Magnetic resonance imaging (MRI) plays an important role in disease diagnosis. The noise that appears in MRI images is commonly governed by a Rician distribution. The bendlets system is a second-order shearlet transform with bent elements. Thus, the bendlets system is a powerful tool with which to represent images with curve contours, such as the brain MRI images, sparsely. By means of the characteristic of bendlets, an adaptive denoising method for microsection images with Rician noise is proposed. In this method, the curve contour and texture can be identified as low-frequency components, which is not the case with other methods, such as the wavelet, shearlet, and so on. It is well known that the Rician noise belongs to a high-frequency channel, so it can be easily removed without blurring the clarity of the contour. Compared with other algorithms, such as the shearlet transform, block matching 3D, bilateral filtering, and Wiener filtering, the values of Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) obtained by the proposed method are better than those of other methods.

Because of noise interference, improper exposure, and the over thickness of human tissues, the detailed information of DR (digital radiography) images can be masked, including unclear edges and reduced contrast. An image-enhancement algorithm based on wavelet multiscale decomposition is proposed to address the shortcomings of existing single-scale image-enhancement algorithms. The proposed algorithm is based on Shannon–Cosine wavelets by taking advantage of the interpolation, smoothness, tight support, and normalization properties. Next a multiscale interpolation wavelet operator is constructed to divide the image into several sub-images from high frequency to low frequency, and to perform different multi-scale wavelet transforms on the detailed image of each channel. So that the most subtle and diagnostically useful information in the image can be effectively enhanced. Moreover, the image will not be over-enhanced and combined with the high contrast sensitivity of the human eye’s visual system in smooth regions, different attenuation coefficients are used for different regions to achieve the purpose of suppressing noise while enhancing details. The results obtained by some simulations show that this method can effectively eliminate the noise in the DR image, and the enhanced DR image detail information is clearer than before while having high effectiveness and robustness.

Using the wavelet transform defined in the infinite domain to process the signal defined in finite interval, the wavelet transform coefficients at the boundary are usually very large. It will bring severe boundary effect, which reduces the calculation accuracy. The construction of interval wavelet is the most common method to reduce the boundary effect. By studying the properties of Shannon-Cosine interpolation wavelet, an improved version of the wavelet function is proposed, and the corresponding interval interpolation wavelet based on Hermite interpolation extension and variational principle is designed, which possesses almost all of the excellent properties such as interpolation, smoothness, compact support and normalization. Then, the multi-scale interpolation operator is constructed, which can be applied to select the sparse feature points and reconstruct signal based on these sparse points adaptively. To validate the effectiveness of the proposed method, we compare the proposed method with Shannon-Cosine interpolation wavelet method, Akima method, Bezier method and cubic spline method by taking infinitesimal derivable function $cos\left(x\right)$ and irregular piecewise function as an example. In the reconstruction of $cos\left(x\right)$ and piecewise function, the proposed method reduces the boundary effect at the endpoints. When the interpolation points are the same, the maximum error, average absolute error, mean square error and running time are $1.20$ × 10${}^{-4}$, $2.52$ × 10${}^{-3}$, $2.76$ × 10${}^{-5}$, $1.68$ × 10${}^{-2}$ and $4.02$ × 10${}^{-3}$, $4.94$ × 10${}^{-4}$, $1.11$ × 10${}^{-3}$, $9.27$ × 10${}^{-3}$, respectively. The four indicators mentioned above are all lower than the other three methods. When reconstructing an infinitely derivable function, the curve reconstructed by our method is smoother, and it satisfies $C^2$ and $G^2$ continuity. Therefore, the proposed method can better realize the reconstruction of smooth curves, improve the reconstruction efficiency and provide new ideas to the curve reconstruction method.

This paper investigates the mean-square stability of uncertain time-delay stochastic systems driven by G-Brownian motion, which are commonly referred to as G-SDDEs. To derive a new set of sufficient stability conditions, we employ the linear matrix inequality (LMI) method and construct a Lyapunov–Krasovskii function under the constraint of uncertainty bounds. The resulting sufficient condition does not require any specific assumptions on the G-function, making it more practical. Additionally, we provide numerical examples to demonstrate the validity and effectiveness of the proposed approach.

Weight is an important indicator of the growth and development of dairy cows. The traditional static weighing methods require considerable human and financial resources, and the existing dynamic weighing algorithms do not consider the influence of the cow motion state on the weight curve. In this paper, a dynamic weighing algorithm for cows based on a support vector machine (SVM) and empirical wavelet transform (EWT) is proposed for classification and analysis. First, the dynamic weight curve is obtained by using a weighing device placed along a cow travel corridor. Next, the data are preprocessed through valid signal acquisition, feature extraction, and normalization, and the results are divided into three active degrees during motion for low, medium, and high grade using the SVM algorithm. Finally, a mean filtering algorithm, the EWT algorithm, and a combined periodic continuation-EWT algorithm are used to obtain the dynamic weight values. Weight data were collected for 910 cows, and the experimental results displayed a classification accuracy of 98.6928%. The three algorithms were used to calculate the dynamic weight values for comparison with real values, and the average error rates were 0.1838%, 0.6724%, and 0.9462%. This method can be widely used at farms and expand the current knowledgebase regarding the dynamic weighing of cows.