Low-frequency Part Research Articles

Resonance Detection Method of AC-DC Hybrid Micro-grid Based on Wavelet Transform and Fast Fourier Transform

The grid connection of a mass of distributed power sources in the AC/DC hybrid micro-grid will cause harmonics, voltage sags, voltage fluctuations, and flicker in the grid, which seriously affects the power quality of the grid. Therefore, the power quality problems such as the resonance generated by the AC/DC hybrid micro-grid need to be studied urgently. In this paper, a resonance detection technology based on the combination of wavelet transform (WT) and fast Fourier transform (FFT) is proposed. This method uses wavelet transform to process the high-frequency and low-frequency parts of the signal separately, and eliminates part of the interference signal. The method then uses the FFT to obtain the resonance content. The AC/DC hybrid micro-grid resonance detection method based on WT and FFT can not only determine the time and amplitude of the resonance signal, but also filter the interference signal and improve the accuracy of frequency domain analysis. It is verified by simulation that the algorithm can detect the resonance of the AC/DC hybrid micro-grid.

Multiple topological states within a common bandgap of two non-trivial photonic crystals.

Topological photonic crystals (PCs) provide an effective method for controlling how light propagates and concentrates through their topological states. However, it remains unclear whether topological states can be obtained by combining two different two-dimensional (2D) PCs with topological non-trivial states. In this Letter, two types of 2D Penrose-square (P-S) PCs are proposed. These PCs can generate topological edge states (TESs) and topological corner states (TCSs) within the low-frequency part of the bandgap. Moreover, by combining these two non-trivial PCs, a total of two groups of TESs and four groups of TCSs can be generated in both the high-frequency and low-frequency parts of the common bandgap. To the best of our knowledge, the two proposed P-S PCs offer a new platform for investigating topological photonics and related devices, providing novel approaches and perspectives for generating topological states in 2D PCs.

Finite amplitude wave propagation through bubbly fluids

The existence of only a few bubbles could drastically reduce the acoustic wave speed in a liquid. Wood’s equation models the linear sound speed, while the speed of an ideal shock waves is derived as a function of the pressure ratio across the shock. The common finite amplitude waves lie, however, in between these limits. We show that in a bubbly medium, the high frequency components of finite amplitude waves are attenuated and dissipate quickly, but a low frequency part remains. This wave is then transmitted by the collapse of the bubbles and its speed decreases with increasing void fraction. We demonstrate that the linear and the shock wave regimes can be smoothly connected through a Mach number based on the collapse velocity of the bubbles.

Estimating elastic properties of sediments by pseudo-wells generation utilizing simulated annealing optimization method

The hydrate concentration model considerably affects elastic properties, including bulk and shear modulus. Defining seismic properties of sediments, such as compressional and shear wave velocity and density, provides valuable information to identify rock facies and fluid types. This information commonly results from pre-stack seismic inversion, while post-stack seismic information provides acoustic impedance as a layer-based property. Traditionally, seismic inversion requires well logs to produce an initial guess of inversion routines and provide a low-frequency part of the amplitude spectrum. Eventually, seismic inversion methods could not be performed in the areas without well-log data, such as deep sea areas. In such cases, pseudo-well logs derived from pre-stack seismic data are a solution. Pseudo-well generation is a title used to estimate the elastic parameters of sediments in areas, such as deep marine environments, where drilled wells are absent or sparse. Metaheuristic optimization algorithms are suitable tools for minimizing the cost function as they best match real and synthetic seismic data. In this study, the SEAM earth model has been used as a reference to investigate the quality of pseudo-well generation utilizing a simulated annealing (SA) algorithm as an optimization method of property model change, which minimizes the cost function of seismic inversion. As a result, considering an initial model type of the SEAM model, simultaneous seismic inversion introduced the best compressional and shear wave velocities and density logs, which provide the best real and synthetic seismic data match when synthetic data is calculated from the simplified Zoeppritz equation.

