A Hybrid Approach to Spectral Reconstruction of Piecewise Smooth Functions

HYBRID FUNCTIONS APPROACH AND PIECEWISE CONSTANT FUNCTION BY COLLOCATION METHOD FOR THE NONLINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS

In this work, we will compare two approximation method based on hybrid Legendre andBlock-Pulse functions and a computational method for solving nonlinear Fredholm-Volterraintegral equations of the second kind which is based on replacement of the unknown functionby truncated series of well known Block-Pulse functions (BPfs) expansion

Reducing the Effects of Noise in Image Reconstruction

Fourier spectral methods have proven to be powerful tools that are frequently employed in image reconstruction. However, since images can be typically viewed as piecewise smooth functions, the Gibbs phenomenon often hinders accurate reconstruction. Recently, numerical edge detection and reconstruction methods have been developed that effectively reduce the Gibbs oscillations while maintaining h...

Spectral Reconstruction of Piecewise Smooth Functions

Planelet Transform: A New Geometrical Wavelet for Compression of Kinect-like Depth Images

With the advent of cheap indoor RGB-D sensors, proper representation of piecewise planar depth images is crucial toward an effective compression method. Although there exist geometrical wavelets for optimal representation of piecewise constant and piecewise linear images (i.e. wedgelets and platelets), an adaptation to piecewise linear fractional functions which correspond to depth variation ov...

Spectral Reconstruction of Piecewise Smooth Functions from Their Discrete Data

Abstract. This paper addresses the recovery of piecewise smooth functions from their discrete data. Reconstruction methods using both pseudo-spectral coefficients and physical space interpolants have been discussed extensively in the literature, and it is clear that an a priori knowledge of the jump discontinuity location is essential for any reconstruction technique to yield spectrally accurat...