Since the discovery of the compactly supported conjugate quadrature filter (CQF) based discrete wavelet transform (DWT) (Smith & Barnwell, 1986; Daubechies, 1988), a variety of data and image processing tools have been developed. It is well known that real-valued CQFs have nonlinear phase, which may cause image blurring or spatial dislocations in multi-resolution analysis. In many applications ...

State-of-the-art image compression and reconstruction techniques utilize wavelets. Recently published research demonstrated that a genetic algorithm (GA) is capable of evolving non-wavelet transforms that consistently outperform wavelets when applied to a broad class of images under conditions subject to quantization error. This paper describes new results that build upon previous research by d...

This paper deals with the design of interpolating wavelets based on a variety of Lagrange functions, combined with novel signal processing techniques for digital imaging. Halfband Lagrange wavelets, B-spline Lagrange wavelets and Gaussian Lagrange (Lagrange distributed approximating functional (DAF)) wavelets are presented as specific examples of the generalized Lagrange wavelets. Our approach ...

This paper studies the construction of highly symmetric compactly supported wavelets for hexagonal data/image and triangle surface multiresolution processing. Recently hexagonal image processing has attracted attention. Compared with the conventional square lattice, the hexagonal lattice has several advantages, including that it has higher symmetry. It is desirable that the filter banks for hex...

We study the scaling behavior of the fluctuations, as extracted through wavelet coefficients based on discrete wavelets. The analysis is carried out on a variety of physical data sets, as well as Gaussian white noise and binomial multi-fractal model time series and the results are compared with continuous wavelet based average wavelet coefficient method. It is found that high-pass coefficients ...

This paper concerns the construction of highly symmetric compactly supported wavelets for hexagonal data/image and triangle surface multiresolution processing. Recently hexagonal image processing has attracted attention. Compared with the conventional square lattice, the hexagonal lattice has several advantages, including that it has higher symmetry. It is desirable that the filter banks for he...

This paper introduces triangular wavelets, which are two-dimensional nonseparable biorthogonal wavelets defined on the regular triangular lattice. The construction that we propose is aimed at preserving isotropy, and a simple nonseparable extension of one-dimensional interpolating wavelets followed by a straightforward generalization. Resulting three oriented high-pass filters are symmetrically...