Gabor Functions Research Articles

Improved MRF rail surface defect segmentation method based on clustering features

Aiming at the characteristics of small number and many types of rail surface defect samples, as well as the problems of unstable transfer learning effect and threshold segmentation being easily affected by environmental factors in real scenes, an improved Markov defect segmentation method with zero samples is proposed. Firstly, the collected data is processed by Gabor function to highlight the defect features and reduce the data dimension to obtain the reduced dimension feature map; Kmeans clustering is performed on the processed feature map to reduce the distribution of data and reduce the influence of reflection and shadow, and the clustering result is used as the pre-classification matrix; an improved Markov random field two-layer graph model is constructed and inferred through the reduced dimension feature map and the pre-classification matrix; the local geometric structure of the defect part is analyzed according to the eigenvalues of the classification matrix inferred by the model; finally, the defect area is marked and the defect segmentation is completed. The experimental part uses a self-sampling data set, and the final conclusion is drawn based on the comparative experiment and ablation experiment. The experimental results show that the pixel accuracy, average pixel accuracy, weighted intersection-over-union ratio, and average intersection-over-union ratio of this method on the self-sampling data set are respectively 93.6%、80.7%、89.4%、68.2% , which exceeds the accuracy of other comparative detection algorithms.

Estimating receptive fields of simple and complex cells in early visual cortex: A convolutional neural network model with parameterized rectification.

Neurons in the primary visual cortex respond selectively to simple features of visual stimuli, such as orientation and spatial frequency. Simple cells, which have phase-sensitive responses, can be modeled by a single receptive field filter in a linear-nonlinear model. However, it is challenging to analyze phase-invariant complex cells, which require more elaborate models having a combination of nonlinear subunits. Estimating parameters of these models is made additionally more difficult by cortical neurons' trial-to-trial response variability. We develop a simple convolutional neural network method to estimate receptive field models for both simple and complex visual cortex cells from their responses to natural images. The model consists of a spatiotemporal filter, a parameterized rectifier unit (PReLU), and a two-dimensional Gaussian "map" of the receptive field envelope. A single model parameter determines the simple vs. complex nature of the receptive field, capturing complex cell responses as a summation of homogeneous subunits, and collapsing to a linear-nonlinear model for simple type cells. The convolutional method predicts simple and complex cell responses to natural image stimuli as well as grating tuning curves. The fitted models yield a continuum of values for the PReLU parameter across the sampled neurons, showing that the simple/complex nature of cells can vary in a continuous manner. We demonstrate that complex-like cells respond less reliably than simple-like cells. However, compensation for this unreliability with noise ceiling analysis reveals predictive performance for complex cells proportionately closer to that for simple cells. Most spatial receptive field structures are well fit by Gabor functions, whose parameters confirm well-known properties of cat A17/18 receptive fields.

Gabor-net with multi-scale hierarchical fusion of features for fundus retinal blood vessel segmentation

This paper proposes a fundus retinal blood vessel segmentation model based on a deep convolutional network structure and biological visual feature extraction mechanism. It aims to solve the multi-scale problem of blood vessels in the fundus retinal blood vessel segmentation task in the field of medical image processing on the basis of increasing the biological interpretability of the model. First, the subject feature information of the retinal blood vessel image is obtained by using the non-subsampled Residual Bolck convolution main channel. Secondly, combined with the study of biological vision mechanisms, an information processing model of the Retina-Exogenius-Primary visual cortex (V1) ventral visual pathway was established. Gabor functions of different scales are used to simulate the structure of different levels of the visual pathway, and the scale information at different levels is integrated into the corresponding hierarchical stages of the convolutional main pathway network to enrich the information of small blood vessels and enhance the semantic information of the overall blood vessels. Finally, considering the imbalance of the ratio of vessel and nonvessel pixels, an adaptive optimization scheme using hybrid loss function weights is proposed to enhance the priority of blood vessel pixels in the calculation of the loss function. According to the experimental results on the STARE, DRIVE and CHASE_DB1 data sets, the model still achieves superior performance evaluation indicators overall compared with the existing optimal methods in the fundus retinal blood vessel segmentation task. This research is of great significance to the field of medical image processing and can provide more accurate auxiliary diagnostic information for clinical diagnosis and treatment.

