Orthogonal wavelet bases have been developed using multiple mother wavelet functions. Applying the discrete multiwavelet transform requires the input data to be preprocessed to obtain a more economical decomposition. Four characteristics of a preprocessing method are presented: length, degree, orthogonality and frequency response. A minimal preelter is deened to have length one and highest atta...

Multiwavelet transform can be implemented by treestructured matrix lter bank, which operates on vector sequence input instead of scalar ones. Therefore, unlike in scalar wavelet system, preprocessing is usually required to extract vector sequence input from the input signal for better performance. A 2-D approximation-based preprocessing scheme for GHM (Geronimo, Hardin and Massopust) discrete m...

A recent paper reported highly accurate density functional theory results for atomization energies and dipole moments using a multiwavelet-based method and compared the results with those obtained by standard Gaussian basis sets of the aug-cc-pVXZ type. Typical errors with the large aug-cc-pV5Z basis set were in the 0.2 kcal/mol range with outliers displaying errors of ∼2 kcal/mol, and these re...

This paper presents a new video coding technique using multiwavelet transform and multi-stage vector quantization. Three types of redundancies that are common in video sequence are spatial, temporal and psycho visual redundancies. In this work, the spatial redundancy in the video is minimized using multiwavelet transform. The transform coefficients are then quantized using multi-stage vector qu...

We review some recent results on multiwavelet methods for solving integral and partial differential equations and present an efficient representation of operators using discontinuous multiwavelet bases, including the case for singular integral operators. Numerical calculus using these representations produces fast O(N) methods for multiscale solution of integral equations when combined with low...

Multiwavelet is attracting more and more attention for its good properties such as orthogonality, symmetry, compactly supported, high vanishing moment and balance contrast with the traditional wavelet. These properties, along with optimum time-frequency resolution (OPTFR) are all very important in image processing. Multifilter banks having all properties of symmetry, balancing, optimum time-fre...

Motivated by [B. Han and Q. Mo, Adv. Comp. Math. 18 (2003) 211-245] and [B. Han and Z. Shen, Constr. Approx. 29 (2009) 369-406], we propose dual two-direction frames in dual Sobolev spaces (H(R), H−s(R)), with s > 0. Based on the dual two-direction frames from a pair of two-direction refinable functions, dual multiwavelet frames with symmetry {Ψ(x) := (ψ 1(x), ψ 2(x)) T }`=1 and {Ψ̃(x) : = (ψ̃ 1(...

In this paper, we propose digital image watermarking algorithm in the multiwavelet transform domain. The embedding technique is based on the quantization index modulation technique and this technique does not require the original image in the watermark extraction. We have developed an optimization technique using the genetic algorithm to search for optimal quantization steps to improve the qual...