Robust engine slipping start control of hybrid electric vehicles with uncertainty in clutch slipping torque and change in driver demand torque

The engine slipping start (ESS) benefits parallel hybrid electric vehicles from stable ignition and emission reduction. However, inappropriate coordination between the traction motor torque and clutch slipping torque during the ESS will lead to poor smoothness of the vehicle and failed start of the engine. Uncertainty in clutch slipping torque and change in driver demand torque bring tough challenges with sluggish convergence and intensive vehicle jerk in practice. To deal with this problem, a novel two-layer model reference adaptive controller (MRAC) which contains two parallel reference models is proposed to improve robustness and convergence rate simultaneously. On one hand, uncertainties of clutch slipping torque are divided into a low-frequency part and a high-frequency part, and adaptive laws based on the output feedback are designed contrapuntally to enhance robustness. On the other hand, two parallel reference models are designed to accelerate the tracking error convergence rate without changing the reference profiles, which is generated according to the driver demand torque in real time. To test the robustness and convergence rate, the proposed two-layer MRAC is compared with the classical MRAC and proportional–integral controller under the driving scenario with uncertain clutch slipping torque and abrupt change in driver demand torque. The sensitivity with different adaptive gains and low-frequency and high-frequency uncertainties in clutch slipping torque are examined. Finally, hardware-in-the-loop experiments are performed to verify the effectiveness of the proposed two-layer MRAC.

Reinforced PEO/Cs polymers blend with Al2O3/TiO2 hybrid nanofillers: Nanocomposites for optoelectronics and energy storage

This work focuses on the meticulous preparation and characterization of polyethylene oxide (PEO)/chitosan (Cs) polymer blends infused with aluminum oxide nanoparticles (Al2O3 NPs) and sol-gel synthesized titanium oxide nanoparticles (TiO2 NPs). Employing the casting method, the study delves into a comprehensive analysis of the structural, optical, electrical, and dielectric properties exhibited by the resulting PEO/Cs-Al2O3/TiO2 nanocomposites. Structural evaluations utilized transmission electron microscopy (TEM), scanning electron microscopy (SEM), X-ray diffraction (XRD), and Fourier-transform infrared spectroscopy (FT-IR). UV–Vis spectra showed enhanced optical properties, with the indirect optical energy gap decreasing from 5.23 eV to 5.01 eV for blends with 2.4 wt% Al2O3/TiO2 NPs. The AC conductivity of the polymeric nanocomposites showed enhanced values compared with the pure blend. Additionally, dielectric permittivity and modulus exhibit tunability, presenting advantageous prospects with varying Al2O3/TiO2 NPs concentrations in the PEO/Cs blend. The Nyquist plots reveal distinctive features, including semicircular arcs at the low-frequency part and an inclined spike at the high-frequency part, with decreasing arc radius corresponding to increasing nanofiller contents. These observations are best fitted to two models of equivalent circuits. The engineered PEO/Cs-Al2O3/TiO2 nanocomposite capacitor showed enhanced storage capacity and controlled conductance characteristics. The findings of this study revealed that these nanocomposites hold promise as bandgap tuners, optical sensors, permittivity-tunable nanodielectrics, and novel host matrices for the development of solid polymer flexible electrolytes, thereby contributing to the next generation of energy storage and conversion devices with superior performance.

FSformer: A combined frequency separation network and transformer for LDCT denoising

Low-dose computed tomography (LDCT) has been widely concerned in the field of medical imaging because of its low radiation hazard to humans. However, under low-dose radiation scenarios, a large amount of noise/artifacts are present in the reconstructed image, which reduces the clarity of the image and is not conducive to diagnosis. To improve the LDCT image quality, we proposed a combined frequency separation network and Transformer (FSformer) for LDCT denoising. Firstly, FSformer decomposes the LDCT images into low-frequency images and multi-layer high-frequency images by frequency separation blocks. Then, the low-frequency components are fused with the high-frequency components of different layers to remove the noise in the high-frequency components with the help of the potential texture of low-frequency parts. Next, the estimated noise images can be obtained by using Transformer stage in the frequency aggregation denoising block. Finally, they are fed into the reconstruction prediction block to obtain improved quality images. In addition, a compound loss function with frequency loss and Charbonnier loss is used to guide the training of the network. The performance of FSformer has been validated and evaluated on AAPM Mayo dataset, real Piglet dataset and clinical dataset. Compared with previous representative models in different architectures, FSformer achieves the optimal metrics with PSNR of 33.7714 dB and SSIM of 0.9254 on Mayo dataset, the testing time is 1.825 s. The experimental results show that FSformer is a state-of-the-art (SOTA) model with noise/artifact suppression and texture/organization preservation. Moreover, the model has certain robustness and can effectively improve LDCT image quality.