A Novel Learning Approach to Remove Oscillations in First‐Order Takagi–Sugeno Fuzzy System: Gradient Descent‐Based Neuro‐Fuzzy Algorithm Using Smoothing Group Lasso Regularization

AbstractAs a universal approximator, the first order Takagi–Sugeno fuzzy system possesses the capability to approximate widespread nonlinear systems through a group of IF THEN fuzzy rules. Although group lasso regularization has the advantage of inducing group sparsity and handling variable selection issues, it can lead to numerical oscillations and theoretical challenges in calculating the gradient at the origin when employed directly during training. The paper addresses the aforementioned obstacle by invoking a smoothing function to approximate group lasso regularization. On this basis, a gradient‐based neuro fuzzy learning algorithm with smoothing group lasso regularization for the first order Takagi–Sugeno fuzzy system is proposed. The convergence of the proposed algorithm is rigorously proved under gentle conditions. In addition, experimental outcomes acquired on two approximations and two classification simulations demonstrate that the proposed algorithm outperforms the algorithm with original group lasso regularization and L2 regularization in terms of error, pruned neurons, and accuracy. This is particularly evident in significant advancements in pruned neurons due to group sparsity. In comparison to the algorithm with L2 regularization, the proposed algorithm exhibits improvements of 6.3, 5.3, and 142.6 in pruned neurons during sin function, Gabor function, and Sonar benchmark dataset simulations, respectively.

Denoising odontocete echolocation clicks using a hybrid model with convolutional neural network and long short-term memory network.

Ocean noise negatively influences the recording of odontocete echolocation clicks. In this study, a hybrid model based on the convolutional neural network (CNN) and long short-term memory (LSTM) network-called a hybrid CNN-LSTM model-was proposed to denoise echolocation clicks. To learn the model parameters, the echolocation clicks were partially corrupted by adding ocean noise, and the model was trained to recover the original echolocation clicks. It can be difficult to collect large numbers of echolocation clicks free of ambient sea noise for training networks. Data augmentation and transfer learning were employed to address this problem. Based on Gabor functions, simulated echolocation clicks were generated to pre-train the network models, and the parameters of the networks were then fine-tuned using odontocete echolocation clicks. Finally, the performance of the proposed model was evaluated using synthetic data. The experimental results demonstrated the effectiveness of the proposed model for denoising two typical echolocation clicks-namely, narrowband high-frequency and broadband echolocation clicks. The denoising performance of hybrid models with the different number of convolution and LSTM layers was evaluated. Consequently, hybrid models with one convolutional layer and multiple LSTM layers are recommended, which can be adopted for denoising both types of echolocation clicks.

Research on Object Detection and Recognition Method for UAV Aerial Images Based on Improved YOLOv5

In this paper, an object detection and recognition method based on improved YOLOv5 is proposed for application on unmanned aerial vehicle (UAV) aerial images. Firstly, we improved the traditional Gabor function to obtain Gabor convolutional kernels with better edge enhancement properties. We used eight Gabor convolutional kernels to enhance the object edges from eight directions, and the enhanced image has obvious edge features, thus providing the best object area for subsequent deep feature extraction work. Secondly, we added a coordinate attention (CA) mechanism to the backbone of YOLOv5. The plug-and-play lightweight CA mechanism considers information of both the spatial location and channel of features and can accurately capture the long-range dependencies of positions. CA is like the eyes of YOLOv5, making it easier for the network to find the region of interest (ROI). Once again, we replaced the Path Aggregation Network (PANet) with a Bidirectional Feature Pyramid Network (BiFPN) at the neck of YOLOv5. BiFPN performs weighting operations on different input feature layers, which helps to balance the contribution of each layer. In addition, BiFPN adds horizontally connected feature branches across nodes on a bidirectional feature fusion structure to fuse more in-depth feature information. Finally, we trained the overall improved YOLOv5 model on our integrated dataset LSDUVD and compared it with other models on multiple datasets. The results show that our method has the best convergence effect and mAP value, which demonstrates that our method has unique advantages in processing detection tasks of UAV aerial images.

