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Scaling fractional-order memristors (fracmemristors) are a new research topic. Although remarkable progress has been made in the study of such memristors, there are some problems that require further study, for example, the effect of input signals on the instantaneous valid frequency range, failure to obtain the corresponding time-domain electrical characteristic expression of the fracmemristor, and the requirement of circuit schematics for using numerous memristor emulators. Most memristors in string scaling fracmemristor (SSF) circuit configurations must be of the floating-type. Therefore, the design and implementation of the circuit schematic are challenging. Motivated by this need, a SSF with a fixed valid frequency range was implemented using a simple circuit in this study. First, the circuit configuration of the SSF with a fixed valid frequency range and high approximation benefit was proposed. Subsequently, a simple circuit schematic of an incremental and decremental SSF was designed, and the corresponding time-domain electrical characteristic expression of the fracmemristor was obtained. Finally, rich analysis results for the electrical characteristics of the SSF were obtained. A circuit implementation of the SSF was used to verify the applicability of the theory. The main contributions of this study are as follows: the SSF circuit configuration and its simple circuit schematic with a fixed valid frequency range and high approximation benefit were devised, and the corresponding expressions of the time-domain electrical characteristics and the analysis results for the electrical characteristics were obtained. [ABSTRACT FROM AUTHOR]

This paper presents a multi-scale hybrid method for speckle reduction in ultrasound (US) images. Speckle is removed by guided filtering, directional filtering, and fractional order filtering on the coarse to fine resolution images of a wavelet pyramid. For the directional filter, the eigen-analysis of each pixel is firstly carried out to obtain its structural features, and then it is classified into edges for filtering. Speckle noise, corresponding to the homogeneous anatomical regions, is then alleviated by the guided filter. Thereby, the algorithm reduces speckle noise while enhancing edge sharpness regardless of the size of the edges. In the synthetic images, the proposed method showed statistically significant improvements in peak signal-to-noise ratio(PSNR), structural similarity(SSIM), feature similarity index(FSIM) index and Mean Squared Error(MSE) compared with other speckle reduction methods, e.g., the squeeze boxes (SBF) filter, optimal Bayesian NLM (OBNLM) filter, speckle reducing anisotropic diffusion filter (SRAD), nonlocal low-rank framework (NLLRF) and multi-scale attention-guided neural network (MSANN). Similarly, our method outperformed the other methods in terms of mainly metrics. All the clinical images that were denoised using the six speckle reduction methods were reviewed by four radiologists for evaluation based on each radiologist's diagnostic preferences. All the radiologists showed a significant preference for the liver images and arotid artery images obtained using our methods in terms of effectively suppresses speckle noise while preserving the structural details. For the kidney and thyroid images, our method showed similar improvement over other methods. The experimental results show that this method has better performance than other state-of-the-art medical ultrasonic image speckle removal methods. [ABSTRACT FROM AUTHOR]

K-means is a clustering method with an interpretable mechanism. However, its clustering results are significantly affected by the location of the initial cluster centers. More importantly, for it and its improved versions, it is extremely hard to adaptively determine the number of cluster centers. In contrast, ordinary neural networks have powerful information representation ability but lack interpretability. Moreover, to the best of our knowledge, the use of interpretable neural networks to determine the number of cluster centers of K-means is absent. This paper proposes K-meaNet that combines the interpretable mechanism of K-means and the powerful information representation ability of neural networks. For the neural network in K-meaNet, its inputs, weights, and mathematical expressions of each layer have clear meanings. During training, if one cluster center is critical, the value of one of the weights in the neural network, the gate, corresponding to this cluster center will increase. At the same time, the position of this cluster center will be close to the ideal cluster center. Besides, the location of the cluster center(s) and the value(s) of the corresponding gate(s) will not change significantly. This endows K-meaNet with the ability to adaptively determine the location and number of cluster centers compared with K-means and its improved versions. Moreover, this adaptive ability is robust to the location of the initial cluster centers, the number of the initial cluster centers, and the number of features. On six synthetic datasets and three real datasets, numerical experiments verify that K-meaNet can adaptively determine the number of cluster centers and is robust to the location of the initial cluster centers, the number of the initial cluster centers, and the number of features. [ABSTRACT FROM AUTHOR]

