International Journal of Wavelets, Multiresolution and Information Processing

This note investigates a kind of filter banks related to the Fibonacci sequence. The Fibonacci sequence cannot be directly considered as a low-pass filter since the convergence radius of its $z$-transform does not contain the unit disc centered at the origin. Adopting the Hadamard product of the Fibonacci sequence and a geometric sequence, a low-pass filter is designed and its corresponding filter banks are constructed.

Motion estimation is a means, which consists in studying the displacement of objects in a video sequence, seeking the correlation between two successive frames, to predict the change in the contents position. Motion estimation is becoming a progressively significant requirement in a variety of applications such as medicine, robotics and video compression. In recent years, wavelets are effective tools for motion estimation, but the DWT (Discrete Wavelet Transform) will suffer from problems like translation sensitivity, poor directionality and absence of phase information. These three disadvantages make classical wavelets incapable of calculating motion in complex sequences (contain several directions.). In order to improve these negative aspects, we will choose geometric wavelet. Therefore, our objective is to propose a method capable of estimating the motion in terms of performance (speed and accuracy). This method will be based on the geometric wavelet transform and more precisely on the Contourlet transform. This work consists of two parts: in the first stage, the denoising process is examined by the Contourlet transform to ensure the precision of motion; in the second phase, we applied the iterative method of Horn and Schunck to calculate the motion in order to guarantee good speed. Comparative experimental results of artificial sequences show that the proposed algorithm obtains considerably better performance than several state-of-the-art methods.

Although neural networks are most commonly used in the field of image super-resolution (SR), methods based on decision trees are still discussed. These kinds of algorithm need less time to compute than others because of their simple structure but still yield high quality image SR. In this paper, we propose an SR algorithm using the multi-grained cascade forest (SRGCF) method. Our algorithm first uses multi-grained scanning to process the spatial relationships of image features, thus the representational learning ability is improved. During the reconstruction process, the image obtained by cascade forest training is used as the input of the next training, therefore, the image features are continuously emphasized. The training of the cascade forest ends when the evaluation value is optimal. Because the decision tree uses a divide-and-conquer strategy, the SR of an image is improved in an iterative manner simply and quickly. Compared with existing methods, our method not only avoids the tradeoff between reconstruction quality and run time, but also has a good generalization capability. It can be quickly applied to the many cases of image SR.

Recent advances have shown a great potential of collaborative representation (CR) for multiclass classification. However, conventional CR-based classification methods adopt the mean square error (MSE) criterion as the cost function, which is sensitive to gross corruption and outliers. To address this limitation, inspired by the success of robust statistics, we develop a Huber collaborative representation-based classification (HCRC) method for robust multiclass classification. Concretely, we cast the classification problem as a Huber collaborative representation problem with the Huber estimator. Our another contribution is to design an efficient half-quadratic (HQ) algorithm with guaranteed convergence to solve the proposed model efficiently. Furthermore, we also give a theoretical analysis of the classification performance of HCRC. Experiments on real-world datasets corroborate that HCRC is an effective and robust algorithm for multiclass classification tasks.

In this paper, we investigated the fractional Fourier transform (FrFT) of the continuous fractional wave packet transform and studied some properties of continuous fractional wave packet transform. The product of continuous fractional wave packet transforms (CFrWPTs) is defined. Parseval’s relation and an inversion formula for product of CFrWPT are obtained. An example is also given.

We consider the continuous wavelet transform ${\mathrm{\Phi }}_h$ associated with the spherical mean operator. We investigate the localization operators for ${\mathrm{\Phi }}_h$, in particular, we prove that they are in the Schatten-von Neumann class. Next, we analyze the concentration of this transform on sets of finite measure. In particular, Donoho-Stark and Benedicks-type uncertainty principles are given. Finally, we prove many versions of quantitative uncertainty principles for ${\mathrm{\Phi }}_h$.

