In This paper, we give a necessary condition for function in L 2 with its dual to generate a dual SHEARLET tight frame with respect to admissibility.

Parabolic scaling and anisotropic dilation form the core of famous multi-resolution transformations such as curvelet and SHEARLET, which are widely used in signal processing applications like denoising. These non-adaptive geometrical wavelets are commonly used to extract structures and geometrical features of multi-dimensional signals and preserve them in noise removal treatments. In discrete setups, it is shown that SHEARLETs can outperform other rivals since in addition to scaling, they are formed by shear operator which can fully remain on integer grid. However, the redundancy of multidimensional SHEARLET transform exponentially grows with respect to the number of dimensions which in turn leads to the exponential computational and space complexity. This, seriously limits the applicability of SHEARLET transform in higher dimensions. In contrast, separable transforms process each dimension of data independent of other dimensions which result in missing the informative relations among different dimensions of the data. Therefore, in this paper a modified discrete SHEARLET transform is proposed which can overcome the redundancy and complexity issues of the classical transform. It makes a better tradeoff between completeness of the analysis achieved by processing full relations among dimensions on one hand and the redundancy and computational complexity of the resulting transform on the other hand. In fact, how dilation matrix is decomposed and block diagonalized, gives a tuning parameter for the amount of inter dimension analysis which may be used to control computation complexity and also redundancy of the resultant transform. In the context of video denoising, three different decompositions are proposed for 3x3 dilation matrix. In each block diagonalization of this dilation matrix, one dimension is separated and the other two constitute a 2D SHEARLET transform. The three block SHEARLET transforms are computed for the input data up to three levels and the resultant coefficients are treated with automatically adjusted thresholds. The output is obtained via an aggregation mechanism which combine the result of reconstruction of these three transforms. Using experiments on standard set of videos at different levels of noise, we show that the proposed approach can get very near to the quality of full 3D SHEARLET analysis while it keeps the computational complexity (time and space) comparable to the 2D SHEARLET transform.

Traditional noise removal methods like Non-Local Means create spurious boundaries inside regular zones. Visushrink removes too many coefficients and yields recovered images that are overly smoothed. In Bayesshrink method, sharp features are preserved. However, PSNR (Peak Signal-to-Noise Ratio) is considerably low. BLS-GSM generates some discontinuous information during the course of denoising and destroys the flatness of homogenous area. Wavelets are not very effective in dealing with multidimensional signals containing distributed discontinuities such as edges. This paper develops an effective SHEARLET-based denoising method with a strong ability to localize distributed discontinuities to overcome this limitation. The approach introduced here presents two major contributions: (a) SHEARLET Transform is designed to get more directional subbands which helps to capture the anisotropic information of the image; (b) coefficients are divided into low frequency and high frequency subband. Then, the low frequency band is refined by Wiener filter and the high-pass bands are denoised via NeighShrink model.Our framework outperforms the wavelet transform denoising by %7.34 in terms of PSNR (peak signal-to-noise ratio) and %13.42 in terms of SSIM (Structural Similarity Index) for‘Lena’ image. Our results in standard images show the good performance of this algorithm, and prove that the algorithm proposed is robust to noise.

In this paper, using SHEARLET frames, we present a numerical method for solving the wave equation.We define a new SHEARLET system and by the Plancherel theorem, we calculate the SHEARLET coefficients.

This paper is devoted to definition standard higher dimension SHEARLET group S=R+ Rn-1 Rn and determination of squareintegrable sub representations of this group. Also we give a characterisation of ADMISSIBLE vectors associated with the Hilbert spaces corresponding to each sub representation.

We study composition operators acting between weighted Bergman spaces with ADMISSIBLE Bekolle weights. The boundedness and compactness of composition operators are characterized in terms of the generalized Nevanlinna counting function associated with the inducing map of the composition operator and the associated weight function of Bergman space. For a special case, we also give the estimate of the essential norm.

In this article a method for determining the ADMISSIBLE acceleration of the end-effector is presented for the suspended cable robot in the different points of the workspace. The presented acceleration analysis is different with the dynamic work space. Indeed, the dynamic work space is defined as the set of all end-effector poses satisfying the acceleration conditions. While in the proposed analysis in this paper, the allowable acceleration range of the end-effector in each direction is obtained for any point of the workspace. To this end, after deriving the kinematic equations of the four-cable suspended robot, its dynamic equations are derived using the Lagrange method. Then, on the base of the positive tension constraint in the cables and the torque constraint of the actuators, the obtained equations are simplified to obtain the simple relation between the constrains and the end-effector acceleration in such a way that the lower and upper limit of the ADMISSIBLE acceleration is obtained. Some simulations are done in order to present the ADMISSIBLE acceleration in different point of the workspace. The simulation results show that the acceleration range is in the form of the pyramid with the rhomboid base. So the allowable range of the acceleration is changed in different direction. The results obtained in this paper can be used for online trajectory planning in high speed motion of cable robot.

Necessary conditions for SHEARLET and cone-adapted SHEARLET systems to be frames are presented with respect to the admissibility condition of generators.