International Journal of Wavelets, Multiresolution and Information Processing

The multiscaling function of Alpert multiwavelet system and Chui–Lian multiwavelet system consist of one symmetric and one antisymmetric scaling functions. In its single level decomposition, only one of 16 subband blocks may be considered as a core part because the antisymmetric scaling function may play the high pass filter. We complete the Alpert multiwavelet system by determining the high pass filter using the algorithm of paraunitary extension principle. Taking the advantage of the symmetric/antisymmetric (SA) feature of Alpert and Chui–Lian multiscaling functions, our iteration (SA iteration) of multiwavelet decomposition continues to the core part (1/16 of subbands) for the image denoising problem while the traditional iteration applies to the one fourth of 16 subbands as core parts. The numerical results demonstrate that our method of symmetric/antisymmetric iteration exhibits performance superior to the traditional ways.

Wavelet packets are subsets of a multiresolution analysis and retain many of the orthogonality, smoothness and localization properties of their parent wavelets. In this paper, we study the construction of p-wavelet packets associated with multiresolution p-analysis defined by Farkov for L²(ℝ⁺). The collection of all dilations and translations of the wavelet packets defines the general wavelet packets and is an overcomplete system.

Rate control plays an essential role in video coding and transmission to provide the best video quality at the receiver's end given the constraint of certain network conditions. In this paper, a rate control algorithm using the Quality Factor (QF) optimization method is proposed for the wavelet-based video codec and implemented on an open source Dirac video encoder. A mathematical model which we call Rate-QF (R - QF) model is derived to generate the optimum QF for the current coding frame according to the target bitrate. The proposed algorithm is a complete one pass process and does not require complex mathematical calculation. The process of calculating the QF is quite simple and further calculation is not required for each coded frame. The experimental results show that the proposed algorithm can control the bitrate precisely (within 1% of target bitrate in average). Moreover, the variation of bitrate over each Group of Pictures (GOPs) is lower than that of H.264. This is an advantage in preventing the buffer overflow and underflow for real-time multimedia data streaming.

Deblurring in the presence of noise is a hard problem, especially in ultrasonic and CT images. In this paper, we propose a new method of image deblurring in presence of noise, using symmetric Daubechies complex wavelet transform. The proposed method is based on shrinkage of multilevel Daubechies complex wavelet coefficients, and is adaptive as it uses shrinkage function based on the variance of wavelet coefficients as well as the mean and the median of absolute wavelet coefficients at a particular level. The results obtained after the application of the proposed method demonstrate an improved performance over other related methods available in literature.

This paper deals with the theory of frames for vector-valued Weyl–Heisenberg wavelets (VVWHW). We derive frame and the corresponding frame bounds for VVWHW.

This paper presents a novel biologically-inspired and wavelet-based model for extracting features of faces from face images. The biological knowledge about the distribution of light receptors, cones and rods, over the surface of the retina, and the way they are associated with the nerve ends for pattern vision forms the basis for the design of this model. A combination of classical wavelet decomposition and wavelet packet decomposition is used for simulating the functional model of cones and rods in pattern vision. The paper also describes the experiments performed for face recognition using the features extracted on the AT & T face database (formerly, ORL face database) containing 400 face images of 40 different individuals. In the recognition stage, we used the Artificial Neural Network Classifier. A feature vector of size 40 is formed for face images of each person and recognition accuracy is computed using the ANN classifier. Overall recognition accuracy obtained for the AT & T face database is 95.5%.

Statistical modeling of wavelet coefficients is a critical issue in wavelet domain signal processing. By analyzing the defects of other existing methods, and exploiting the local dependency of wavelet coefficients, an efficient statistical model is proposed. Improved variance estimation of the local wavelet coefficients can be obtained using the new model. Then we apply an approximate minimum mean squared error (MMSE) estimation procedure to restore the wavelet image coefficients. The modeling process is computational cost saving, and the denoising experiments show the algorithm outperforms other approaches in peak-signal-to-noise ratio (PSNR).

