Non-equispaced B-spline wavelets

This paper has three main contributions. The first is the construction of wavelet transforms from B-spline scaling functions defined on a grid of non-equispaced knots. The new construction extends the equispaced, biorthogonal, compactly supported Cohen-Daubechies-Feauveau wavelets. The new construction is based on the factorisation of wavelet transforms into lifting steps. The second and third contributions are new insights on how to use these and other wavelets in statistical applications. The second contribution is related to the bias of a wavelet representation. It is investigated how the fine scaling coefficients should be derived from the observations. In the context of equispaced data, it is common practice to simply take the observations as fine scale coefficients. It is argued in this paper that this is not acceptable for non-interpolating wavelets on non-equidistant data. Finally, the third contribution is the study of the variance in a non-orthogonal wavelet transform in a new framework, replacing the numerical condition as a measure for non-orthogonality. By controlling the variances of the reconstruction from the wavelet coefficients, the new framework allows us to design wavelet transforms on irregular point sets with a focus on their use for smoothing or other applications in statistics.Comment: 42 pages, 2 figure

Single Frame Image super Resolution using Learned Directionlets

In this paper, a new directionally adaptive, learning based, single image super resolution method using multiple direction wavelet transform, called Directionlets is presented. This method uses directionlets to effectively capture directional features and to extract edge information along different directions of a set of available high resolution images .This information is used as the training set for super resolving a low resolution input image and the Directionlet coefficients at finer scales of its high-resolution image are learned locally from this training set and the inverse Directionlet transform recovers the super-resolved high resolution image. The simulation results showed that the proposed approach outperforms standard interpolation techniques like Cubic spline interpolation as well as standard Wavelet-based learning, both visually and in terms of the mean squared error (mse) values. This method gives good result with aliased images also.Comment: 14 pages,6 figure

Adaptive Wavelet Collocation Method for Simulation of Time Dependent Maxwell's Equations

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 fields are sparse, there will be less grid points. On the adapted grid, update schemes with high spatial order and explicit time stepping are formulated. The method has high compression rate, which substantially reduces the computational cost allowing efficient use of computational resources. This adaptive wavelet collocation method is especially suitable for simulation of guided-wave optical devices

Reversible color video watermarking scheme based on hybrid of integer-to-integer wavelet transform and Arnold transform

Unauthorized redistribution and illegal copying of digital contents are serious issues which have affected numerous types of digital contents such as digital video. One of the methods, which have been suggested to support copyright protection, is to hide digital watermark within the digital video. This paper introduces a new video watermarking system which based on a combination of Arnold transform and integer wavelet transforms (IWT). IWT is employed to decompose the cover video frames whereby Arnold transform is used to scramble the watermark which is a grey scale image. Scrambling the watermark before the concealment makes the transmission more secure by disordering the information. The system performance was benchmarked against related video watermarking schemes, in which the evaluation processes consist of testing against several video operations and attacks. Consequently, the scheme has been demonstrated to be perfectly robust