We present a characterization of the approximation errors of the Post-Widder and the Gamma operators in Lp[0, ∞), 1 ≤ p ≤ ∞, with a weight x γ for any real γ. Two types of characteristics are used – weighted K-functionals of the approximated function itself and the classical fixed step moduli of smoothness taken on a simple modification of it.

We prove that the level sets of a real C function of two variables near a non-degenerate critical point are of class C [s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at an elliptic or hyperbolic point, and in particular at an umbilic point. We go on to use the results to study symmetry sets of the planar sections. We also anal...

We consider the smoothness of solutions of a system of reenement equations written in the form as = X 2ZZ a()(2 ?) where the vector of functions = (1 ; : : : ; r) T is in (L p (IR)) r and a is a nitely supported sequence of r r matrices called the reenement mask. We use the generalized Lipschitz space Lip (; L p (IR)), > 0, to measure smoothness of a given function. Our method is to relate the ...

Deferring discretization can occasionally change our perspective on imaging problems. To illustrate, we offer a reformulation of regularized computed tomography (CT) in which the large system of coupled equations for the unknown smoothed image is decoupled into many smaller and simpler equations, each for a separate projection. Regularized CT thus becomes a two-stage process of (nonhomogeneous)...

Accurate measurement of longitudinal changes of anatomical structure is important and challenging in many clinical studies. Also, for identification of disease-affected regions due to the brain disease, it is extremely necessary to register a population data to the common space simultaneously. In this paper, we propose a new method for simultaneous longitudinal and groupwise registration of a s...

We establish absolute continuity of the elliptic measure associated to certain second order elliptic equations in either divergence or nondivergence form, with drift terms, under minimal smoothness assumptions on the coefficients.

The study aimed at comparing the resolution and effectiveness of three-electrode arrays (Wenner-α, Wenner-β, Wenner-γ) in 2D Electrical resistivity method using Numerical analysis geological models. Three synthetic models that simulate block-one dyke water layer were generated RES2DMOD software. inversion used for was based on smoothness-constrained least-square which carried out with RES2DINV....

Besov spaces classify signals and images through the Besov norm, which is based on a deterministic smoothness measurement. Recently, we revealed the relationship between the Besov norm and the likelihood of an independent generalized Gaussian wavelet probabilistic model. In this paper, we extend this result by providing an information-theoretic interpretation of the Besov norm as the Shannon co...

Producing an accurate motion flow field is very difficult at motion boundaries. We present a novel, noniterative approach for segmentation from image motion, based on two voting processes, in different dimensional spaces. By expressing the motion layers as surfaces in a 4-D space, a voting process is first used to enforce the smoothness of motion and determine an estimation of pixel velocities,...