A compact and narrow-band bandpass filter based on substrate integrated waveguide and spoof surface plasmon polaritons for millimeter-wave applications

This paper presents bandpass filter (BPF) comprising substrate integrated waveguide (SIW) and spoof surface plasmon polaritons (SSPPs), achieving miniaturized size, low insertion loss in the millimeter-wave band. SIW with single-slotted SSPP structure is employing to obtain the transmission zero (TZ) at the low-frequency part, and by introducing the SIW with rhombic periodic walls to enhance the low-frequency rejection. The target passband and TZ of the high-frequency part are realized by increasing the number of etching slots. Furthermore, we innovatively incorporate nonradiative (NR) slots etched below the SSPP structure to gain high out-of-band rejection level. SIW with rhombic periodic walls and slotted SSPP structure as one unit cell is analyzed and demonstrated. Ultimately, the two SIW unit cells are cascaded together to get better out-of-band rejection characteristics and serve as our final design. To validate the proposed design, the BPF prototype is fabricated and measured, showing good electrical performance in terms of high selectivity, low loss, and compact size.

An Acoustic Array Sensor Signal Recognition Algorithm for Low-Altitude Targets Using Multiple Five-Element Acoustic Positioning Systems with VMD

To solve the problem in target acoustic signal processing and recognition when the target flies at a low altitude based on the acoustic positioning system, which is often affected by external interference and brings false information, this paper proposes a target signal processing and recognition algorithm for low-altitude target acoustic positioning based on variational modal decomposition and the test method of multiple five-element acoustic arrays. This algorithm uses VMD to decompose the target signal into modal components with different central frequencies and then performs wavelet threshold processing on the low-frequency part of the signal. After determining the remaining signal components and the low-frequency part’s threshold, the residual component is reconstructed. Based on the test principle and calculation model of the five-element acoustic positioning system, following processing of the low-altitude target acoustic positioning signal using variational modal decomposition, the cross-correlation function method is introduced to perform correlation operations on the basic array of five acoustic sensors and then obtain the time value and time difference of the target acoustic information in each acoustic sensor, ultimately determining the spatial position of the target. Finally, we used the data fusion processing method for target coordinates in multi-acoustic basic arrays to determine the actual target position. By comparing the results obtained using the high-speed camera method with those of the proposed approach, it was found that the average error in the test area of 100 × 100 m was less than 1 m.

Investigation of a Nonlinear XNOR Logic Gate Based on an Induced Nonlinear Phase Shift of Spin Waves

Introduction. Recent years have seen a growing interest in studying the nonlinear properties of spin waves. Nonlinear phenomena, such as envelope solitons, nonlinear frequency shifts of intense spin waves, and etc., have attracted particular attention. However, a number of important issues remain to be underexplored, including the problem of induced nonlinear phase shift of spin waves. The relevance of this problem is related to the need to develop spin-wave logic gates that could be controlled by changing the spin wave phase.Aim. To study a nonlinear XNOR logic gate whose operation is based on the induced nonlinear phase shift of a spin wave.Materials and methods. An original theory is used to simulate the frequency response of a nonlinear XNOR logic gate. The operating principle of the nonlinear XNOR logic gate is substantiated. The possibility of implementing the nonlinear XNOR logic gate in a circuit similar to a spin-wave Mach-Zehnder interferometer is experimentally demonstrated.Results. An experimental study of the induced nonlinear phase shift of operating signals incident on identical nonlinear spin-wave phase shifters located in the arms of the logic gate was carried out. It is shown that an increase in the pump signal power up to 60 mW, supplied to nonlinear phase shifters, changes the induced nonlinear phase shift of the operating signal by more than 180°. Hence, nonlinear phase shifters can be used for constructing spin-wave logic gates. In addition, the operating principle of a spin-wave logic gate was experimentally studied. It is shown that the XNOR logical function is implemented in the low-frequency part of the device’s frequency response characteristic.Conclusion. Numerical simulation of the characteristics of a nonlinear XNOR logic gate based on the Mach-Zehnder interferometer circuit was carried out. It is shown that its logical functions are implemented due to the effect of an induced nonlinear phase shift of spin waves in nonlinear phase shifters located in different arms of the logic gate.

