Abstract: In seismic data processing, attenuation of random noise
is the basic step to improve quality of data for further application
of seismic data in exploration and development in different gas
and oil industries. The signal-to-noise ratio of the data also highly
determines quality of seismic data. This factor affects the reliability
as well as the accuracy of seismic signal during interpretation
for different purposes in different companies. To use seismic data
for further application and interpretation, we need to improve the
signal-to-noise ration while attenuating random noise effectively.
To improve the signal-to-noise ration and attenuating seismic
random noise by preserving important features and information
about seismic signals, we introduce the concept of anisotropic
total fractional order denoising algorithm. The anisotropic total
fractional order variation model defined in fractional order bounded
variation is proposed as a regularization in seismic denoising. The
split Bregman algorithm is employed to solve the minimization
problem of the anisotropic total fractional order variation model
and the corresponding denoising algorithm for the proposed method
is derived. We test the effectiveness of theproposed method for
synthetic and real seismic data sets and the denoised result is
compared with F-X deconvolution and non-local means denoising
algorithm.
Abstract: In the present paper, we consider the generalized form of Baskakov Durrmeyer operators to study the rate of convergence, in simultaneous approximation for functions having derivatives of bounded variation.
Abstract: We present a new quadrature rule based on the spline
interpolation along with the error analysis. Moreover, some error
estimates for the reminder when the integrand is either a Lipschitzian
function, a function of bounded variation or a function whose
derivative belongs to Lp are given. We also give some examples
to show that, practically, the spline rule is better than the trapezoidal
rule.
Abstract: This paper is concerned with the numerical minimization
of energy functionals in BV (
) (the space of bounded variation
functions) involving total variation for gray-scale 1-dimensional inpainting
problem. Applications are shown by finite element method
and discontinuous Galerkin method for total variation minimization.
We include the numerical examples which show the different recovery
image by these two methods.