A new approach to fault diagnosis of bearings based on the Teager–Huang Transform (THT) is presented. This method is based on the Empirical Mode Decomposition (EMD) and Teager Kaiser Energy Operator (TKEO) techniques. EMD can adaptively decompose the vibration signal into a series of zero mean Amplitude Modulation-Frequency Modulation (AM-FM) Intrinsic Mode Functions (IMFs). TKEO can track the instantaneous amplitude and instantaneous frequency of the AM-FM component at any instant. The experimental examples are conducted to evaluate the effectiveness of the proposed approach. The experimental results provide strong evidence that the performance of the Teager–Huang Transform approach is better than that of the Hilbert–Huang Transform approach for bearing fault detection. The Teager–Huang Transform has better resolution than the Hilbert–Huang Transform. The Teager–Huang Transform can effectively diagnose the faults of the bearing, thus providing a viable processing tool for gearbox defect monitoring.

In this paper, we incorporate Trellis Coded Quantization (TCQ) into a two-stage multiple description coding structure to obtain granular gain over two-stage multiple description Scalar Quantizer (SQ). Analysis and experiment on Gaussian signal show that the performance of the proposed scheme can achieve larger gain than that of the two-stage SQ scheme because of better performance of TCQ. The proposed scheme for image coding is shown to be more effective than other relevant multiple description image coding schemes in terms of central-side-distortion rate performance.

A wavelet-based perceptual image coder for the compression of color images is proposed here in which the coding structure is coupled with Human Visual System models to produce high quality images. The major contribution is the development of a new model for the compression of the color components based on psychovisual experiments, which quantifies the optimum amount of compression that can be applied to the color components for a given rate. The model is developed for YCbCr color space and the perceptually uniform CIE Lab color space. A complete coding structure for the compression of color images is developed by incorporating the new perceptual model. The performance of the proposed coder is compared with a wavelet-based coder that uses the quantization stage of the JPEG2000 standard. The perceptual quality of the compressed images is tested using the wavelet-based subjective and objective perceptual quality matrices such as Mean Opinion Score, Visual Information Fidelity and Visual Signal to Noise Ratio. Though the model is developed for a perceptually lossless high quality image compression, results obtained reveal that the proposed structure gives very good perceptual quality compared to the existing schemes for lower bit rates. These advantages make the proposed coder a candidate for replacing the encoder stage of the current image compression standards.

The dyadic lifting schemes, which generalize Sweldens lifting schemes, have been applied to design dyadic wavelet with higher number of vanishing moments. But the existing dyadic lifting methods cannot give the free parameters (i.e. lifting factors) explicitly under vanishing moment constraints, and the exact vanishing moments of the lifted wavelet is unknown a priori. This paper provides a solution of these problems for spline dyadic wavelets. It proposes a novel constructive method for lifting constructing spline dyadic wavelets with desirable numbers of vanishing moments. This new lifting construction scheme can be applied to design spline dyadic wavelet filters with any number of vanishing moments starting from one single dyadic wavelet with 1 or 2 vanishing moments. Its computational advantage is that the lifting factor parameters can be chosen and given explicitly under vanishing moment constraints. At the end of this paper, some spline dyadic wavelet filters are designed by using our method.

Instantaneous frequency, defined as the derivative of the phase of a complex analytic representation of the signal, is a basic concept and plays an important role in communication and information processing. It is not unusual to expect that the instantaneous frequency of an analytic signal is nonnegative. In this note, we exhibit new families of analytic signals with band-limited amplitudes and positive nonlinear instantaneous frequencies. The structures of analytic signals with band-limited amplitude and rational as well as linear plus periodic instantaneous frequencies have been analyzed.

When n coherent pulses u_s against additive independent noises u_n are received, n voltages u_s + u_n1, …, u_s + u_nn can be obtained in the outputs of a delay line. After addition of these voltages in the matched filter, an improvement of the signal-to-noise ratio SNR is obtained due to random character of summation of the noises and in-phase summation of the signal pulses. As a result, the signal power increases faster than the noise power. However, availability of n pointed voltages enables us to use another processing. It is based on a selection of one of these and of their mean voltages in accordance with its characteristic feature. As shown in the paper, the SNR improvement can be achieved if the selection of the maximum and minimum voltages is performed. The maximum SNR value is obtained by the selection of the noises with the minimum instantaneous power. In this case, the SNR improvement exceeds the one obtained by summation. The results are confirmed by modeling.