A New Method for Deformation Monitoring of Structures by Precise Point Positioning

Although deformations are mostly insignificant, they can be catastrophic when accumulated to certain amounts. Precise point positioning (PPP) can work with one receiver, preventing problems caused by the base station constrain upon employment of current methods such as real-time kinematics (RTK). However, current methods employing PPP focus on high-frequency monitoring such as earthquake or geological calamity monitoring, and these methods are not suitable for structures. Thus, this study proposes a new method for the deformation monitoring of structures via PPP. First, we obtained the coordinate sequence of structures via static PPP when setting the interval. Then, we transformed the coordinates to the same coordinate system with the same basis. Finally, we decomposed the sequences via empirical mode decomposition (EMD) to obtain a low-frequency part, which is the deformation of the target structure. The result of the monitoring experimentation on IGS stations shows that the monitoring index, Sd, of the sequence under different intervals using this method could be 1–2 mm on average in the directions of E, N, and U, which is much better than the original monitoring sequence. Alongside that, it prevented a fall in accuracy when the interval decreased. Therefore, all results proved the feasibility and validity of the method.

Efficient bandwidth extension of musical signals using a differentiable harmonic plus noise model

The task of bandwidth extension addresses the generation of missing high frequencies of audio signals based on knowledge of the low-frequency part of the sound. This task applies to various problems, such as audio coding or audio restoration. In this article, we focus on efficient bandwidth extension of monophonic and polyphonic musical signals using a differentiable digital signal processing (DDSP) model. Such a model is composed of a neural network part with relatively few parameters trained to infer the parameters of a differentiable digital signal processing model, which efficiently generates the output full-band audio signal. We first address bandwidth extension of monophonic signals, and then propose two methods to explicitly handle polyphonic signals. The benefits of the proposed models are first demonstrated on monophonic and polyphonic synthetic data against a baseline and a deep-learning-based ResNet model. The models are next evaluated on recorded monophonic and polyphonic data, for a wide variety of instruments and musical genres. We show that all proposed models surpass a higher complexity deep learning model for an objective metric computed in the frequency domain. A MUSHRA listening test confirms the superiority of the proposed approach in terms of perceptual quality.

A Distorted Light Field Image Correction Method Based on Improved Hough Transform

Introduction: In using a camera to take photos, due to environmental limitations, uneven lighting can cause uneven distribution of the image light field, resulting in distortion of the image background and target, blurring of details, and distorted light field images. Method: In view of this, research is conducted on the correction of distorted light field images based on the Hough transform. First, the improved Hough transform is utilized to locate the four coordinates, the matrix information of the normal image is applied to calculate the corresponding parameter amount, and then the low-frequency part of the image spectrum is removed. Finally, it uses the Gaussian function for difference, inputs the original data, and gets the correction result of the distorted light field image. Result: The research results indicate that in the practical application of the distorted light field image correction algorithm based on the Hough transform, the improved Hough transform algorithm is superior to the traditional one. Conclusion: In comparative experiments, the research algorithm outperforms the other three algorithms, with an average color restoration of 93.76% and an average signal-to-noise ratio of 54.22dB. The superiority of the research algorithm has been verified, indicating that the research method can perfectly correct distorted light field images and achieve good correction results.

Effectively boosting hydration capacity and oxygen reduction activity of cobalt-free perovskite cathode by K+ doping strategy for protonic ceramic fuel cells

Development of triple-conducting cathode can extend the electrochemically active region to the entire cathode to more effectively promoting oxygen reduction reaction (ORR). Herein, a cobalt-free perovskite Sr1.75K0.25Fe1.5Mo0.5O6−δ (SKFM) was developed as a single-phase triple-conducting cathode material for protonic ceramic fuel cells (PCFCs). Introduction of K into Sr-site leads to a 21.54 % increase in the hydration capacity compared to the undoped Sr2Fe1.5Mo0.5O6−δ (SFM). The bulk diffusion coefficient and surface exchange coefficient of SKFM are 3.8 and 5.2 times higher than those of SFM at 550 °C, respectively. XAS and EPR results demonstrate that the average valence state of Fe and the concentration of surface oxygen vacancies in SKFM are higher than those in SFM. The polarization resistances (Rp) value of SKFM cathode in wet air is 0.06 Ω cm2 at 700 °C, while it is 0.11 Ω cm2 for SFM cathode, which is reduced by 45.5 %, indicating significantly improved ORR activity. The Rp is dominated by the adsorption and diffusion process of oxygen associated with low-frequency part in wet air. The single cell with a configuration of Ni-BZCY4/21-μm-thick BZCY4/SKFM delivers a power output of 1000.8 mW cm−2 in wet H2 at 700 °C and steady operation at 600 °C for a total of 100 h.

