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...

To construct a very smooth nonseparable multiscaling function, we impose polynomial approximation order 2 and add new conditions on the polyphase highpass filters. We work with a dilation matrix generating quincunx lattices, and fix the index set. Other imposed conditions are orthogonal filter bank and balancing. We construct a smooth, compactly supported multiscaling function and multiwavelet,...

The Gabor expansion, which maps the time domain signal into the joint time and frequency domain, has long been recognized as a very useful tool in signal processing. Its applications, however, were limited due to the difficulties associated with selecting the Gabor coefficients. Because timeshifted and frequency-modulated elementary functions in general do not constitute an orthogonal basis, th...

This paper presents a construction of compactly supported biorthogonal spline wavelets in L2(IR ). In particular, a concrete method for the construction of bivariate compactly supported biorthogonal wavelets from box splines of increasing smoothness is provided. Several examples are given to illustrate the method. Key-Words:multivariate biorthogonal wavelets, multivariate wavelets, box splines,...

We present a study on applications of multiwavelet analysis to image compression, where filter coefficients form matrices. As a multiwavelet filter bank has multiple channels of inputs, we investigate the data initialization problem by considering prefilters and postfilters that may give more efficient representations of the decomposed data. The interpolation postfilter and prefilter are formul...

Biorthogonal bases of compactly-supported wavelets are characterized by the FIR perfect-reconstruction filterbanks to which they correspond. In this paper we develop explicit representations of all such filterbanks, allowing us to generate every possible biorthogonal compactly-supported wavelet basis. For these filterbanks, the product H(z) = H(z) e H(z) of the two lowpass filters must have N 2...

The objective of this paper is to establish a complete characterization of multiwavelet packets associated with matrix dilation on general lattices $Gamma$ in $mathbb R^d$ by virtue of time-frequency analysis, matrix theory and operator theory.

In this paper, the properties of the all phase biorthogonal transform (APBT) matrix are deduced based on the concepts of all phase biorthogonal transform. A novel algorithm is presented to compress color image using the all phase Walsh biorthogonal transform (APWBT), the all phase discrete cosine biorthogonal transform (APDCBT) and the all phase inverse discrete cosine biorthogona transform (AP...

We construct oblique multi-wavelets bases which encompass the orthogonal multi-wavelets and the biorthogonal uni-wavelets of Cohen, Deaubechies and Feauveau. These oblique multi-wavelets preserve the advantages of orthogonal and biorthogonal wavelets and enhance the flexibility of wavelet theory to accommodate a wider variety of wavelet shapes and properties. Moreover, oblique multi-wavelets ca...

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...