International Journal of Wavelets, Multiresolution and Information Processing

In this paper, we propose a novel occlusion robust face recognition algorithm in gradient direction domain (GDD) using scattering operator. The proposed algorithm transforms image into the GDD to remove pseudo-edges, then scattering operator is used to extract face feature from face image in GDD. Since scattering operators can effectively extract the structural information in face owing to locally translation invariant and deformation stability, the proposed approach is robust to occlusion and varying expression. Our scheme has demonstrated the state-of-the-art performance on several datasets. Especially, our method on the sunglasses images and the scarf in AR database achieves a recognition rate of 100 and 95% respectively, which significantly outperforms most existing methods.

Generalizing the result of Bownik and Speegle [Approximation Theory X: Wavelets, Splines and Applications, Vanderbilt University Press, pp. 63–85, 2002], we provide plenty of non-MSF A-wavelets with the help of a given A-wavelet set. Further, by showing that the dimension function of the non-MSF A-wavelet constructed through an A-wavelet set W coincides with the dimension function of W, we conclude that the non-MSF A-wavelet and the A-wavelet set through which it is constructed possess the same nature as far as the multiresolution analysis is concerned. Some examples of non-MSF d-wavelets and non-MSF A-wavelets are also provided. As an illustration we exhibit a pathwise connected class of non-MSF non-MRA wavelets sharing the same wavelet dimension function.

We present two strategies for detecting patterns and clusters in high-dimensional time-dependent functional data. The use on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant local time and scale features. The multiresolution aspect of the wavelet transform provides a time-scale decomposition of the signals allowing to visualize and to cluster the functional data into homogeneous groups. For each input function, through its empirical orthogonal wavelet transform the first strategy uses the distribution of energy across scales to generate a representation that can be sufficient to make the signals well distinguishable. Our new similarity measure combined with an efficient feature selection technique in the wavelet domain is then used within more or less classical clustering algorithms to effectively differentiate among high-dimensional populations. The second strategy uses a similarity measure between the whole time-scale representations that is based on wavelet-coherence tools. The clustering is then performed using a k-centroid algorithm starting from these similarities. Practical performance is illustrated through simulations as well as daily profiles of the French electricity power demand.

In this paper, an efficient multi-scale image disparity estimation algorithm is proposed which estimates the local displacements needed to align different regions between a pair of images. This phase-based approach is based on fractional dual-tree complex wavelet transform (FrDTCWT). In the proposed FrDTCWT, initially we obtained the fractional Fourier transform of the image. We decomposed the fractional transformed image by dual-tree complex wavelet transform into real and imaginary parts. The complex analytic signal is obtained from the real-valued function which is obtained from this FrDTCWT. The FRDTCWT inherits the excellent mathematical properties of DTCWT and FrFT. Phase and amplitude of the image are computed from the complex analytic signal. The disparity is estimated as the optical flow using the phase difference method. The efficiency of the proposed algorithm is carried out by different experiments on synthetic as well as on realistic image sequences.

We consider Gabor systems with compactly supported windows and rational sampling rate. Two modification techniques for tight frame Gabor windows, splitting for shorter support and smoothing for better smoothness, are introduced. As an illustration of such techniques, we construct multiwindow tight frame Gabor windows with smaller support and C^∞ continuity from certain tight frame Gabor windows.

Wavelet has become an appealing image processing technique, due to the fact that the sparseness of wavelet expansion is equivalent to smoothness measure in Besov spaces so that the regularization of image can be performed by manipulating its wavelet coefficients. Unfortunately, wavelets have good performance especially at representing point singularities, but they fail to efficiently represent object edges. As one of computational harmonic analysis tools, curvelets have an essentially optimal representation of objects which is C² away from a C² edge. In this paper, we first apply constraint of curvelet-type decomposition spaces as a regularizing term to variational model for image denoising. Based on the equivalent relationship between semi-norm of curvelet-type decomposition spaces and the weighted curvelet coefficients, solution to the proposed model approximately equals to different curvelet shrinkages. As a second contribution, we also propose another image restoration model from image decomposition point of view. Furthermore, an equivalent theorem of two proposed models is given. Finally, the experiment results show the superiority of proposed models over traditional wavelet-based ones.

This is a continuation of the study of adaptive Fourier decomposition (AFD).¹⁵ Under a mild condition not in terms of smoothness, a convergence rate is provided. We prove that the selection of the parameters corresponding to Fourier series in the average sense is optimal. We also present the transformation matrices between the adaptive rational orthogonal system and the related sequence of the shifted Cauchy kernels and their derivatives.

We consider the approximate consistent sampling process in the space L²(ℝ) of signals of finite energy, where multi-, pre- and post-filters and are from L²(ℝ). We take {(f * h_i)(qk)| 1 ≤ i ≤ M, k ∈ ℤ} as measurements(or generalized samples) of an input signal f and then seek its consistent approximation in the reconstruction space V(Φ), which is a shift-invariant subspace of L²(ℝ) generated by N post-filters . Here is a rational number and the consistency means that f and have the same measurements. We find equivalent conditions for the existence of such consistent approximation in L²(ℝ) together with some relevant properties such as performance analysis.

In this paper a full-scale commercially available magnetorheological (MR) brake installed in a semi-active suspension (SAS) system is modeled and simulated. Two well-known phenomenological hysteresis models are explored: Bouc–Wen and Dahl ones. In particular, influence of their parameters on the response is evaluated and assessed. The next step is to introduce the artificial neural networks and discuss their application in the field of systems identification. Subsequently, two feedforward neural networks are created and trained to estimate parameters characterizing each of the MR damper models described. The semi-active suspension (SAS) system equipped with a MR brake is described and the detailed procedure for acquisition of the reference data used in the models validation stage is elaborated. The models outputs obtained by simulating them with the values of coefficients as identified by the networks are compared to each other as well as to the reference experimental data. Thanks to that, the comparative analysis between the suggested vibration suppression models and the full-scale MR brake is done and it is concluded which of the discussed models has a better performance. The usability of neural networks in the field of parameters estimation of the mathematical models of the real world phenomena is described as well. The novelty of the presented methodology is the application of artificial intelligence methods to estimate model parameters of a MR brake utilized in a SAS system. The results of this approach have a strong potential to be successfully implemented in the area of model-based control of semi-active vibration suppression systems.

In this paper, we focus on the design of oversampled filter banks and the resulting framelets. The framelets obtained exhibit improved shift invariant properties over decimated wavelet transform. Shift invariance has applications in many areas, particularly denoising, coding and compression. Our contribution here is on filter bank completion. In addition, we propose novel factorization methods to design wavelet filters from given scaling filters.