An Image Arbitrary-Scale Super-Resolution Network Using Frequency-domain Information

Image super-resolution (SR) is a technique to recover lost high-frequency information in low-resolution (LR) images. Since spatial-domain information has been widely exploited, there is a new trend to involve frequency-domain information in SR tasks. Besides, image SR is typically application-oriented and various computer vision tasks call for image arbitrary magnification. Therefore, in this article, we study image features in the frequency domain to design a novel image arbitrary-scale SR network. First, we statistically analyze LR-HR image pairs of several datasets under different scale factors and find that the high-frequency spectra of different images under different scale factors suffer from different degrees of degradation, but the valid low-frequency spectra tend to be retained within a certain distribution range. Then, based on this finding, we devise an adaptive scale-aware feature division mechanism using deep reinforcement learning, which can accurately and adaptively divide the frequency spectrum into the low-frequency part to be retained and the high-frequency one to be recovered. Finally, we design a scale-aware feature recovery module to capture and fuse multi-level features for reconstructing the high-frequency spectrum at arbitrary scale factors. Extensive experiments on public datasets show the superiority of our method compared with state-of-the-art methods.

Spanwise correlation of unsteady lift due to vortex shedding on the square cylinder: Perspectives provided by a time–frequency analysis

Spanwise correlation of unsteady lift due to vortex shedding is of particular interest for slender structures. In this paper, Hilbert transform and Wavelet transform were applied as time–frequency analysis tools to the sectional lift of a square cylinder. For Wavelet transform, the complex Morlet wavelet and the generalized Morse wavelet were considered as the mother wavelets, and the synchrosqueezing technique was used for post-processing. At high Reynolds number and in smooth flow, Hilbert transform and Wavelet transform mutually confirm that vortex shedding is characterized by an instantaneous shedding frequency fluctuating in real-time. As an example, at Reynolds number 3.9×104, the results of Wavelet transform suggest a standard deviation of the instantaneous shedding frequency of at least 4% about the conventional Strouhal frequency. The extracted instantaneous frequency is found stochastic, showing reasonably good Gaussian properties for its probability density function. The instantaneous frequencies simultaneously extracted at two cross sections of a spanwise separation are correlated, being the correlation coefficient lower than that calculated with fluctuating lifts. The shape of the coherence of the instantaneous frequency is found quite similar to that of turbulence, and the magnitude overall decreases with the increase of spanwise separation. The fluctuation of the instantaneous vortex shedding frequency, especially the low-frequency part (lower than about one-half of the Strouhal frequency), is believed critical in determining the spanwise correlation of unsteady lift, which was confirmed reconstructable via the extracted instantaneous shedding frequency. Finally, attention in this paper has also been paid to a reliable extraction and quantification of the concerning time–frequency characteristics. For instance, tests of the used time–frequency tools first on the purposely prepared artificial signal suggest, that the high-frequency fluctuation in the instantaneous vortex shedding frequency (higher than the Strouhal frequency) can actually not be reliably extracted.

S2O-FSPI: Fourier single pixel imaging via sampling strategy optimization

It is necessary to artificially set the sampling strategy of Fourier single-pixel imaging (FSPI) to obtain more useful information of the image under the assumption that the image information is mainly concentrated in the low-frequency part of the spatial frequency domain. However, due to the empiricism sampling strategy, it is easy to sample the spatial frequencies with low contribution to image reconstruction, resulting in a waste of sampling resources. To solve this problem, a one-stage FSPI reconstruction network with sampling strategy optimization is designed to obtain the efficient sampling strategy and improve the reconstruction quality. The proposed one-stage FSPI reconstruction network contains the sampling strategy optimization module and reconstruction module, which are jointly trained to obtain high-quality reconstructed results and efficient sampling strategy simultaneously. Experiments and numerical simulations demonstrate the effectiveness of the proposed method. Moreover, the geometric topology of the optimal sampling strategy for FSPI reconstruction trained on various categories of datasets is summarized. It is found that the dataset with similar categories have the similar geometric topology of the optimal sampling strategy, which provides support for sampling strategy selection in subsequent Fourier single-pixel imaging studies.