Medical image fusion has a crucial role in many areas of modern medicine like diagnosis and therapy planning. Methods based on principal component analysis (PCA) have been extensively used in area of medical image fusion due to their computational simplicity. Methods based on multiresolution analysis are of attraction now due to their ability in extracting image details. A new method is proposed in this paper to benefit from these advantages. For this aim, firstly, images are transformed into multiscale space based on nonsubsampled shearlet transform (NSST). Secondly, principal components and weights of each subband are calculated. Averaging them yields weights necessary for fusion step. Finally, fused image is achieved by merging source images according to weights. Quantitative and qualitative analysis prove outperformance of our methods compared to well-known fusion methods and improvement compared to subsequent best method, in terms of standard deviation $(+4.51\%)$, entropy $(+6.88\%)$, structural similarity $(+1.35\%)$, signal to noise ratio $(+7.57\%)$ and fusion performance metric $(+3.81\%)$.

We are concerned with a class of generalized coherent states (GCS) attached to Euclidean Landau levels (or to $m$-true-polyanalytic spaces), which can be obtained by displacing a Gaussian–Hermite function as an admissible (or window) function. Precisely, we evaluate the Wehrl entropy for a density operator representing a projector on a Fock state (pure states) and we give an upper bound for this entropy. We also establish an exact formula of this entropy for the heat operator (mixed states) associated with the harmonic oscillator. In this case, the behavior of the entropy with respect to the temperature parameter shows the dependence of its minimum to the Landau level or equivalently to the window function by means of which the GCS involved in the Wehrl entropy were constructed.

Image registration is regarded as an important component of medical procedures. The present study aimed to introduce a new transformation model based on dual-tree complex wavelet transform (DT-CWT). To this aim, parametric registration methods was revised based on the function expansion theory and the gradient descent algorithm was used to introduce a general formulation for transformation models based on spatio-spectral transforms. Then, the performance of the proposed method was evaluated on a public dataset of 3D real magnetic resonance images (MRI) and compared with the transformation model based on wavelets. Finally, the performance of the proposed method was compared with the current state-of-the-art methods (IRTK, SyN and SPM-DARTEL). Based on the experimental results, the proposed method could deliver superior registration performance compared with the previous methods.

In this paper, we present a solution method for fractional nonlinear ordinary differential equations. We propose a method by utilizing the sine–cosine wavelets (SCWs) in conjunction with quasilinearization technique. The fractional nonlinear differential equations are transformed into a system of discrete fractional differential equations by quasilinearization technique. The operational matrices of fractional order integration for SCW are derived and utilized to transform the obtained discrete system into systems of algebraic equations and the solutions of algebraic systems lead to the solution of fractional nonlinear differential equations. Convergence analysis and procedure of implementation for the proposed method are also considered. To illustrate the reliability and accuracy of the method, we tested the method on fractional nonlinear Lane–Emden type equation and temperature distribution equation.

Feature extraction plays a key role in pattern recognition problems. The texture feature is an important feature which helps to describe an image with textural information. A new texture descriptor, the Local Symmetric Tetra Pattern (LSTP), is proposed in this work. This descriptor is developed for the local description of an image. It considers not only the surrounding eight neighbors, but also the eight pixels at the next level to describe the texture efficiently. For every pixel, the maximum edge value, the number of negative sign bits and the number of positive sign bits for each degree of symmetry are computed. Image classification is experimented using the Original Brodatz, Outex and Kylberg Texture Dataset v.1.0 databases. The investigation results are compared with existing method which shows promising achievement of the proposed techniques in terms of their evaluation measures. It is also found that the proposed texture descriptor is rotationally invariant.

In this paper, we propose a sparse discriminative least squares regression (SDLSR) for multicategory classification. The main mechanism of SDLSR is to apply L1-norm for regularizing the objective function of discriminative least squares regression (DLSR). Through theoretical analysis, it is obtained that SDLSR can be viewed as a relaxation of L1-SVM. Moreover, we theoretically prove that sparsity of objective function can effectively decrease the number of support vectors (SV). To optimize our proposed SDLSR, an efficient iterative algorithm is proposed. The experimental results confirm the effectiveness of our proposed SDLSR.