Two-dimensional Filters Research Articles

Synthesis of High-Selectivity Two-Dimensional Filter Banks Using Sigmoidal Function

This paper explores an application of the sigmoidal function—the complementary integral Gaussian error function (erfc(.))—in two-dimensional (2D) uniform and nonuniform filter bank synthesis. The complementary integral Gaussian error function graph represents a smooth low-pass filter magnitude response. A parameter changes the function slope and increases the magnitude response selectivity. The theory is applied to 2D band-pass filter banks. Exact expressions for the magnitude response parameters are determined. As a result, 2D uniform and nonuniform filter banks with very high selectivity and exact shapes are obtained. Three synthesis examples of 2D filter banks with circular and fan-shaped magnitude responses are provided. The theoretical exposition is supplemented with two examples of image analysis using 2D uniform and nonuniform filter banks. A procedure to reduce the computations in image analysis is proposed. A comparison of filter synthesis between Parks–McLellan’s 2D filters and the erfc(.) demonstrates the significantly shorter calculation time of the proposed method.

Interferometric phase diagram generation method based on dot trace texture information and semantic segmentation of correlation coefficients

This paper proposes a method for generating interferometric phase diagrams, which includes interferometric image registration based on Dot Trace Texture Information (DTTI) and interferometric phase filtering based on semantic segmentation. First, the InSAR images are sharpened according to the different backscattering characteristics of various pixel values, and DTTI is extracted to generate the Dot Trace Texture Map (DTTM). Second, SIFT feature points are extracted from two InSAR coherent complex images. They are then screened by comparison with DTTI. These selected points are used to calculate the registration relationship, ensuring precise registration of the two images. Third, the interferometric phase diagram is segmented by semantics based on correlation coefficients. For high-quality interferometric phase regions, we use two-dimensional frequency domain rotational symmetric Gaussian Laplace and wavelet domain filters successively. For low-quality regions, we use an average filter to smooth out noise. The superiority of the proposed algorithm was verified through comparative experiments.

Online two-dimensional filter for anti-interference aging features extraction to accurately predict the battery health

Reliable and precise extraction of features plays a critical role in predicting the State of Health (SOH) of lithium batteries. Nevertheless, noise-tainted measurement signal can cause the distortion of differential curves, consequently compromising the accuracy of feature extraction. This paper develops an online two-dimensional filtering framework by fusing the Adaptive Taylor Kalman filter (ATKF) and the Improved Gaussian filter (IGF), applying it to both incremental capacity analysis and differential thermal voltammetry methods. Firstly, the Taylor series is harnessed to construct a state model for the noise-affected measurement signal. Then, an adaptive algorithm is introduced to diminish the dependence on human judgment when configuring variances. Finally, the IGF filters the curve from the two-dimensions of time and period. Experimental results demonstrate that the two-dimensional filtering method exhibits robust noise mitigation capabilities, enhancing the stability of feature extraction while maintaining system causality. Furthermore, this method has strong robustness to battery inconsistency and temperature uncertainty. When applying the proposed filter to extract aging features from battery data provided by CALCE and Oxford datasets, the correlation coefficient between the extracted aging features and SOH increases by 34.75% and 10.71%, respectively. Additionally, the RMSE of the SOH prediction results decreases by 60.57% and 59.46%, respectively.

High-Noise Grayscale Image Denoising Using an Improved Median Filter for the Adaptive Selection of a Threshold

Grayscale image processing is a key research area in the field of computer vision and image analysis, where image quality and visualization effects may be seriously damaged by high-density salt and pepper noise. A traditional median filter for noise removal may result in poor detail reservation performance under strong noise and the judgment performance of different noise characteristics has strong dependence and rather weak robustness. In order to reduce the effects of high-density salt and pepper noise on image quality when processing high-noise grayscale images, an improved two-dimensional maximum Shannon entropy median filter (TSETMF) is proposed for the adaptive selection of a threshold to enhance the filter performance while stably and effectively retaining the details of the images. The framework of the proposed improved TSETMF algorithm is designed in detail. The noise in images is filtered by means of automatically partitioning a window size, the threshold value of which is adaptively calculated using two-dimensional maximum Shannon entropy. The theoretical model is verified and analyzed through comparative experiments using three kinds of classical grayscale images. The experimental results demonstrate that the proposed improved TSETMF algorithm exhibits better processing performance than that of the traditional filter, with a higher suppression of high-density noise and denoising stability. This stronger ability while processing high-density noise is demonstrated by a higher peak signal-to-noise ratio (PSNR) of 24.97 dB with a 95% noise density located in the classical Lena grayscale image. The better denoising stability, with a noise density from 5% to 95%, is demonstrated by the minor decline in the PSNR of approximately 10.78% relative to a PSNR of 23.10 dB located in the classical Cameraman grayscale image. Furthermore, it can be advanced to promote higher noise filtering and stability for processing high-density salt and pepper noise in grayscale images.

