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Speckle noise removal in ultrasound images is one of the important tasks in biomedical-imaging applications. Many filtering -based despeckling methods are discussed in many existing works. Two-dimensional (2-D) transforms are also used enormously for the reduction of speckle noise in ultrasound medical images. In recent years, many soft computing-based intelligent techniques have been applied to noise removal and segmentation techniques. However, there is a requirement to improve the accuracy of despeckling using hybrid approaches.

The work focuses on double-bank anatomy with framelet transform combined with Gaussian filter (GF) and also consists of a fuzzy kind of clustering approach for despeckling ultrasound medical images. The presented transform efficiently rejects the speckle noise based on the gray scale relative thresholding where the directional filter group (DFB) preserves the edge information.

The proposed approach is evaluated by different performance indicators such as the mean square error (MSE), peak signal to noise ratio (PSNR) speckle suppression index (SSI), mean structural similarity and the edge preservation index (EPI) accordingly. It is found that the proposed methodology is superior in terms of all the above performance indicators.

Fuzzy kind clustering methods have been proved to be better than the conventional threshold methods for noise dismissal. The algorithm gives a reconcilable development as compared to other modern speckle reduction procedures, as it preserves the geometric features even after the noise dismissal.

The purpose of this paper is to obtain a numerical scheme for finding numerical solutions of linear and nonlinear Hadamard-type fractional differential equations.

The aim of this paper is to develop a numerical scheme for numerical solutions of Hadamard-type fractional differential equations. The classical Haar wavelets are modified to align them with Hadamard-type operators. Operational matrices are derived and used to convert differential equations to systems of algebraic equations.

The upper bound for error is estimated. With the help of quasilinearization, nonlinear problems are converted to sequences of linear problems and operational matrices for modified Haar wavelets are used to get their numerical solution. Several numerical examples are presented to demonstrate the applicability and validity of the proposed method.

The numerical method is purposed for solving Hadamard-type fractional differential equations.

The purpose of the present work is to propose a wavelet method for the numerical solutions of Caputo–Hadamard fractional differential equations on any arbitrary interval.

The author has modified the CAS wavelets (mCAS) and utilized it for the solution of Caputo–Hadamard fractional linear/nonlinear initial and boundary value problems. The author has derived and constructed the new operational matrices for the mCAS wavelets. Furthermore, The author has also proposed a method which is the combination of mCAS wavelets and quasilinearization technique for the solution of nonlinear Caputo–Hadamard fractional differential equations.

The author has proved the orthonormality of the mCAS wavelets. The author has constructed the mCAS wavelets matrix, mCAS wavelets operational matrix of Hadamard fractional integration of arbitrary order and mCAS wavelets operational matrix of Hadamard fractional integration for Caputo–Hadamard fractional boundary value problems. These operational matrices are used to make the calculations fast. Furthermore, the author works out on the error analysis for the method. The author presented the procedure of implementation for both Caputo–Hadamard fractional initial and boundary value problems. Numerical simulation is provided to illustrate the reliability and accuracy of the method.

Many scientist, physician and engineers can take the benefit of the presented method for the simulation of their linear/nonlinear Caputo–Hadamard fractional differential models. To the best of the author’s knowledge, the present work has never been proposed and implemented for linear/nonlinear Caputo–Hadamard fractional differential equations.

How to model blind image deblurring that arises when a camera undergoes ego-motion while observing a static and close scene. In particular, this paper aims to detail how the blurry image can be restored under a sequence of the linear model of the point spread function (PSF) that are derived from the 6-degree of freedom (DOF) camera’s accurate path during the long exposure time.

There are two existing techniques, namely, an estimation of the PSF and a blind image deconvolution. Based on online and short-period inertial measurement unit (IMU) self-calibration, this motion path has discretized a sequence of the uniform speed of 3-DOF rectilinear motion, which unites with a 3-DOF rotational motion to form a discrete 6-DOF camera’s path. These PSFs are evaluated through the discrete path, then combine with a blurry image to restoration through deconvolution.

This paper describes to build a hardware attachment, which is composed of a consumer camera, an inexpensive IMU and a 3-DOF motion mechanism to the best of the knowledge, together with experimental results demonstrating its overall effectiveness.

First, the paper proposes that a high-precision 6-DOF motion platform periodically adjusts the speed of a three-axis rotational motion and a three-axis rectilinear motion in a short time to compensate the bias of the gyroscope and the accelerometer. Second, this paper establishes a model of 6-DOF motion and emphasizes on rotational motion, translational motion and scene depth motion. Third, this paper addresses a novel model of the discrete path that the motion during long exposure time is discretized at a uniform speed, then to estimate a sequence of PSFs.