International Journal of Wavelets, Multiresolution and Information Processing

Remote sensing (RS) technology provides essential data for monitoring the Earth. To fully utilize the data, image classification is often needed to convert data to information. The success of image classification methods greatly depends on the quality and quantity of training samples. To effectively select more informative training samples, this paper proposes a new active learning (AL) technique for classification of remote sensing (RS) images based on graph theory. A new diversity criterion is proposed based on geometrical features of the support vector machines (SVM) outputs. The diversity selection procedure is converted to the densest k-subgraph $(\mathrm{\text{D}}k\mathrm{\text{S}})$ maximization problem in graph theory. The $\mathrm{\text{D}}k\mathrm{\text{S}}$ maximization problem is solved by a greedy algorithm. The proposed technique is compared with competing methods adopted in RS community. Experimental tests are performed on very high resolution (VHR) multispectral and hyperspectral images. Experimental results demonstrate that the proposed technique leads to comparable or even better classification accuracies with respect to competing methods on the two datasets.

In this paper, an image encryption scheme based on reversible integer wavelet transform (IWT) with chaotic logistic map is designed. The proposed cryptosystem is applicable to encipher both the medical and natural images in lossless and lossy manners, respectively. Initially, the original image is transformed with the multilevel of IWT, then the image data set is divided into low sub-band (approximation part) and high sub-bands (detail part). The approximation part gets confused with the chaotic logistic map followed by the bit plane decomposition. Next, the individual bit planes are further diffused with several binary key metrics, generated using a chaotic logistic map. The proposed key schedule derives several large size of binary key metrics from a small size of key. Based on the type of applications, the detail part is considered for lossless/lossy compression. The lossless/lossy compressed detail part is further considered only for confusion process using the logistic map for the sake of enhancing the security level. Finally, the cipher image obtained after inverse IWT is significantly dissimilar than original image. The scheme has been tested on several standard medical and natural images and the experimental results substantiate that a small size of key is enough to protect the content of images completely. The security analysis reveals that the proposed scheme is suitable for protecting the image data effectively.

We study distributed learning with partial coefficients regularization scheme in a reproducing kernel Hilbert space (RKHS). The algorithm randomly partitions the sample set ${\{z_i\}}_{i=1}^N$ into $m$ disjoint sample subsets of equal size. In order to reduce the complexity of algorithms, we apply a partial coefficients regularization scheme to each sample subset to produce an output function, and average the individual output functions to get the final global estimator. The error bound in the $L^2$-metric is deduced and the asymptotic convergence for this distributed learning with partial coefficients regularization is proved by the integral operator technique. Satisfactory learning rates are then derived under a standard regularity condition on the regression function, which reveals an interesting phenomenon that when $m\le N^s$ and $s$ is small enough, this distributed learning has the same convergence rate with the algorithm processing the whole data in one single machine.

In this paper, we establish inhomogeneous coorbit spaces related to the continuous shearlet transform and the weighted Lebesgue spaces $L_{p,v},p\ge 1,$ for certain weights $v$. We present an inhomogeneous shearlet frame for $L_2({ℝ}^d)$ which gives rise to a reproducing kernel $R_{𝔉}$ that is not contained in the space ${{𝒜}}_{1,m_v}$. We show that the inhomogeneous shearlet coorbit spaces are Banach spaces by introducing a generalization of the approach of Fornasier, Rauhut and Ullrich.

The Sobolev space over local fields $H^s(𝕂)$ is defined. A multiresolution analysis for the Sobolev space is developed. Orthonormal wavelets with respect to these space are constructed and an example is also presented.

An efficient and secure platform is needed for data storage and transmission, specially for the multimedia content like audio, image and video. In this paper, a new methodology is proposed for the secured medical image compression. Initially, Bandelet transform is applied to the input medical image to obtain the coefficients. Using unequal error protection (UEP) method, the obtained coefficients are prioritized. These coefficients are encrypted using data encryption standard (DES) and will be encoded using listless set partitioning embedded block (Listless SPECK) technique. For the performance evaluation, peak signal-to-noise ratio (PSNR), mean square error (MSE), structural similarity index (SSIM), image quality index (IQI), average difference (AD), normalized cross-correlation (NK), structural content (SC), maximum difference (MD), Laplacian mean squared error (LMSE) and normalized absolute error (NAE) are taken. From the experimental results and performance evaluation, it is shown that the proposed approach is producing good results.