Rega-Net: Retina Gabor Attention for Deep Convolutional Neural Networks

Extensive research works demonstrate that the attention mechanism in convolutional neural networks (CNNs) effectively improves accuracy. Nevertheless, few works design attention mechanisms using large receptive fields. In this work, we propose a novel attention method named Rega-Net to increase CNN accuracy by enlarging the receptive field. To the best of our knowledge, increasing the receptive field of the convolutional neural network requires increasing the size of the convolution kernel, which also increases the number of parameters. For solving this problem, we design convolutional kernels to resemble the non-uniformly distributed structure inspired by the mechanism of the human retina. Then, we sample variable-resolution values in the Gabor function distribution and fill these values in retina-like kernels. This distribution allows essential features to be more visible in the center position of the receptive field. We further design an attention module including these retina-like kernels. Experiments demonstrate that our Rega-Net achieves 79.96% Top-1 accuracy on ImageNet-1K for classification and 43.1% mAP on COCO2017 for object detection. The mAP of the Rega-Net increased by up to 3.5% compared to baseline networks.

Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of 'stripe' formation in human data.

When two streams of pedestrians cross at an angle, striped patterns spontaneously emerge as a result of local pedestrian interactions. This clear case of self-organized pattern formation remains to be elucidated. In counterflows, with a crossing angle of 180°, alternating lanes of traffic are commonly observed moving in opposite directions, whereas in crossing flows at an angle of 90°, diagonal stripes have been reported. Naka (1977) hypothesized that stripe orientation is perpendicular to the bisector of the crossing angle. However, studies of crossing flows at acute and obtuse angles remain underdeveloped. We tested the bisector hypothesis in experiments on small groups (18-19 participants each) crossing at seven angles (30° intervals), and analyzed the geometric properties of stripes. We present two novel computational methods for analyzing striped patterns in pedestrian data: (i) an edge-cutting algorithm, which detects the dynamic formation of stripes and allows us to measure local properties of individual stripes; and (ii) a pattern-matching technique, based on the Gabor function, which allows us to estimate global properties (orientation and wavelength) of the striped pattern at a time T. We find an invariant property: stripes in the two groups are parallel and perpendicular to the bisector at all crossing angles. In contrast, other properties depend on the crossing angle: stripe spacing (wavelength), stripe size (number of pedestrians per stripe), and crossing time all decrease as the crossing angle increases from 30° to 180°, whereas the number of stripes increases with crossing angle. We also observe that the width of individual stripes is dynamically squeezed as the two groups cross each other. The findings thus support the bisector hypothesis at a wide range of crossing angles, although the theoretical reasons for this invariant remain unclear. The present results provide empirical constraints on theoretical studies and computational models of crossing flows.

Design of a Gabor Filter-Based Image Denoising Hardware Model

The intervention of noise into images during data acquisition and transmission is inevitable. Hence, the denoising of such affected images is essential in order to have effective image analysis where it needs image filtering. The Gabor filter is widely adapted in various image processing applications for feature extraction, texture analysis, pattern analysis, etc. The Gabor-based filtering technique adopted in work is aimed for image filtering in order to extract edges. The design of a low-power portable system deploys hardware accelerators to achieve high performance per watt in feature extraction and edge detection. In this paper, an image denoising hardware accelerator model is mapped from the Gabor filter function. Moreover, hardware models for realizing various parameters involved in the Gabor function are also presented. A MATLAB model for the proposed denoising hardware accelerator is simulated and performance is measured in terms of the peak-signal-to-noise ratio, mean square error, histograms and compared with algorithm level performance reported in the literature. It is observed that the proposed hardware architecture model showed better performance compared to the mathematical models reported in the literature. However, the key limitation is the degradation of hardware performance due to a truncation or rounding of the sample’s word length.

