International Journal of Wavelets, Multiresolution and Information Processing

Trajectory representation model has been proposed to describe non-rigid deformation. An optimal trajectory space finding algorithm for 3D non-rigid structure from motion (OTSF-NRSFM) based on this model also has been proposed. However, the influence of the wavelet basis selection on the OTSF-NRSFM algorithm has still not been studied. To help OTSF-NRSFM researchers select wavelet basis properly, we investigated the influences of wavelet basis selection. Two typical wavelet bases, DCT basis and WHT basis, are discussed in this paper. The spectrum properties of wavelet basis and feature point trajectory, trajectory representation results on synthetic shark data, OTSF-NRSFM reconstruction results on synthetic data and real data are analyzed. The results show that the wavelet selection has much influence on OTSF-NRSFM reconstruction results of some non-rigid feature points, which have complicated trajectory. This paper gives researchers some inspiration about wavelet basis selection in OTSF-NRSFM algorithm.

In this paper, we introduce the definitions of SIP-I and SIP-II X_d-frames in a uniformly convex, separable Banach space X with respect to a BK-space X_d (here SIP represents semi-inner product), both of them are defined as sequence of elements in X. We characterize SIP-I and SIP-II X_d-frames in terms of the corresponding synthesis and analysis operators, respectively, then we consider perturbations for both of them. Furthermore, we also introduce the definitions of SIP Banach frames and SIP atomic decompositions. Under certain assumptions, we establish the relationship between SIP Banach frames and SIP atomic decompositions, and therefore obtain reconstruction formulas for every element in X and X* by using a pair of SIP-I and SIP-II X_d-frames for X. Finally, we discuss perturbations of SIP Banach frames and SIP atomic decompositions.

We consider the Inverse Problem (IP) associated to an equation of the form Af = g, where A is a pseudodifferential operator with symbol. It consists in finding a solution f for given data g. When the operator A is not strongly invertible and the data is perturbed with noise, the IP may be ill-posed and the solution must be approximate carefully. For the present application we regard a particular orthonormal wavelet basis and perform a wavelet projection method to construct a solution to the Forward Problem (FP). The approximate solution to the IP is achieved based on the decomposition of the perturbed data calculating the elementary solutions that are nearly the preimages of the wavelets. Based on properties of both, the basis and the operator, and taking into account the energy of the data, we can handle the error that arises from the partial knowledge of the data and from the non-exact inversion of each element of the wavelet basis. We estimate the error of the approximation and discuss the advantages of the proposed scheme.

In this paper, a lossless data hiding method based on histogram shifting for MR images using Discrete Wavelet Transform (DWT) and Discrete Cosine Transform (DCT) are presented. In this method, the algorithms are validated to hide the data in wavelet coefficients of high frequency subbands. This scheme has the advantage of comparing the DCT coefficients and the DWT coefficients which permit low distortion between the watermarked image and the original image. It also shifts a part of the histogram of high frequency subbands and embeds the data by using the created histogram zero point. To prevent the overflows and underflows in the spatial domain, caused by the modification of the DCT coefficients and the DWT coefficients, the histogram modification technique is applied. Therefore, we present a validated method to evaluate and compare the performance of DWT and DCT on task, in terms of data embedding payload and the Peak Signal to Noise Ratio (PSNR) in the medical image. A careful experimental analysis validates the method showing its superiority over the existing methods.

The only quadrature operator of order two on L₂(ℝ²) which covaries with orthogonal transforms, in particular rotations is (up to the sign) the Riesz transform. This property was used for the construction of monogenic wavelets and curvelets. Recently, shearlets were applied for various signal processing tasks. Unfortunately, the Riesz transform does not correspond with the shear operation. In this paper, we propose a novel quadrature operator called linearized Riesz transform which is related to the shear operator. We prove properties of this transform and analyze its performance vs. the usual Riesz transform numerically. Furthermore, we demonstrate the relation between the corresponding optical filters. Based on the linearized Riesz transform we introduce finite discrete quasi-monogenic shearlets and prove that they form a tight frame. Numerical experiments show the good fit of the directional information given by the shearlets and the orientation obtained from the quasi-monogenic shearlet coefficients. Finally, we provide experiments on the directional analysis of textures using our quasi-monogenic shearlets.

Currently, the wavelet transform is widely used in the signal processing domain, especially in the image compression because of its excellent de-correlation property and the redundancy property included in the wavelet coefficients. This paper investigates the redundancy relationships between any two or three components of the wavelet coefficients, the wavelet bases and the original signal. We discuss those contents for every condition according to the continuous form and the discrete form, respectively, by which we also derive a uniform formula which illuminates the inherent connection among the redundancy of the wavelet coefficients, the wavelet bases and the original signals. Finally, we present the application of the wavelet coefficient redundancy property in the still image compression domain and compare the properties of the Discrete Wavelet Transform (DWT) with that of the Discrete Cosine Transform (DCT).

Based on wavelet transform and chaos algorithm, this paper presents a Network Traffic Forecasting Combination Model. The model introduces chaos algorithm for training the BP network and optimizing weights so as to avoid gradient descent algorithm that slowly converges and likely obtains local optimum results. Before forecasting, we first perform wavelet decomposition on the pretreated flow. Then, we utilize the FARIMA model and the improved Elman neural network model to forecast according to approximate components and detailed components, respectively. At last, we use the combination model for the network traffic forecasting. Simulation results confirmed the improved accuracy of the model, and comparing to traditional FARIMA model and wavelet neural network (WNN) model, the model can reduce the deviation.