To utilize the full second-order statistical information of the complex-valued signal, a widely linear complex-valued LMM (WL-CLMM) algorithm is proposed by using different M-estimate functions. The proposed WL-CLMM algorithm can process both circular and noncircular complex-valued signals in impulsive noise environments. Moreover, a novel adaptive threshold adjustment method for the M-estimate function is designed according to the probability density function of the complex-valued error signal. In addition, to decrease the sensitivity of the input signal to the performance of the algorithm, the normalized version of WL-CLMM (WL-CNLMM) has been developed. Then, we carry out the mean behavior and mean square behavior analysis of the proposed algorithms. Simulation results show that the proposed algorithms outperform some existing complex-valued algorithms and the theoretical results are well matched. [ABSTRACT FROM AUTHOR]

Chain-scaling fractional-order memristors (fracmemristors) refers to the concept of implementing them in circuits. Despite its advantages, a few issues that require urgent attention remain, including the effect of input signals on its instantaneous valid frequency range, failure to find the corresponding time-domain electrical characteristic expression of the fracmemristor, and the use of several memristor emulators in circuit schematics. Accordingly, a simple circuit for implementing a chain-scaling fracmemristor (CSF) within a fixed valid frequency range is proposed in this paper. First, a CSF circuit configuration with a fixed valid frequency range is described. Subsequently, a simple circuit schematic of an incremental/decremental CSF is presented, and the corresponding time-domain electrical characteristic expressions of the fracmemristor are obtained. Finally, rich theoretical analysis results are obtained along with the CSF circuit implementation. The accuracy of the theoretical analysis is verified experimentally. In this study, we developed a method to achieve a CSF with a fixed valid frequency range through the replacement of all the capacitors with memcapacitors, which also facilitated the design of circuit schematics. [ABSTRACT FROM AUTHOR]

In this article, a widely linear complex-valued affine projection sign algorithm is proposed for handling nonstationary noise in the complex domain. Apart from using the second-order statistical information in the complex domain adequately, the proposed algorithm can succeed in obtaining the robustness against the impulsive noise. With the help of the Price's theorem and some rational assumptions, the steady-state mean-square analysis of the proposed algorithm has been shown in this paper. In addition, we achieve a low computational complexity combining the l1-norm operation of the error signal. Moreover, we still analyze the stability of our finding, providing the range of the step size of its widely linear model. In the end, the results of experiments with the impulsive noise make clear that the proposed algorithm obtains the robustness for both complex circular and noncircular signals. However, simulation results without the impulsive noise indicate that the proposed algorithm gets a worse behavior in terms of normalized mean-square deviation compared with various existing algorithms. In the stereophonic acoustic echo cancellation, our finding still achieves a good performance. [ABSTRACT FROM AUTHOR]

Images captured in low-light environment often lower its quality due to low illumination and high noise. Hence, the low visibility of images notably degrades the overall performance of multimedia and vision systems that are typically designed for high-quality inputs. To resolve this problem, numerous algorithms have been proposed in extant literature to improve the visual quality of low-light images. However, existing approaches are not good at improving overexposed portions and produce unnecessary distortion, which leads to poor visibility in images. Therefore, in this paper, a new model is proposed to prevent overenhancement, handle uneven illumination, and suppress noise in underexposed images. Firstly, the input image is converted into HSV color space. Then, the obtained V component is decomposed into high- and low-frequency subbands using the dual-tree complex wavelet transform. Secondly, a denoised model based on fractional-order anisotropic diffusion is applied on high-pass subbands. Thirdly, multiscale decomposition is used to extract more details from low-pass subbands, and inverse transformation is performed to compute final V. Next, sigmoid function and tone mapping are used on V-channel to prevent data loss and achieve robust results. Finally, the image is reconstructed and converted to RGB color space to achieve enhanced performance. Comparative experimental statistics show that the proposed method achieves high efficacy and outperforms the traditional approaches in terms of overall performance. [ABSTRACT FROM AUTHOR]

