International Journal of Wavelets, Multiresolution and Information Processing

Computing solutions of singular differential equations has always been a challenge as near the point of singularity it is extremely difficult to capture the solution. In this research paper, Haar wavelet coupled with quasilinearization approach (HWQA) is proposed for computing numerical solution of nonlinear SBVPs popularly also referred as Lane–Emden equations. This technique is the combination of quasilinearization and Haar wavelet collocation method. To show the accuracy of the HWQA, several examples are presented. Convergence of the proposed method is also established in this paper, which shows that proposed method converges very fast.

This research presents a client and server-based mobile application for recognition and authentication of banknotes; the system extracted the shape context (SC), Scale Invariant Feature Transform (SIFT), gradient location and orientation histogram (GLOH), and Histogram of Gradient (HOG). It then reduces the feature set using Principal Component Analysis (PCA), Bag of Words and proposed two-dimension reduction approach based on low variance and high correlation filter. The classification was done using a 2-fold Weighted Majority Average (WMA) Ensemble technique with MPLNN and MCSVM as base classifiers. The application was built using Unity 3D; it was tested on Naira, USD, CAD and Euro banknotes and the experimental results proved that the implemented feature vector and the proposed feature reduction and classification technique presented the best results and with promising recognition accuracy, detection rate, and processing time.

In this paper, the numerical solutions of multi-dimensional stochastic Itô–Volterra integral equations have been obtained by second kind Chebyshev wavelets. The second kind Chebyshev wavelets are orthonormal and have compact support on $[0,1]$. The block pulse functions and their relations to second kind Chebyshev wavelets are employed to derive a general procedure for forming stochastic operational matrix of second kind Chebyshev wavelets. The system of integral equations has been reduced to a system of nonlinear algebraic equations and solved for obtaining the numerical solutions. Convergence and error analysis of the proposed method are also discussed. Furthermore, some examples have been discussed to establish the accuracy and efficiency of the proposed scheme.

It is well known that the system of translates in $L^2(ℝ)$ has been characterized as Bessel sequences, frames and Riesz bases in terms of the Fourier transform. The aim of this paper is to obtain similar types of characterization for the wavelet system emerging out of integer translations and dyadic dilations. The existence of the biorthogonal dual system and nonredundancy properties of the wavelet system are also investigated here.

In this paper, the generalized Bayes estimator of elliptical distribution parameter’s under asymmetric Linex error loss function is considered. The new shrinkage generalized Bayes estimator by applying wavelet transformation is investigated. We develop admissibility and minimaxity of shrinkage estimator on multivariate normal distribution.We present the simulation in order to test validity of purpose estimator.

A new notion in frame theory has been introduced recently under the name woven-weaving frames by Bemrose et al. In the study of frames, some operators like analysis, synthesis, Gram and frame operators play the central role. In this paper, for the first time, we introduce and define these operators for woven-weaving frames and review some of their properties. In continuation, we investigate the effect of different types of operators on the woven frames and their bounds. Also, we provide some conditions that shows sum of woven frames are also woven frames. Finally, we apply these properties with an example.

Top performing algorithms are trained on massive amounts of labeled data. Alternatively, domain adaptation (DA) provides an attractive way to address the few labeled tasks when the labeled data from a different but related domain are available. Motivated by Fisher criterion, we present the novel discriminative regularization term on the latent subspace which incorporates the latent sparse domain transfer (LSDT) model in a unified framework. The key underlying idea is to make samples from one class closer and farther away from different class samples. However, it is nontrivial to design the efficient optimization algorithm. Instead, we construct a convex surrogate relaxation optimization constraint to ease this issue by alternating direction method of multipliers (ADMM) algorithm. Subsequently, we generalize our model in the reproduced kernel Hilbert space (RKHS) for tracking the nonlinear domain shift. Empirical studies demonstrate the performance improvement on the benchmark vision dataset Caltech-4DA.