Two-Dimensional Hankel Norm Performance of Roesser-Type Filters

This article introduces a novel approach to examining the unfavorable memory effects of two-dimensional (2-D) Roesser-type filters based on the 2-D Hankel norm performance. Novel analysis criteria are obtained such that the 2-D Roessertype filters associated with saturation have the guaranteed 2-D Hankel norm performance bound. These criteria can analyze the undesired effect reduction of Roesser-type filters for past horizontal and vertical excitations. Without external horizontal and vertical input signals, the 2-D asymptotic convergence of Roesser-type filters is ascertained under the proposed novel criteria. Finally, a numerical demonstration is given to verify the validity of the obtained criteria. The criteria presented in this paper for 2-D filters and those reported in our recent paper for one-dimensional (1-D) filters can provide a whole analysis framework for the undesired memory effects of filters.

Four mathematical modeling forms for correlation filter object tracking algorithms and the fast calculation for the filter

<p>The correlation filter object tracking algorithm has gained extensive attention from scholars in the field of tracking because of its excellent tracking performance and efficiency. However, the mathematical modeling relationships of correlation filter tracking frameworks are unclear. Therefore, many forms of correlation filters are susceptible to confusion and misuse. To solve these problems, we attempted to review various forms of the correlation filter and discussed their intrinsic connections. First, we reviewed the basic definitions of the circulant matrix, convolution, and correlation operations. Then, the relationship among the three operations was discussed. Considering this, four mathematical modeling forms of correlation filter object tracking from the literature were listed, and the equivalence of the four modeling forms was theoretically proven. Then, the fast solution of the correlation filter was discussed from the perspective of the diagonalization property of the circulant matrix and the convolution theorem. In addition, we delved into the difference between the one-dimensional and two-dimensional correlation filter responses as well as the reasons for their generation. Numerical experiments were conducted to verify the proposed perspectives. The results showed that the filters calculated based on the diagonalization property and the convolution property of the cyclic matrix were completely equivalent. The experimental code of this paper is available at <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://github.com/110500617/Correlation-filter/tree/main">https://github.com/110500617/Correlation-filter/tree/main</ext-link>.</p>

Novel Low-Pass Two-Dimensional Mittag–Leffler Filter and Its Application in Image Processing

This paper presents an innovative Mittag–Leffler two-dimensional filter and its application in image processing. The proposed filter leverages the utilization of a Mittag–Leffler function within the probability density function. It introduces three adjustable filter parameters that enable the manipulation of the curve shape and the filter’s forgetting factor. Moreover, a two-dimensional Mittag–Leffler distribution was defined and used for the first time in an image filter. By conducting a comparative analysis against conventional filtering techniques, the paper showcases the distinct advantages of the proposed filter through illustrative examples. Additionally, the paper provides detailed implementation explanations and presents the Matlab function corresponding to the proposed two-dimensional filter.

An adaptive steganography insertion technique based on wavelet transform

Over the past few decades, there have been several successful methods developed for steganography. One popular technique is the insertion method, which is favored for its simplicity and ability to hold a reasonable amount of hidden data. This study introduces an adaptive insertion technique based on the two-dimensional discrete Haar filter (2D DHF). The technique involves transforming the cover image into the wavelet domain using 2D DWT and selecting a predetermined number of coefficients to embed the binary secret message. The selection process is carried out by analyzing the cover image in two non-orthogonal domains: 2D discrete cosine transform and 2D DHF. An adaptive algorithm is employed to minimize the impact on the unrepresented parts of the cover image. The algorithm determines the weights of each coefficient in each domain, and coefficients with low weights are chosen for embedding. To evaluate the effectiveness of the proposed approach, samples from the BOSSbase and custom databases are used. The technique’s performance is measured using three metrics: mean squared error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM). Additionally, a visual inspection by humans is conducted to assess the resulting image. The results demonstrate that the proposed approach outperforms recently reported methods in terms of MSE, PSNR, SSIM, and visual quality.

