Application of symmetric orthogonal multiwavelets and prefilter technique for image compression

Multiwavelets are new addition to the body of wavelet theory. There are many types of symmetric multiwavelets such as Geronimo-Hardin-Massopust (GHM) and Chui-Lian (CL) multiwavelets. However, the matrix filter generating the GHM system multiwavelets does not satisfy the symmetric property. For this reason, this paper presents a new method to construct the symmetric orthogonal matrix filter, which leads to the symmetric orthogonal multiwavelets (SOM). Moreover, we analyze the prefilter technique, corresponding to the symmetric orthogonal matrix filter, to get a good combining frequency response. To prove the good property of SOM in image compression application, we compared the compression effect with other writers' work, which was in published literature.Facultad de Informátic

Denoising by multiwavelet singularity detection

Wavelet denoising by singularity detection was proposed as an algorithm that combines Mallat and Donoho’s denoising approaches. With wavelet transform modulus sum, we can avoid the error and ambiguities of tracing the modulus maxima across scales and the complicated and computationally demanding reconstruction process. We can also avoid the visual artifacts produced by shrinkage. In this paper, we investigate a multiwavelet denoising algorithm based on a modified singularity detection approach. Improved signal denoising results are obtained in comparison to the single wavelet case

Low Bit-rate Color Video Compression using Multiwavelets in Three Dimensions

In recent years, wavelet-based video compressions have become a major focus of research because of the advantages that it provides. More recently, a growing thrust of studies explored the use of multiple scaling functions and multiple wavelets with desirable properties in various fields, from image de-noising to compression. In term of data compression, multiple scaling functions and wavelets offer a greater flexibility in coefficient quantization at high compression ratio than a comparable single wavelet. The purpose of this research is to investigate the possible improvement of scalable wavelet-based color video compression at low bit-rates by using three-dimensional multiwavelets. The first part of this work included the development of the spatio-temporal decomposition process for multiwavelets and the implementation of an efficient 3-D SPIHT encoder/decoder as a common platform for performance evaluation of two well-known multiwavelet systems against a comparable single wavelet in low bitrate color video compression. The second part involved the development of a motion-compensated 3-D compression codec and a modified SPIHT algorithm designed specifically for this codec by incorporating an advantage in the design of 2D SPIHT into the 3D SPIHT coder. In an experiment that compared their performances, the 3D motion-compensated codec with unmodified 3D SPIHT had gains of 0.3dB to 4.88dB over regular 2D wavelet-based motion-compensated codec using 2D SPIHT in the coding of 19 endoscopy sequences at 1/40 compression ratio. The effectiveness of the modified SPIHT algorithm was verified by the results of a second experiment in which it was used to re-encode 4 of the 19 sequences with lowest performance gains and improved them by 0.5dB to 1.0dB. The last part of the investigation examined the effect of multiwavelet packet on 3-D video compression as well as the effects of coding multiwavelet packets based on the frequency order and energy content of individual subbands

An Orthogonal Scaling Vector Generating a Space of C1C^1 Cubic Splines Using Macroelements

The main result of this paper is the creation of an orthogonal scaling vector of four differentiable functions, two supported on $[-1,1]$ and two supported on $[0,1]$, that generates a space containing the classical spline space \s_{3}^{1}(\Z) of piecewise cubic polynomials on integer knots with one derivative at each knot. The author uses a macroelement approach to the construction, using differentiable fractal function elements defined on $[0,1]$ to construct the scaling vector. An application of this new basis in an image compression example is provided

Disparity estimation using TI multi-wavelet transform

A multi-resolution image matching technique based on translation invariant discrete multi-wavelet transform followed by a coarse to fine matching strategy is presented. The technique addresses the estimation of optimal corresponding points and the corresponding disparity maps in the presence of occlusion, ambiguity and illuminative variations in the two perspective views taken by two different cameras or at different lighting conditions. The problem of occlusion and ambiguity is addressed explicitly by a geometric optimization approach along with the uniqueness constraint whereas the illuminative variation is dealt with by using windowed normalized correlation on the discrete multi-wavelet coefficients.<br /

Color Texture Classification Using Adaptive Discrete Multiwavelets Transform

The classification of textures images has attracted the attention of many researchers. The multiscale techniques for gray level texture analysis have been intensively studied. In this paper, we aim on extending texture classification of color images by using the multiwavelets transform, a new notion addition to wavelet. The recognition of textures deals with both feature extraction and classification phases. In the classification phase the evolutionary computation techniques (genetic programming) was used for more speed recognition result evaluation. In our experiment results the proposed method has achieved 99.6% test accuracy on an average. In addition, the experimental results also show that classification rules generated by this approach are robust to some noises on texture

Guest Editorial: Special Issue On Multirate Systems, Filter Banks, Wavelets, And Applications

The last decade has seen a tremendous amount of activity and emergence of applications in the areas of filter banks and wavelets. These topics are of such wide interest that there have been papers in many different journals, conferences, and workshops in diverse disciplines. However, many aspects of the theory, design, and application of filter banks and wavelets are of great interest to the circuits and systems community as well. Our editorial team felt that this was a perfect time to put together a special issue with state-of-the-art papers on these popular topics. All of the papers have been peer-reviewed according to the usual practice of this TRANSACTIONS. Almost in parallel, there is also a similar special issue (April 1998) by the IEEE TRANSACTIONS ON SIGNAL PROCESSING, with a slightly greater emphasis on applications. Many well-known authors have contributed articles to these special issues and we expect these to serve as valuable references for a long time to come