The orthogonal wavelet lowpassed filters coefficients with arbitrary length are constructed in this paper. When N=2k and N k = − 1 2 , the general analytic constructions of orthogonal wavelet filters are put forward, respectively. The famous Daubechies filter and many other wavelet filters are tested by the proposed novel method, which is very useful for wavelet theory research and many applica...

Wavelet-based analysis has been broadly used in the study of brain computer interfaces(BCI), but in most cases these wavelet functions have not been designed taking into account the requirements of this field. In this study we propose a method to automatically generate wavelet-like functions by means of genetic algorithms. Results strongly indicate that it is possible to generate (evolve) wavel...

Wavelet methods are widely used to decompose fMRI, EEG, or MEG signals into time series representing neurophysiological activity in fixed frequency bands. Using these time series, one can estimate frequency-band specific functional connectivity between sensors or regions of interest, and thereby construct functional brain networks that can be examined from a graph theoretic perspective. Despite...

Explicit algorithms are presented for the generation of Daubechies compact orthogonal least asymmetric wavelet filter coefficients and the computation of their Holder regularity. The algorithms yield results for any number N of vanishing moments for the wavelets. These results extend beyond order N = 10 those produced by Daubechies for the values of the filter coefficients and those produced by...

During the past decade, with the birth of wavelet theory and multiresolution analysis, image processing techniques based on wavelet transform have been extensively studied and tremendously improved. JPEG 2000 uses wavelet transform and provides an integrated toolbox to better address increasing needs for compression. In this report, we study the basic concepts of JPEG2000, the LeGall 5/3 and Da...

In recent years Image and Signal compression have been receiving a lot of attention by scientists and researchers in order to improve storage and transmission capabilities. In this study we have compared the performance of Kekre’s wavelet with other wavelets viz. Haar and Daubechies 2 with respect to energy in the Low-Low (LL ), Low-High (LH) ,High-Low (HL) and High-High (HH) bands. The energy ...

The paper presents a novel despeckling method, based on Daubechies complex wavelet transform, for medical ultrasound images. Daubechies complex wavelet transform is used due to its approximate shift invariance property and extra information in imaginary plane of complex wavelet domain when compared to real wavelet domain. A wavelet shrinkage factor has been derived to estimate the noise-free wa...

Recent wavelet research has primarily focused on real-valued wavelet bases. However, complex wavelet bases offer a number of potential advantageous properties. For example, it has been recently suggested that the complex Daubechies wavelet can be made symmetric. However, these papers always imply that if the complex basis has a symmetry property, then it must exhibit linear phase as well. In th...

In this paper, we present an evaluation of various wavelet filters in the context of a JPEG 2000 based inter frame video coding system both on software and on hardware side. The software system itself is based on coding of a combination of intra frames and/or differential frames. Motion indicators are introduced and performed on the differential frames to determine the motion content (high or l...

In the last years, applying wavelets analysis has called the attention in a wide variety of practical problems, in particular for the numerical solutions of partial differential equations using different methods, as finite differences, semi-discrete techniques or the finite element method. In the construction of wavelet-based elements, instead of traditional polynomial interpolation, scaling an...