Anti-scattering medium computational ghost imaging with modified Hadamard patterns

Illumination patterns of computational ghost imaging (CGI) systems suffer from reduced contrast when passing through a scattering medium, which causes the effective information in the reconstruction result to be drowned out by noise. A two-dimensional (2D) Gaussian filter performs linear smoothing operation on the whole image for image denoising. It can be combined with linear reconstruction algorithms of CGI to obtain the noise-reduced results directly, without post-processing. However, it results in blurred image edges while performing denoising and, in addition, a suitable standard deviation is difficult to choose in advance, especially in an unknown scattering environment. In this work, we subtly exploit the characteristics of CGI to solve these two problems very well. A kind of modified Hadamard pattern based on the 2D Gaussian filter and the differential operation features of Hadamard-based CGI is developed. We analyze and demonstrate experimentally that using Hadamard patterns for illumination but using our developed modified Hadamard patterns for reconstruction (MHCGI) can enhance the robustness of CGI against turbid scattering medium. Our method not only helps directly obtain noise-reduced results without blurred edges but also requires only an approximate standard deviation, i.e., it can be set in advance. The experimental results on transmitted and reflected targets demonstrate the feasibility of our method. Our method helps to promote the practical application of CGI in the scattering environment.

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.

Investigation of angle-insensitive grating color filters at periods much smaller than the wavelength of incidence.

We designed and simulated one-dimensional (1D) and two-dimensional (2D) reflective grating color filters inside the aluminized polyethylene (PE) film. The filters have several advantages: high angle insensitivity (up to 45° for the 1D filter, 40° for the 2D filter), high reflectance at non-resonant wavelengths, deep resonance dips, and a large color gamut. Both structures are characterized by with their grating periods being much smaller than the wavelength of incidence. A grating modal analysis was utilized to reveal the physical mechanism behind such structures that exhibit angle-insensitive spectral responses which are favored in the fields of color display and packaging.

Two-dimensional filtering in the Fourier domain of transient grating coherent artifacts in time-resolved spectroscopy

Removal of coherent artifacts is important in the analysis of time and wavelength resolved spectroscopy data. By taking advantage of the strong correlation between spectra acquired sequentially in time, artifact removal can be formulated as a 2D problem for improved effectiveness. This paper proposes a 2D method to remove transient grating coherent artifacts from femtosecond time-resolved spectroscopy data based on filtering in the Fourier domain, leading to better estimation of the material parameters from the measured data. The method is simple, intuitive, and light on computation resources. The effectiveness of the method is demonstrated with experimental data acquired from a bare gold film with and without coherent artifacts using mutually parallel and perpendicular pump/probe polarizations, as well as with more complex samples (nanostructured gold film on a glass substrate and rhodamine fluorophores in solution). The proposed method is expected to be applicable to coherent artifact removal in other types of time and wavelength-resolved spectroscopy data.

Overflow Oscillation Elimination in Fixed-Point 2D Digital Filters Based on the Roesser Model

This paper investigates the overflow oscillation elimination problem in the fixed-point two-dimensional (2D) digital filter (DF) based on Roesser model subjected to two’s complement overflow (TCO) nonlinearities. By utilizing the system information and behavior of TCO nonlinearities more effectively, a new global asymptotic stability (GAS) criterion for 2D DFs is presented. A comparison of the obtained criterion with existing criteria is made with the help of examples.

Mode-1 N2 internal tides observed by satellite altimetry

Abstract. Satellite altimetry provides a unique technique for observing the sea surface height (SSH) signature of internal tides from space. Previous studies have constructed empirical internal tide models for the four largest constituents M2, S2, K1, and O1 by satellite altimetry. Yet no empirical models have been constructed for minor tidal constituents. In this study, we observe mode-1 N2 internal tides (the fifth largest constituent) using about 100 satellite years of SSH data from 1993 to 2019. We employ a recently developed mapping procedure that includes two rounds of plane wave analysis and a two-dimensional bandpass filter in between. The results show that mode-1 N2 internal tides have millimeter-scale SSH amplitudes. Model errors are estimated from background internal tides that are mapped using the same altimetry data but with a tidal period of 12.6074 h (N2 minus 3 min). The global mean error variance is about 25 % that of N2, suggesting that the mode-1 N2 internal tides can overcome model errors in some regions. We find that the N2 and M2 internal tides have similar spatial patterns and that the N2 amplitudes are about 20 % of the M2 amplitudes. Both features are determined by the N2 and M2 barotropic tides. The mode-1 N2 internal tides are observed to propagate hundreds to thousands of kilometers in the open ocean. The globally integrated N2 and M2 internal tide energies are 1.8 and 30.9 PJ, respectively. Their ratio of 5.8 % is larger than the theoretical value of 4 % because the N2 internal tides contain relatively larger model errors. Our mode-1 N2 internal tide model is evaluated using independent satellite altimetry data in 2020 and 2021. The results suggest that the model can make internal tide correction in regions where the model variance is greater than twice the error variance. This work demonstrates that minor internal tidal constituents can be observed using multiyear multi-satellite altimetry data and dedicated mapping techniques.