Accurate scale estimation of the target plays an important role in object tracking. Most state-of-the-art methods estimate the target size by employing an exhaustive scale search. These methods can achieve high accuracy but suffer significantly from large computational cost. In this paper, we first propose an adaptive scale search strategy with the scale selection factor instead of an exhaustive scale search. This proposed strategy contributes to reducing computational costs by adaptive sampling. Furthermore, the boundary effects of correlation filters are suppressed by investigating background information so that the accuracy of the proposed tracker can be boosted. Experiments’ empirical evaluations of 61 challenging benchmark sequences demonstrate that the overall tracking performance of the proposed tracker is very successfully improved. Moreover, our method obtains the top rank in performance by outperforming 17 state-of-the-art trackers on OTB2013.

In this paper, we present a novel semi-supervised classification method based on sparse representation (SR) and multiple one-dimensional embedding-based adaptive interpolation (M1DEI). The main idea of M1DEI is to embed the data into multiple one-dimensional (1D) manifolds satisfying that the connected samples have shortest distance. In this way, the problem of high-dimensional data classification is transformed into a 1D classification problem. By alternating interpolation and averaging on the multiple 1D manifolds, the labeled sample set of the data can enlarge gradually. Obviously, proper metric facilitates more accurate embedding and further helps improve the classification performance. We develop a SR-based metric, which measures the affinity between samples more accurately than the common Euclidean distance. The experimental results on several databases show the effectiveness of the improvement.

In this paper, we develop the generalized fractional order Chebyshev wavelets (GFCWs) from generalized fractional order of Chebyshev polynomials. The operational matrices for the presented wavelets are constructed and derived. We also proposed a technique by utilizing the GFCWs, the method of steps and quasilinearization technique for solving nonlinear fractional delay-type differential equations. According to the development, the method of step is used to transform the fractional nonlinear delay-type differential equation to a fractional nonlinear non-delay differential equation, and then apply the quasilinearization technique to discretize the obtained nonlinear equation. The GFCW method is utilized in each iteration of quasilinearization method for the improvement of solution. We perform the error analysis for the proposed technique. Procedure of implementation for the present method is also provided. Numerical simulation of some examples will be presented to demonstrate the benefits of computing with the present technique over existing methods in literature.

This paper is devoted to the study of the dual $K$-g-Bessel sequences of $K$-g-frames. We firstly make use of the g-preframe operators of a g-Bessel sequence to investigate the constructions of $K$-g-frames. And then, taking the g-preframe operators into account, we present several necessary and sufficient conditions under which a g-Bessel sequence is the dual $K$-g-Bessel sequence of a given $K$-g-frame. We also give a simple example to show that the duality of $K$-g-frames is not transitive.

Synthetic Aperture Radar (SAR) is an all-weather, day and night satellite imaging technology where the radar is mounted on aircraft and successive pulses of radio waves are transmitted to illuminate the target scene. The signal processing of the recorded backscattered echoes produce SAR images. SAR images contain inherent multiplicative speckle noise which is formed due to the constructive and destructive interference of transmitted signals with the returning signals. Speckle noise appears as granular patterns and makes the image interpretation difficult. Non-local means approaches like Block Matching and 3D filtering (BM3D) are effective scheme for removing speckle noise from SAR images. This method gives good performance for additive noise but is not adaptive to curved edges and discontinuities that occur in SAR images affected by multiplicative noise. This paper proposes a three-step refined algorithm to adapt BM3D for despeckling multiplicative speckle noise. In the proposed scheme curvelet is used to find the transform coefficients and this modification in the transform domain improves the despeckling accuracy of BM3D. Also Wiener filtering is replaced with Importance Sampling Unscented Kalman Filtering (ISUKF) for better adapting to discontinuities in the real SAR image. An improved method of grouping is proposed here based on Manhattan distance which better adapts to constantly changing multiplicative noise statistics. A detailed comparative study is carried out on each step using various well-known performance measures. From the results, it is found that the proposed Curvelet-ISUKF-Manhattan BM3D (CIM-BM3D) method of despeckling has better values for all the performance measure and the results are also visually verified.