We consider the semilinear stochastic heat equation perturbed by additive noise. After time-discretization by Euler’s method the equation is split into a linear stochastic equation and a non-linear random evolution equation. The linear stochastic equation is discretized in space by a non-adaptive wavelet-Galerkin method. This equation is solved first and its solution is substituted into the non...

This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell’s equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of the field at that time instant. In the regions where the fields are highly localized, the method assigns more grid points; and in the regions where the fiel...

The paper presents computations of decaying two{dimensional turbulence in an adaptive wavelet basis. At each time step the vorticity is represented by an adaptively selected set of wavelet functions which adjusts to the instantaneous distribution of vorticity. The results of this new algorithm are compared to a classical Fourier method and a Fourier method supplemented with wavelet compression ...

In this paper, a robust digital image watermarking approach using adaptive quantization of wavelet packet coefficients was proposed. The original image is decomposed by discrete wavelet packet transform and the dominant wavelet coefficients are selected for watermark embedding from each sub-band except the lowest frequency one. Then, each watermark bit is adaptively embedded with different stre...

This paper aims to make the super-resolution of a high-resolution image from a sequence of low-resolution frames containing non-stationary objects. The challenges of making super-resolution image, like unavoidable smoothing effects, introduction of artifacts, computational efficiency in time and computational efficiency in memory requirements, are considered and a novel method is proposed to so...

We present an adaptive wavelet method for the numerical solution of elliptic operator equations with nonlinear terms. This method is developed based on tree approximations for the solution of the equations and adaptive fast reconstruction of nonlinear functionals of wavelet expansions. We introduce a constructive greedy scheme for the construction of such tree approximations. Adaptive strategie...

We study a spline wavelet alternative direction implicit (SW-ADI) algorithm for solving two-dimensional reaction diffusion equations. This algorithm is based on a collocation method for PDEs with a specially designed spline wavelet for the Sobolev space H 2(I ) on a closed interval I. By using the tensor product nature of adaptive wavelet meshes, we propose a SW-ADI method for two-dimensional p...

In the fluorescence detection system, noise will affect the sensitivity of the system. The method using Stationary Wavelet Transform to de-noise fluorescence signals based on adaptive wavelet entropy is studied. The de-noising effects of dbN families are compared, and then the db7 wavelet is chosen as the optimal wavelet. The noised fluorescence signal is decomposed at 5 levels via Discrete Wav...

An adaptive wavelet-based method is proposed for solving TV(total variation)–Allen–Cahn type models for multi-phase image segmentation. The adaptive algorithm integrates (i) grid adaptation based on a threshold of the sparse wavelet representation of the locally-structured solution; and (ii) effective finite difference on irregular stencils. The compactly supported interpolating-type wavelets e...

In this paper we propose the use of integer wavelet [2] as a decorrelation stage for adaptive context based lossless audio coding. The original wideband audio signal is first decomposed in wavelet subbands. The resulted coefficients are integer valued and therefore can be transmitted using an adaptive context based method, in a lossless manner, the decoder being able to reconstruct them and aft...