International Journal of Wavelets, Multiresolution and Information Processing

It is shown under a divisibility condition the sampling matrix for a filter bank can be replaced without loss of perfect reconstruction. This is the generalization of the common knowledge that removing up/downsampling will not alter perfect reconstruction. The result provides a simple way to implement redundant perfect reconstruction filter banks, which constitute tight frames of l₂(Zⁿ) when iterated. As an example, a quincunx-sampled frame is presented, which is nearly shift-invariant as well as limited-redundancy.

Automatic target tracking is a challenging task in video surveillance applications. Here, an offline target-tracking system in video sequences using Discrete Wavelet Transform is presented. The proposed algorithm uses co-occurrence features, derived from sub-bands of discrete wavelet transformed sub-blocks, obtained from individual video frames, to identify a seed in the frame. Then, the region-growing algorithm is applied to detect and track the target. The results of the proposed target detection and tracking system in video sequences are found to be satisfactory. The effectiveness of the target-tracking algorithm has been proved as the target gets detected, irrespective of size of the target, perspective view and cluttered environment.

Representing the image to be inpainted in an appropriate sparse dictionary, we introduce a novel method for the filling-in of structure and texture in regions of missing image information. In the morphological component analysis (MCA) inpainting approach, a TV penalty is added to better reduce ringing artifacts. However, the incorporation of TV penalty terms leads to PDE schemes that are numerically intensive. Inspired by the works of Daubechies–Teschke and Borup–Nielsen, we replace the TV term by a term. It results in an iterative curvelet thresholding scheme for the structure image inpainting. In the whole inpainting process, an alternative approach is presented to layer inpainting. Experimental results show the performance of the algorithm.

Since its advent, the use of digital camera in mobile phones is getting more popular, where information retrieval based on visual appearance of an object is very useful when specific parameters for the object are not known. Though it is well-liked, it needs energy aware algorithms to carry out the various tasks such as segmentation and feature extraction. In this paper, a new energy aware fuzzy color segmentation algorithm is proposed and which has been applied for face segmentation in criminal identification using mobile devices. The criminals in the application are in three classes. They are New Criminal (NC), Suspected Criminal (SC) and Confirmed Criminal (CC). It is basically a mobile image-based content search engine that takes photographs of criminals as image queries and finds their relevant contents by matching them to the similar contents in the criminal databases. The energy aware fuzzy color segmentation is used to obtain the most significant parts of an image — facial regions of the persons and which are used in building image-based queries to the databases. Content search methodology in the application is also improved through the fuzzy modeling to make the application more flexible and simpler. Through the experiment conducted, it has been found that the proposed color segmentation algorithm is more robust and it reduces the computational time in searching process by minimizing the number of false cases. It could detect the faces in the images where the other known algorithms have failed to detect.

A new method by combining wavelet packet transform with kernel learning algorithms is proposed to estimate the mental fatigue state in this paper. The first step of this method is to investigate the impact of long term mental arithmetic task on psychology and physiology of subjects by subjective self-reporting measures, action performance test, power spectral indices of HRV and wavelet packet parameters of EEG. The second step is to calculate the wavelet packet features of all EEG data segments, including relative wavelet packet energy parameters in four frequency bands, wavelet packet entropy and three ratio indices. Finally, kernel principal component analysis (KPCA) and support vector machine (SVM) are jointly applied to differentiate two mental fatigue states. The investigation suggests that the joint KPCA-SVM method is able to effectively reduce the dimensionality of the feature vectors, speed up the convergence in the training of SVM and achieve higher classification accuracy (88%) of the mental fatigue state. Hence KPCA-SVM could be a promising model for the estimation of mental fatigue.

A basic function D(x,y,z) associated with the general wavelet transform is defined and its properties are investigated. Using D(x,y,z) associated with the wavelet transform, translation and convolution for this transform are defined and certain existence theorems are proved. An approximation theorem involving wavelet convolution is also proved.

Most of the interesting groups encountered in the physics literature are semidirect product groups. These groups are of the general form G = H ×_τ K, where H and K are locally compact groups. In this paper, we consider the quasi regular representation on such a group G and investigate when it is possible to construct a family of coherent states associated to this representation.

In recent years, image coding based on wavelet transform has made rapid progress. In this paper, quincunx lifting scheme in wavelet transform is introduced and all phase interpolation filter banks which can be used in the lifting scheme for prediction and update are designed. Based on the basic idea of set partitioning in hierarchical trees (SPIHT) algorithm, the binary tree image coding algorithm is proposed. Just like SPIHT, the encoding algorithms can be stopped at any compressed file size or let run until the compressed file is a representation of a nearly lossless image. The experimental results on test images show that compared with SPIHT algorithm, the PSNRs of the proposed algorithm are superior by about 0.5 dB at the same bit rates and the subjective quality of reconstructed images is also better.