This papers gives an overview of wavelet transforms application to signal denoising problem. Wavelets perform well for this application and have been used before with great success. To further improve the transform efficiency adaptivity is introduced to traditional wavelet transforms. The lifting framework as a method to construct wavelets facilitates the effort to develop efficient adaptation ...

The ghost fluid method for the poor (GFMP) is an elegant, computationally efficient, and nearly conservative method for the solution of two-phase flow problems. It was developed in one dimension for the stiffened gas equation of state (EOS) and one-step time-discretization algorithms. It naturally extends to three dimensions but its extension to higher-order, multi-step time-discretization sche...

This paper proposes a three-dimensional (3D) integer wavelet transform with reduced amount of rounding noise. Non-separable multi-dimensional lifting structures are introduced to decrease the total number of lifting steps. Since the lifting step contains a rounding operation, variance of the rounding noise generated due to the rounding operation inside the transform is reduced. This paper also ...

We discuss a new transpose split method for parallel computations of three-dimensional Fourier transforms. By splitting the data along two dimensions over the processors it allows for a higher degree of parallelization than the original transpose split method. The traditional transpose split method involves one alltoall communication. The new method involves two communication steps in which eac...

We examine corresponding Cauchy-Riemann equations by using the non-commutativity for the product on split-biquaternions. Additionally, we describe the regularity of functions and properties of their differential equations on split-biquaternions. We investigate representations and calculations of the derivatives of functions of split-biquaternionic variables. c ©2016 all rights reserved.