field in determining the magnetization of the sample with the coexistence phase. Our results demonstrate electric-field control of magnetism by harnessing the strain-mediated coupling in multiferroic heterostructures with perpendicular magnetic anisotropy and are helpful for electric-field modulations of Dzyaloshinskii-Moriya interaction and Rashba effect at interfaces to engineer new functionalities.

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Topological insulators (TIs) have emerged as some of the most efficient spin-to-charge convertors because of their correlated spin-momentum locking at helical Dirac surface states. While endeavors have been made to pursue large "charge-to-spin" conversions in novel TI materials using spin-torque-transfer geometries, the reciprocal process "spinto-charge" conversion, characterized by the inverse Edelstein effect length (λ IEE ) in the prototypical TI material (Bi 2 Se 3 ), remains moderate. Here, we demonstrate that, by incorporating a "second" spin-splitting band, namely, a Rashba interface formed by inserting a bismuth interlayer between the ferromagnet and the Bi 2 Se 3 (i.e., ferromagnet/Bi/Bi 2 Se 3 heterostructure), λ IEE shows a pronounced increase (up to 280 pm) compared with that in pure TIs. We found that λ IEE alters as a function of bismuth interlayer thickness, suggesting a new degree of freedom to manipulate λ IEE by engineering the interplay of Rashba and Dirac surface states. Our finding launches a new route for designing TI-and Rashba-type quantum materials for next-generation spintronic applications.

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The epitaxial growth of ultrathin Fe film on Si(111) surface provides an excellent opportunity to investigate the contribution of magnetic anisotropy to magnetic behavior. Here, we present the anisotropic magnetoresistance (AMR) effect of Fe single crystal film on vicinal Si(111) substrate with atomically flat ultrathin p(2 × 2) iron silicide as buffer layer. Owing to the tiny misorientation from Fe(111) plane, the symmetry of magnetocrystalline anisotropy energy changes from the six-fold to a superposition of six-fold, four-fold and a weakly uniaxial contribution. Furthermore, the magnitudes of various magnetic anisotropy constants were derived from torque curves on the basis of AMR results. Our work suggests that AMR measurements can be employed to figure out precisely the contributions of various magnetic anisotropy constants.