In this work, we provide polyphase, modulation, and frame theoretical analyses of a filter bank on a discrete abelian group. Thus, multi-dimensional or cyclic filter banks as well as filter banks for signals in ${\ell }^2({\mathbb{Z}}^d\times {\mathbb{Z}}_s)$ or ${\ell }^2({\mathbb{Z}}_r\times {\mathbb{Z}}_s)$ spaces are studied in a unified way. We obtain perfect reconstruction conditions and the corresponding frame bounds in this particular context.

In this paper, asymptotic behavior of the uncertainty product of the Gauss–Weierstrass wavelet is investigated. It is shown that the uncertainty product is bounded from above, a feature that distinguishes the Gauss–Weierstrass wavelet from other wavelet families.

Dialect recognition of low resource languages is the next stage in the technological advancement in speech recognition. Traditional methods for dialects recognition such as mel frequency cesptral coefficients (MFCC) and discrete wavelet transform (DWT) work better for high resource languages, however, the performance is low when applied in low resource languages. This paper presents a new approach for Pashto dialects recognition using an adaptive filter bank with MFCC and DWT. In this approach, features are extracted using adaptive filter bank in MFCC and DWT followed by classification through hidden Markov model (HMM), support vector machines (SVM) and K-nearest neighbors (KNN). The results obtained from the proposed method are very satisfactory with an overall dialect recognition accuracy of $88\%$.

In this paper, second-generation wavelet optimized finite difference method (SGWOFD) is developed for solution of Burger’s equation with different boundary conditions. The viscid Burger’s equation is considered with periodic, Dirichlet, Neumann and Robin’s boundary conditions. For the approximations of the differential operators, central finite difference scheme has been used and Crank Nicolson’s scheme is used for the time integration. Numerical solutions have been optimized on an adaptive grid which is generated using the second-generation wavelet. The beauty of the second-generation wavelet is that its construction is not affected by the boundary conditions. For each test problem, the convergence of the method has been verified. The CPU time taken by SGWOFD has been computed for each test problem and is compared with the CPU time taken by the finite difference method on a uniform grid. It has been revealed that SGWOFD is highly efficient.

In this paper, continuous piecewise quadratic finite element wavelets are constructed on general polygons in ${ℝ}^2$. The wavelets are stable in $H^s$ for $\left|s\right|<\frac{3}{2}$ and have two vanishing moments. Each wavelet is a linear combination of 11 or 13 nodal basis functions. Numerically computed condition numbers for $s\in \{-1,0,1\}$ are provided for the unit square.

Deep face recognition model learned on big dataset surpasses humans on difficult unconstrained face dataset. But open set face recognition, i.e. robust to both variations and unknown faces, is still a big challenge. In this paper, we propose a robust open set face recognition approach with deep transfer learning and extreme value statistics. First, we demonstrate that transferring the feature representations of a pre-trained deep face model to specific tasks is an efficient and effective approach for face recognition on small datasets. We learn both higher layer representations and the final linear multi-class SVMs with transferred features. Second, we propose a novel approach for unknown people recognition with extreme value statistics. Different from traditional distribution fitting, our approach only makes use of a simple statistical quantity — standard deviation of tail data. Empirical evidence shows that standard deviation of the tail of multi-class SVMs recognition scores is efficient and robust for unknown people recognition. Finally, we also empirically explore an important open problem — attributes and transferability of different layer features of the deep model. We argue that lower layer features are both local and general, while higher layer ones are both global and specific which embrace both intra-class invariance and inter-class discrimination. The results of unsupervised feature visualization and supervised face identification strongly support our view.