Modeling and Simulation of a Micro strip Antenna in Annular Geometry

In the last decade, the study of multidimensional systems for signal filtering purpose has attracted the attention of many research teams, which are motivated by various interesting real world applications such Image processing, video signal filtering processing, video signal filtering Computational tomography, distributed parameters systems. The representation of the state space realization for two-dimensional (2D) filters by a transfer function, with minimal delays is a crucial problem; the minimal realization can avoidmathematical complexities as well as technical benefit to hardware requirement. Unfortunately, it is not possible to find the minimal state space realization for every 2D system other than the 1D system, but we can find it for a specific cases of all-pole or the all-zero. Lattice filter is classified as an important structure in digital signal processing. In fact, it minimizes the computation complexity, reduces the finite word length and requires less hardware compared to the direct form digital filter with similar design specifications. The authors in two delay units z1-1 , z2-1 are used. In this paper we propose a new lattice-ladder structure of 2-D digital filter, composed of a delay units z1-1 and a basic lattice section z1 and z2-1 - Using matrix representation of the basic lattice sections and we derived transfer functions of the proposed 2-D digital ladder-lattice filters. The proposed structure is composed by a minimal number of delays and a minimal number of basic lattice sections. Furthermore, we have considered the description of the proposed lattice structure by using a state-space n-D Roesser form description presented in below and the implementations suggested by the authors in literatures. Besides, the state space equations for 2-D digital filter are presented, where the dimension of the matrices of the proposed lattice structure verify the minimal state space realization. The remainder of the paper is organized as follows; first is devoted to the proposed -D lattice-ladder structure and realization and in the second is dedicated to the state space realization. As conclusion this work has allowed us to approach a field that has experienced a great growth in recent years which is constantly evolving in order to improve, understanding and control the complex systems and processes that surround us.

Study on the application of multi-angle imaging related technology in the construction process

Abstract The mufti-angle imaging technique is proposed to address the wall position offset and the side flaps and gate flaps caused by the sparse array in the ultra-wide band through-wall radar building layout imaging, using the characteristic that the azimuth upward distance profile is similar around the main flap but different around the side flap/gate flap. Firstly, after the backward projection algorithm obtains the wall image of each viewpoint, the mufti-directional two-dimensional matching filter is used to enhance the image of each viewpoint and eliminate the effect of side flaps and raster flaps. Then the images of each viewpoint are decomposed by combining the multistage transform, i.e., the non-down sampling contour let transform, and the obtained low-frequency components and high-frequency components are fused using the corresponding fusion rules, respectively. Finally, the final fused building layout image is obtained by non-down sampling contour let inverse transform. The simulation experimental data show that the running time of the method in this paper is 10.99s. It shows that the proposed method enhances the outline and detail information of the building wall, and the final fused image obtained has prominent wall image, clearer edge contours, and good retention of overall detail information. The quality of image fusion is greatly improved than other methods, which paves the way for subsequent fusion methods including chatterers such as construction building corners and windows and doors.

Targeting the Human Influenza a Virus: The Methods, Limitations, and Pitfalls of Virtual Screening for Drug-like Candidates Including Scaffold Hopping and Compound Profiling.

In this study, we describe the input data and processing steps to find antiviral lead compounds by a virtual screen. Two-dimensional and three-dimensional filters were designed based on the X-ray crystallographic structures of viral neuraminidase co-crystallized with substrate sialic acid, substrate-like DANA, and four inhibitors (oseltamivir, zanamivir, laninamivir, and peramivir). As a result, ligand-receptor interactions were modeled, and those necessary for binding were utilized as screen filters. Prospective virtual screening (VS) was carried out in a virtual chemical library of over half a million small organic substances. Orderly filtered moieties were investigated based on 2D- and 3D-predicted binding fingerprints disregarding the "rule-of-five" for drug likeness, and followed by docking and ADMET profiling. Two-dimensional and three-dimensional screening were supervised after enriching the dataset with known reference drugs and decoys. All 2D, 3D, and 4D procedures were calibrated before execution, and were then validated. Presently, two top-ranked substances underwent successful patent filing. In addition, the study demonstrates how to work around reported VS pitfalls in detail.