In this work, an improvement of the Complex Wavelet Additive Synthesis (CWAS) algorithm is presented. This algorithm is based on a discrete version of the Complex Continuous Wavelet Transform (CCWT) which analyzes the input signal in a frame-to-frame approach and under variable frequency resolution per octave. After summarizing several Time-Frequency Distributions (TFD), concretely the standard Short Time Fourier Transform (STFT), the Pseudo Wigner–Ville Distribution (PWVD), reassignment and complex wavelets, a comparative study of the accuracy in the instantaneous frequency (IF) estimation is shown. The comparative study includes three different signal processing tools (based on the summarized TFD): the Time-Frequency Toolbox (TFTB) of François Auger, the High Resolution Spectrographic Routines (HRSR) of Sean Fulop and the proposed CWAS algorithm. A set of eight synthetic signals have been analyzed using six different methods: the regular STFT spectrogram, the PWVD, their corresponding reassigned versions, the Nelson crossed spectrum method and finally the Complex Continuous Wavelet Transform (CCWT). Finally, two- and three-dimensional Time-Frequency representations of the IF provided by the CWAS algorithm are presented.

Face recognition (FR) is an important and challenging task in pattern recognition and has many important practical applications. This paper presents an improved technique for Face Recognition, which consists of two phases where in each phase; a technique is employed effectively that is used extensively in computer vision and pattern recognition. Initially, the Robust Principal Component Analysis (RPCA) is used specifically in the first phase, which is employed to reduce dimensionality and to extract abstract features of faces. The framework of the second phase is sparse representation based classification (SRC) and introduced metaface learning (MFL) of face images. Experiments for face recognition have been performed on ORL and AR face database. It is shown that the proposed method can perform much best than other methods. And with the proposed method, we can obtain a best understanding of data.

Nonstationary Gabor frames were recently introduced in adaptive signal analysis. They represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. In this paper, we show a general existence result for this family of frames. Then, we give a perturbation result for nonstationary Gabor frames and construct nonstationary Gabor frames with non-compactly supported windows from a related painless nonorthogonal expansion. Finally, the theoretical results are illustrated by two examples of practical relevance.

In this paper, we discuss the global L₂-error of the nonlinear wavelet estimator of density in the Besov space for the truncation model when the data exhibit strong mixing assumption, and prove that the estimator can achieve the optimal rate of convergence, which is similar to that in the complete and independent data case with term-by-term thresholding of the empirical wavelet coefficients (D. L. Donoho, I. M. Johnstone, G. Kerkyacharian and D. Picard, Density estimation by wavelet thresholding, Ann. Statist.24 (1996) 508–539). In addition, the conclusion shows that the convergence rate of the nonlinear estimator is faster than that of its linear estimator in some range.

A new interspersed orthogonal frequency division multiplexing (OFDM) based on Hadamard coded Discrete Harmonic wavelet transform (DHWT), is proposed for complex modulation under exponential channel model. In this method, real part of complex signal is transformed by DCHWT and imaginary part by DSHWT and summed to form interspersed harmonic wavelet based OFDM (IHWT OFDM). DHWT exploits the useful properties of DCT and DST viz., energy compaction/low leakage, frequency resolution and its real nature, compared to DFT. This wavelet is simple as it has reduced processing due to its harmonic wavelet nature. The harmonic nature has built in decimation, easy interpolation by concatenation of different scales in frequency (DCT and DST) domain without associated anti-aliasing filters for analysis, image rejection filters and complicated delay compensation for synthesis. In this work, we have explored advantages of DHWT to implement IHWP-OFDM for QPSK modulated signals. Hadamard codes are employed in proposed method to further improve BER and PAPR performance. New OFDM provides PAPR reduction of 2.6, 3.8 and 1.4 dB as compared to Haar, Daubechies WT OFDM and DFT, respectively.

Support vector machine (SVM) is originally proposed to solve binary classification problem. Multi-class classification is solved by combining multiple binary classifiers, which leads to high computation cost by introducing many quadratic programming (QP) problems. To decrease computation cost, hyper-sphere SVM is put forward to compute class-specific hyper-sphere for each class. If all resulting hyper-spheres are independent, all training and test samples can be correctly classified. When some of hyper-spheres intersect, new decision rules should be adopted. To solve this problem, a multiple sub-hyper-sphere SVM is put forward in this paper. New algorithm computed hyper-spheres by SMO algorithm for all classes first, and then obtained position relationships between hyper-spheres. If hyper-spheres belong to the intersection set, overlap coefficient is computed based on map of key value index and mother hyper-spheres are partitioned into a series of sub-hyper-spheres. For the new intersecting hyper-spheres, one similarity function or same error sub-hyper-sphere or different error sub-hyper-sphere are used as decision rule. If hyper-spheres belong to the inclusion set, the hyper-sphere with larger radius is partitioned into sub-hyper-spheres. If hyper-spheres belong to the independence set, a decision function is defined for classification. With experimental results compared to other hyper-sphere SVMs, our new proposed algorithm improves the performance of the resulting classifier and decreases computation complexity for decision on both artificial and benchmark data set.