An image zooming method based on the coupling threshold in the wavelet packet transform domain

Aiming at the problem of blurring edge and detail information in the process of image zooming, this paper proposes a new method of image zooming based on wavelet packet transform by combining the characteristics of anisotropic diffusion. First, the initial zoomed image with higher resolution is obtained by wavelet transform, and the wavelet packet decomposition is performed to obtain more high-frequency wavelet packet coefficients reflecting image details. Second, due to the existence of noise, the relationship between wavelet packet transform and anisotropic diffusion is obtained by studying the process of wavelet packet threshold denoising, and the expression of coupling threshold based on diffusion function is given and applied to the high-frequency wavelet packet coefficients. Finally, the original image is used as the low-frequency part after passing the soft threshold, and reconstructed with the denoised high-frequency part to obtain the final zoomed image. The traditional zooming algorithms as well as the learning-based zooming algorithms are selected for comparison. The results show that the algorithm in this paper effectively avoids the blurring of edges and details under the premise of ensuring the similarity between the zoomed image and the original image, so that the zoomed image can obtain more high-frequency information, and achieves the purpose of removing the noise as well as enhancing the detailed information of the image. The effectiveness of this paper’s algorithm in edge protection can be seen from the results of the comparison with the deep learning-based zooming algorithms.

USING ESP32 MICROCONTROLLER FOR PHYSICAL SIMULATION OF THE WIRELESS REMOTE CONTROL MODEM

Context. Due to the need for practical implementation of the theoretical provisions of the proposed method of the wireless transmission of the commands for controlling a moving object in conditions of intentional interference.
 Objective of the work is a practical verification of the possibility of using a phase-pulse modulation of the linear-frequencymodulated signal for transmission a control commands through physical modeling using microcontrollers.
 Method. Analytical calculations of the change in time of the voltage at the input and output of the device for optimal processing of the linear frequency-modulated signal were carried out exclusively using the computing capabilities of the microcontroller. The graphs of changes in time of the relevant parameters were built with the help of Excel using the data output to the monitor of the serial port of the Arduino IDE software environment. A digital oscilloscope with a USB host was used to monitor the operation of a wireless modem to transmit control commands to a moving object.
 Results. Analytical calculations and physical modeling using a modern microcontroller proved the operability of the lowfrequency part the wireless remote control modem with using phase-pulse modulation of the linear frequency-modulated signal.
 Conclusions. The possibility of using phase-pulse modulation of the linear-frequency modulated signal for the transmission of control commands is considered. This method of transmitting the information component, unlike the existing methods, does not require changing the parameters of the linear frequency modulated signal. The use in the receiver of optimal processing of a linearfrequency-modulated signal of sufficiently big base will allow of the wireless transmission of the commands for controlling a moving object in conditions of the intentional interference. The use of modern microcontrollers made it possible to conduct a practical test of the functionality of the low-frequency part the wireless remote control modem with phase-pulse modulation of the linear-frequency modulated signal through physical modeling.

GSDerainNet: A Deep Network Architecture Based on a Gaussian Shannon Filter for Single Image Deraining

With the continuous advancement of target detection technology in remote sensing, target detection technology in images captured by drones has performed well. However, object detection in drone imagery is still a challenge under rainy conditions. Rain is a common severe weather condition, and rain streaks often degrade the image quality of sensors. The main issue of rain streaks removal from a single image is to prevent over smoothing (or underclearing) phenomena. Aiming at the above problems, this paper proposes a deep learning (DL)-based rain streaks removal framework called GSDerainNet, which properly formulates the single image rain streaks removal problem; rain streaks removal is aptly described as a Gaussian Shannon (GS) filter-based image decomposition problem. The GS filter is a novel filter proposed by us, which consists of a parameterized Gaussian function and a scaled Shannon function. Two-dimensional GS filters exhibit high stability and effectiveness in dividing an image into low- and high-frequency parts. In our framework, an input image is first decomposed into a low-frequency part and a high-frequency part by using the GS filter. Rain streaks are located in the high-frequency part. We extract and separate the rain features of the high-frequency part through a deep convolutional neural network (CNN). The experimental results obtained on synthetic data and real data show that the proposed method can better suppress the morphological artifacts caused by filtering. Compared with state-of-the-art single image rain streaks removal methods, the proposed method retains finer image object structures while removing rain streaks.