International Journal of Wavelets, Multiresolution and Information Processing

Samples from stochastic signals having sufficient complexity need reveal only a little unexpected shared structure, in order to reject the hypothesis that they are independent. The mere failure of a test of statistical independence can thereby serve as a basis for recognizing stochastic patterns, provided they possess enough degrees-of-freedom, because all unrelated ones would pass such a test. This paper discusses exploitation of this statistical principle, combined with wavelet image coding methods to extract phase descriptions of incoherent patterns. Demodulation and coarse quantization of the phase information creates decision environments characterized by well-separated clusters, and this lends itself to rapid and reliable pattern recognition.

Two different approaches for joint detection and estimation of signals embedded in stationary random noise are considered and compared, for the subclass of amplitude and frequency modulated signals. Matched filter approaches are compared to time-frequency and time scale based approaches. Particular attention is paid to the case of the so-called "power-law chirps", characterized by monomial and polynomial amplitude and frequency functions. As target application, the problem of gravitational waves at interferometric detectors is considered.

This paper presents a study on applications of multiwavelet analysis to image compression. The biorthogonality and perfect reconstruction conditions are applied to multiwavelet filters. As a multiwavelet filter bank has multiple channels of inputs, the data structure of inputs to the multiwavelet system should be taken into consideration in multiwavelet decomposition and reconstruction algorithms. 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 formulated, which are capable to provide a better approximate image at each coarser resolution level. A design process is given to obtain both filters having compact supports, if exist. Image compression performances of three multiwavelet systems are studied in comparison to those of single wavelet systems.

We investigate the lifting scheme as a method for constructing compactly supported biorthogonal scaling functions and wavelets. A well-known issue arising with the use of this scheme is that the resulting functions are only formally biorthogonal. It is not guaranteed that the new wavelet bases actually exist in an acceptable sense. To verify that these bases do exist one must test an associated linear operator to ensure that it has a simple eigenvalue at one and that all its remaining eigenvalues have modulus less than one, a task which becomes numerically intensive if undertaken repeatedly. We simplify this verification procedure in two ways: (i) we show that one need only test an identifiable half of the eigenvalues of the operator, (ii) we show that when the operator depends upon a single parameter, the test first fails for values of that parameter at which the eigenvalue at one becomes a multiple eigenvalue. We propose that this new verification procedure comprises a first step towards determining simple conditions, supplementary to the lifting scheme, to ensure existence of the new wavelets generated by the scheme and develop an algorithm to this effect.

We propose an integrated wavelet-based framework of the active contour model (snake) for segmentation and motion tracking of deformable objects in video sequences. The input image frame is represented by means of wavelet transform. First, the moduli of wavelet transform coefficients are used in a multi-resolution motion estimation process to find the initial snake contour in the current frame. The presented multi-resolution motion estimation methods allow a larger movement of the tracked object than does traditional image-based motion estimation. Secondly, the wavelet transform modulus at each scale is considered in the energy function of the snake model. The snake computation is based on a coarse-to-fine scale continuation method. Application of the proposed methods to biological cell tracking is demonstrated in experiments.

This paper describes two examples of real-life applications of texture segmentation using M-band wavelets. In the first part of the paper, an efficient and computationally fast method for segmenting text and graphics part of a document image based on textural cues is presented. It is logical to assume that the graphics part has different textural properties than the non-graphics (text) part. So, this is basically a two-class texture segmentation problem. The second part of the paper describes a segmentation scheme for another real-life data such as remotely sensed image. Different quasi-homogeneous regions in the image can be treated to have different texture properties. Based on this assumption the multi-class texture segmentation scheme is applied for this purpose.