Given that the existing image denoising methods damage the texture details of an image, a new method based on fractional integration is proposed. First, the fractional-order integral formula is deduced by generalizing the Cauchy integral, and then the approximate value of the fractional-order integral operator is estimated by a numerical method. Finally, a fractional-order integral mask operator of any order is constructed in eight pixel directions of the image. Simulation results show that the proposed image denoising method can protect the edge texture information of the image while removing the noise. Moreover, this method can obtain higher image feature values and better image vision after denoising than the existing denoising methods, because a texture protection mechanism is adopted during the iterative processing. [ABSTRACT FROM AUTHOR]

We introduce the fractional-order global optimal backpropagation machine, which is trained by an improved fractional-order steepest descent method (FSDM). This is a fractional-order backpropagation neural network (FBPNN), a state-of-the-art fractional-order branch of the family of backpropagation neural networks (BPNNs), different from the majority of the previous classic first-order BPNNs which are trained by the traditional first-order steepest descent method. The reverse incremental search of the proposed FBPNN is in the negative directions of the approximate fractional-order partial derivatives of the square error. First, the theoretical concept of an FBPNN trained by an improved FSDM is described mathematically. Then, the mathematical proof of fractional-order global optimal convergence, an assumption of the structure, and fractional-order multi-scale global optimization of the FBPNN are analyzed in detail. Finally, we perform three (types of) experiments to compare the performances of an FBPNN and a classic first-order BPNN, i.e., example function approximation, fractional-order multi-scale global optimization, and comparison of global search and error fitting abilities with real data. The higher optimal search ability of an FBPNN to determine the global optimal solution is the major advantage that makes the FBPNN superior to a classic first-order BPNN. [ABSTRACT FROM AUTHOR]

The scaling fractal-chuan fractance approximation circuit (SFCFAC), which can realize the rational approximation of arbitrary-order fractances and has an excellent approximation performance, is presented in this paper. For an original SFCFAC, the progression ratios of resistance and capacitance are limited to the range 0–1. However, it is possible for the values of both progression ratios to be greater than one. The impedance function of an SFCFAC can be represented by an irregular scaling equation. By solving the scaling equation approximately, the operational order of an SFCFAC can be obtained using both progression ratios as μ = - lg α / lg (α β) . Therefore, the SFCFAC has fractional operational characteristics, which is explained in theory. Oscillation phenomena are inherent to the SFCFAC. It is necessary to learn about these oscillation characteristics. The approximation performance can be improved by adding a series resistor and a series capacitor to the SFCFAC. The corresponding resistance and capacitance are determined by both progression ratios. The optimization has the advantages of simple operation, evident influence, and good practicality, which will make the SFCFAC competitive in future studies. Moreover, the values of the operational order of SFCFACs are extended from - 1 < μ < 0 to 0 < | μ | < 2 without using inductors, which is feasible for practical applications. [ABSTRACT FROM AUTHOR]

The traditional integer-order computation-based denoising approaches often blur the edges and textural details of an image. To solve this problem, from the viewpoint of system evolution, and based on the features of fractional calculus, we propose to implement a texture image denoising approach based on fractional developmental mathematics (FDM) which applies a novel mathematical method, fractional calculus, to image denoising. First, we synopsize the necessary theoretical background of fractional calculus. Second, we derive the necessary mathematical models for implementation of a texture image denoising approach based on FDM. We derive fractional Green's formula, fractional Gauss' formula, and fractional Stokes' formula, and fractional Euler-Lagrange equation. Then, a texture image denoising approach based on FDM is proposed. Third, we implement comparative experiments. We firstly derive the numerical implementation of FDM. Then, we study the capability of preserving the edges and textural details of FDM by comparative experiments. The comparative experimental results show that the capability of preserving the edges and textural details of the FDM-based denoising algorithm is obviously superior to that of traditional integer-order computation-based algorithms, especially for texture detail rich images. [ABSTRACT FROM AUTHOR]