Lihong Cui

Adaptive Multiwavelet-Based Watermarking Through JPW Masking

In this paper, a multibit, multiplicative, spread spectrum watermarking using the discrete multiwavelet (including unbalanced and balanced multiwavelet) transform is presented. Performance improvement with respect to existing algorithm is obtained by means of a new just perceptual weighting (JPW) model. The new model incorporates various masking effects of human visual perception by taking into account the eyes sensitivity to noise changes depending on spatial frequency, luminance and texture of all the image subbands. In contrast to conventional JND threshold model, JPW describing minimum perceptual sensitivity weighting to noise changes, is fitter for nonadditive watermarking. Specifically, watermarking strength is adaptively adjusted to obtain minimum perceptual distortion by employing the JPW model. Correspondingly, an adaptive optimum decoding is derived using a statistic model based on generalized-Gaussian distribution (GGD) for multiwavelet coefficients of the cover-image. Furthermore, the impact of multiwavelet characteristics on proposed watermarking scheme is also analyzed. Finally, the experimental results show that proposed JPW model can improve the quality of the watermarked image and give more robustness of the watermark as compared with a variety of state-of-the-art algorithms.

A method of construction for biorthogonal multiwavelets system with 2r multiplicity

Biorthogonal multiwavelets systems are consisted of a pair of biorthogonal multiscaling functions and the corresponding a pair of multiwavelets. A method for constructing biorthogonal multiwavelets systems with multiplicity 2r was derived. In particular Hermite interpolation mask was considered as primal masks. A pair of primal and dual masks with high order of sum rules should be firstly designed in order to obtain a biorthogonal multiwavelet with high vanishing moment. Concretely, starting from a short sequence primal masks possessing Hermite interpolation properties, a necessary and sufficient conditions such that primal masks satisfies the preassigned order of sum rules are established, then a dual masks with short support, symmetry and any preassigned order of sum rules is constructed, it follows that two multiscaling functions are obtained and then multiwavelets and dual multiwavelets are derived. From which, a general design framework is obtained for constructing biorthogonal multiwavelets system with multiplicity 2r associated with Hermite interpolation functions. The biorthogonal multiwavelets constructed by our design framework has desirable properties such as symmetry, short support, high vanishing moments and simple structures with explicit expressions. Finally, an example is given.

Some properties and construction of multiwavelets related to different symmetric centers

In this paper we are interested in discuss the symmetry property and construction of an m-band compactly supported orthonormal multiwavelets related to the filters with different symmetric centers. With the development of the several equivalent conditions on this type of symmetry in terms of filter sequences and polyphase matrices, we derive several necessary constraints on the number of symmetric filters of the system, which is crucial for the construction of multiwavelets associated with given multiscaling functions with different symmetry centers. Then, we show how to construct multiwavelets with desired symmetric property by matrix extensions. Finally, to illustrate our proposed general scheme, we give two examples in this paper.

Defect inspection for TFT-LCD images based on the low-rank matrix reconstruction

Abstract Surface defect inspection of TFT-LCD panels is a critical task in LCD manufacturing. In this paper, an automatic defect inspection method based on the low-rank matrix reconstruction is proposed. The textured background of the LCD image is a low-rank matrix and the foreground image with defects can be treated as a sparse matrix. By utilizing the Inexact Augmented Lagrange Multipliers (IALM) algorithm, the segmentation of a LCD image can be converted into the reconstruction of a low-rank matrix with a fraction of its entries arbitrarily corrupted. This low-rank matrix reconstruction problem can be exactly solved via convex optimization that minimizes a combination of the nuclear norm and the l1-norm. Also, adaptive parameter selection strategy is proposed by conducting deep analysis on the IALM algorithm, which improves the generality of the IALM algorithm for different defect types. Experiment results show that our inspection algorithm is robust for the defect shapes and types under different illumination conditions. The shapes and edges of defect areas in the LCD images can be well preserved and segmented from textured background by our detection algorithm.

