International Journal of Wavelets, Multiresolution and Information Processing

In coherent imaging systems, such as the synthetic aperture radar (SAR), the observed images are affected by multiplicative speckle noise. This paper proposes a new variational model based on I-divergence for restoring blurred images with speckle noise. The model minimizes the sum of an I-divergence data fidelity term, a new quadratic penalty term based on the statistical property of the noise and the total-variation regularization term. The existence and uniqueness of a solution of the proposed model with some other characteristics are analyzed. Furthermore, an iterative algorithm is introduced to solve the proposed variational model. Our numerical experiments indicate that the proposed method performs favorably.

By introducing a rotation parameter besides translations and dilations, the continuous wavelet transform has been defined with respect to an admissible function not necessarily radial to study the local regularity of weak solutions $u$ under $Qu=f$, where $f$ is of class $C^{\infty }$ in a neighborhood of some point $x=b_0$ in ${ℝ}^2$, and $Q={\sum }_{\left|\alpha \right|=p}{\partial }^{\alpha }$ is a partial differential operator of order $p>0$. The method used to study this fact is through the local convergence of the continuous wavelet transform.

The main objective of this paper is to study continuous wavelet transform (CWT) using the convolution theory of Kontorovich–Lebedev transform (KL-transform) and discuss some of its basic properties. Plancherel’s as well as Parseval’s relation and Reconstruction formula for CWT are obtained and some examples are also given. The discrete version of the wavelet transform associated with KL-transform is also given and reconstruction formula is derived.

This paper focuses on the problem of lossy compression for hyperspectral images and presents an efficient compression algorithm based on distributed source coding. The proposed algorithm employs a block-based quantizer followed by distributed lossless coding, which is implemented through the use of multilevel coset codes. First, a bitrate allocation algorithm is proposed to assign the rational bitrate for each block. Subsequently, the multilinear regression model is employed to construct the side information of each block, and the optimal quantization step size of each block is obtained under the assigned bitrate while minimizing the distortion. Finally, the quantized version of each block is encoded by distributed lossless compression. Experimental results show that the compression performance of the proposed algorithm is competitive with that of state-of-the-art transform-based compression algorithms. Moreover, the proposed algorithm provides both low encoder complexity and error resilience, making it suitable for onboard compression.

Evaluation on curvature variation is a significant problem in the field of curve fairing, and traditional evaluation is generally performed by observing curvature plots qualitatively. By using the theory of B-spline wavelet, the concept of curvature variation factor (CVF) is put forth in this paper to describe curvature variation quantitatively. It is verified that the quantitative evaluation results by the CVF method agree well with the traditional qualitative judgments. Based on CVF, a new curve-fairing algorithm is further put forward, whose validness is verified by an example. The advantage of the CVF-based algorithm is that it can realize different fairing effect to meet different requirements under diverse circumstances only by adjusting the shape error.

Theory of wavelet transform is a powerful tool for image and video processing. Mathematical concepts of wavelet transform and filter bank have been studied carefully in many works. This work presents application of new construction of linear and robust codes based on wavelet decomposition and its application in ADV612 chips. We present the model of the error-coding scheme that allows to detect errors in the ADV612 chips with high probability. In our work, we will show that developed and presented scheme of protection drastically improves the resistance of ADV612 chips to malfunctions and errors.

In this paper, Chebyshev wavelet method (CWM) has been applied to solve the second-order singular differential equations of Lane–Emden type. Firstly, the singular differential equation has been converted to Volterra integro-differential equation and then solved by the CWM. The properties of Chebyshev wavelets were first presented. The properties of Chebyshev wavelets via Gauss–Legendre rule were used to reduce the integral equations to a system of algebraic equations which can be solved numerically by Newton’s method. Convergence analysis of CWM has been discussed. Illustrative examples have been provided to demonstrate the validity and applicability of the present method.

The capacity convergence rate for a kind of kernel regularized semi-supervised Laplacian learning algorithm is bounded with the convex analysis approach. The algorithm is a graph-based regression whose structure shares the feature of both the kernel regularized regression and the kernel regularized Laplacian ranking. It is shown that the kernel reproducing the hypothesis space has contributions to the clustering ability of the algorithm. If the scale parameters in the Gaussian weights are chosen properly, then the learning rate can be controlled by the unlabeled samples and the algorithm converges with the increase of the number of the unlabeled samples. The results of this paper show that choosing suitable structure the semi-supervised learning approach can not only increase the learning rate, but also finish the learning process by increasing the number of unlabeled samples.

In this paper, a multi-stage matching strategy is proposed to boost the performance of a non-graph matching feature-based face recognition. As the gallery size increases, the problem of recognition degradation gradually arises, due to the fact that the correct matching of feature points becomes more and more difficult. Other than only one round of matching in traditional methods, the multi-stage matching strategy determines the recognition result step by step. Instead of finding the best one matching, each step picks out a small portion of the training candidates and removes the others. The behavior of picking and removing repeats until the number of remaining candidates is small enough to produce the final result. Two multi-stage matching algorithms, n-ary elimination and divide and conquer, are introduced into the non-graph matching feature-based method from the perspectives of global and local, respectively. The experimental result shows that with the multi-stage matching strategy, the recognition accuracy of the non-graph matching feature-based method is evidently boosted. Moreover, the improvement level also increases with the gallery size.