A Robust Algorithm for Photon Denoising and Bathymetric Estimation Based on ICESat-2 Data

The Ice, Cloud, and Land Elevation Satellite 2 (ICESat-2) is equipped with an Advanced Terrain Laser Altimeter System (ATLAS) with the capability of penetrating water bodies, making it a widely utilized tool for the bathymetry of various aquatic environments. However, the laser sensor often encounters a significant number of noise photons due to various factors such as sunlight, water quality, and after-pulse effect. These noise photons significantly compromise the accuracy of bathymetry measurements. In an effort to address this issue, this study proposes a two-step method for photon denoising by utilizing a method combining the DBSCAN algorithm and a two-dimensional window filter, achieving an F1 score of 0.94. A robust M-estimation method was employed to estimate the water depth of the denoised and refraction-corrected bathymetric photons, achieving an RMSE of 0.30 m. The method proposed in this paper preserves as much information as possible about signal photons, increases the number of bathymetric points, enhances the resistance to gross error, and guarantees the accuracy of bathymetry measurements while outlining the underwater topography. While the method is not fully automated and requires setting parameters, the fixed parameter values allow for efficient batch denoising of underwater photon points in different environments.

Anisotropic cellulose nanocrystalline sponge sheets with ultrahigh water fluxes and oil/water selectivity

Oily sewage caused by oil spill accidents has become a severe problem in the last decades. Hence, two-dimensional sheet-like filter materials for oil/water separation have received widespread attention. Porous sponge materials were developed using cellulose nanocrystals (CNCs) as raw materials. They are environmentally friendly and easy to prepare, with high flux and separation efficiency. The 1,2,3,4-butane tetracarboxylic acid cross-linked anisotropic cellulose nanocrystalline sponge sheet (B-CNC) exhibited ultrahigh water fluxes driven by gravity alone, depending on the aligned structure of channels and the rigidity of CNCs. Meanwhile, the sponge gained superhydrophilic/underwater superhydrophobic wettability with an underwater oil contact angle of up to 165.7° due to its ordered micro/nanoscale structure. B-CNC sheets displayed high oil/water selectivity without additional material doping or chemical modification. For oil/water mixtures, high separation fluxes of approximately 100,000 L·m−2·h−1 and separation efficiencies of up to 99.99 % were obtained. For a Tween 80-stabilized toluene-in-water emulsion, the flux reached >50,000 L·m−2·h−1, and the separation efficiency was above 99.7 %. B-CNC sponge sheets showed significantly higher fluxes and separation efficiencies than other bio-based two-dimensional materials. This research provides a facile and straightforward fabrication method of environmental-friendly B-CNC sponges for rapid, selective oil/water separation.

Reference Signal Design and Power Optimization for Energy-Efficient 5G V2X Integrated Sensing and Communications

Recently, the development of integrated sensing and communications (ISAC) has attracted great attention. In this paper, the reference signal (RS) in 5G vehicle-to-everything (V2X) communications is leveraged for radar sensing. Particularly, the scattered RS design is adopted under the constraints of communication channel estimation and radar sensing ambiguity functions. To quantify the influence of RS design on channel estimation, the minimum mean square error (MMSE) via two-dimensional Wiener filter is derived in a closed-form for doubly-selective communication channel. The RS spacing and power allocation for RS and each data subcarrier are further jointly optimized to minimize the transmission power, while satisfying the requirements of communication data rate and radar sensing signal to noise ratio (SNR), which results in a mixed-integer non-linear programming (MINLP) problem. To address this problem, the successive convex approximation (SCA) based method is first developed to achieve a suboptimal solution. Next, we show that if the RS spacing is given, the optimal power allocation among RS and each data subcarrier can be achieved by solving three subproblems sequentially via (reverse) water-filling algorithms. Extensive simulations are carried out to validate the effectiveness of our proposed design. Compared to the existing subcarrier-wise RS design with uniform power allocation for data subcarriers, our design can reduce the power consumption by up to 12 dB.