An algorithm for constructing symmetric orthogonal multiwavelets by matrix symmetric extension

Symmetric extensions of paraunitary matrix is studied. Starting from a given m-band compactly supported orthogonal multiscaling function with some symmetric property, the problem to construct a corresponding m-band multiwavelet which have the symmetric property can be reduced to the symmetric paraunitary extension of a given matrix. It can be shown that such matrix extension is always solvable and an algorithmic approach to solve the symmetric paraunitary extension problem is presented. This leads to a practical method for the construction of compactly supported symmetric orthogonal multiwavelets from a given multiscaling functions with an arbitrary integer dilation factor m>1. As an application, some examples are given, in particular, the well known Chui-Lian multiwavelets is recovered via the method.

Tree-Based Backtracking Orthogonal Matching Pursuit for Sparse Signal Reconstruction

Compressed sensing (CS) is a theory which exploits the sparsity characteristic of the original signal in signal sampling and coding. By solving an optimization problem, the original sparse signal can be reconstructed accurately. In this paper, a new Tree-based Backtracking Orthogonal Matching Pursuit (TBOMP) algorithm is presented with the idea of the tree model in wavelet domain. The algorithm can convert the wavelet tree structure to the corresponding relations of candidate atoms without any prior information of signal sparsity. Thus, the atom selection process will be more structural and the search space can be narrowed. Moreover, according to the backtracking process, the previous chosen atoms’ reliability can be detected and the unreliable atoms can be deleted at each iteration, which leads to an accurate reconstruction of the signal ultimately. Compared with other compressed sensing algorithms, simulation results show the proposed algorithm’s superior performance to that of several other OMP-type algorithms.

A new approach of conditions on δ 2 s (Φ) for s-sparse recovery

In this paper, we provide a unified expression to obtain the conditions on the restricted isometry constant δ2s(Φ). These conditions cover the important results proposed by Candes et al. and each of them is a sufficient condition for sparse signal recovery. In the noiseless case, when δ2s(Φ) satisfies any one of these conditions, the s-sparse signal can be exactly recovered via (l1) constrained minimization.

Analytic separable dictionary learning based on oblique manifold

Sparse representation based on dictionary has gained increasing interest due to its extensive applications. Because of the disadvantages of computational complexity of traditional dictionary learning, we propose an algorithm of analytic separable dictionary learning. Considering the differences of sparse coefficient matrix and dictionary, we divide our algorithm into two phases: 2D sparse coding and dictionary optimization. Then an alternative iteration method is used between these two phases. The algorithm of 2D-OMP (2-dimensional Orthogonal Matching Pursuit) is used in the first phase because of its low complexity. In the second phase, we create a continuous function of the optimization problem, and solve it by the conjugate gradient method on oblique manifold. By employing the separable structure of the optimized dictionary, a competitive result is achieved in our experiments for image de-noising.

Parameterizations of masks for 3-band tight wavelet frames by symmetric extension of polyphase matrix

This paper deals with the construction of 3-band tight wavelet frames with symmetric properties using symmetric extension and parameterizations of the paraunitary matrix. Firstly, we construct a paraunitary matrix which is a symmetric extension of polyphase matrix corresponding to compactly supported wavelet frames with the least number generators. Further, we present symmetric characters and uniformity of wavelet frames with different filter lengths in terms of paraunitary matrix. Then, we focus on investigating the parameterizations of masks for 3-band tight wavelet frames with 3N filter length. Finally, examples of 3-band wavelet frames with good smoothness are constructed based on the parameterizations of masks.

Symmetry Feature and Construction for the 3-Band Tight Framelets with Prescribed Properties

A construction approach for the 3-band tight wavelet frames by factorization of paraunitary matrix is developed. Several necessary constraints on the filter lengths and symmetric features of wavelet frames are investigated starting at the constructed paraunitary matrix. The matrix is a symmetric extension of the polyphase matrix corresponding to 3-band tight wavelet frames. Further, the parameterizations of 3-band tight wavelet frames with filter lengths are established. Examples of framelets with symmetry/antisymmetry and Sobolev exponent are computed by appropriately choosing the parameters in the scheme.