Pressure wrist pulse signal analysis by sparse decomposition using improved Gabor function

Background and objective: In traditional Chinese medicine and Ayurvedic medicine, wrist pulse wave fluctuations are an important indicator for distinguishing different health states. Owing to the development of modern sensing technology, computational methods have been used in the analysis of pulse wave signals. The description and quantification of the peaks in the pulse wave is significant for the identification of health status.Methods: In this study, we decomposed the pressure pulse waveform of the radial artery into several components by sparse decomposition with an improved Gabor function. To better represent the position, shape, and relationship of the peaks, we designed an improved Gabor function structure based on the characteristics of the pulse waveform to generate a time-frequency dictionary. Compared with conventional representation methods, the shape of the Gabor function is more variable. In addition, owing to the limitation of windowing, the Gabor function can reduce the influence on other positions when it represents a specific position. Feature vectors consisting of decomposed components can be used for computerized pulse signal analysis and disease diagnosis.Results: In the binary classification of healthy and diseased pulse signals, the proposed method achieved the best results for health/diabetes, health/cardiac disease, health/hypertension, and health/nephropathy with accuracies of 93.54%, 73.42%, 88.42%, and 82.28%, respectively. The multi-classification performance of the different types of features was evaluated by six classifiers, and the proposed method obtained the highest classification performance with support vector machine-radial basis function for both balanced and imbalanced data.Conclusions: The results indicated that the proposed method enabled to obtain a smaller representation error and exhibited superior performance in distinguishing between the signals collected from patients and healthy individuals. Moreover, for the multi-classification of the pulse signals, the proposed method performed better than the state-of-the-art methods.

Ультразвуковой метод определения ориентации углеродных нанотрубок при использовании разреженного представления

Carbon nanotubes orientation has a significant impact on the performance of carbon nanotubes/epoxy resin (CNTs/EP) composite materials. The ultrasonic velocity is sensitive to the degree of carbon nanotubes orientation. However, the time-of-flight (TOF) is difficulty to accurately measured due to ultrasonic echo aliasing and waveform distortion occurred in the thin CNTs/EP composite material. Therefore, the ultrasonic characterization method of carbon nanotubes orientation based on the sparse representation is studied in this paper. Two groups of CNTs/EP specimens are taken as research objects. Firstly, the dictionary is constructed by Gabor function，and the matching degree between dictionary and ultrasonic echo signals is researched. Then, the matching pursuit (MP) algorithm is used to solve the problem of dictionary redundancy and obtain the best matching atom; the signal reconstruction is completed and ultrasonic TOF of carbon nanotubes is extracted more accurately. Finally, a carbon nanotubes orientation prediction model based on the sparse representation is established. The result shows that the Gabor dictionary has good similarity with ultrasonic echo signals and the root mean square relative error is 0.0147. The degree of carbon nanotubes orientation and ultrasonic velocity have positive correlation. The carbon nanotubes orientation prediction model relative error is 5.58%. This paper has provided an effective method to characterize the degree of carbon nanotubes orientation.

A Compact CNN-Based Speech Enhancement With Adaptive Filter Design Using Gabor Function and Region-Aware Convolution

Speech enhancement (SE) is used in many applications, such as hearing devices, to improve speech intelligibility and quality. Convolutional neural network-based (CNN-based) SE algorithms in literature often employ generic convolutional filters that are not optimized for SE applications. This paper presents a CNN-based SE algorithm with an adaptive filter design (named ‘CNN-AFD’) using Gabor function and region-aware convolution. The proposed algorithm incorporates fixed Gabor functions into convolutional filters to model human auditory processing for improved denoising performance. The feature maps obtained from the Gabor-incorporated convolutional layers serve as learnable guided masks (tuned at backpropagation) for generating adaptive custom region-aware filters. The custom filters extract features from speech regions (i.e., ‘region-aware’) while maintaining translation-invariance. To reduce the high cost of inference of the CNN, skip convolution and activation analysis-wise pruning are explored. Employing skip convolution allowed the training time per epoch to be reduced by close to 40%. Pruning of neurons with high numbers of zero activations complements skip convolution and significantly reduces model parameters by more than 30%. The proposed CNN-AFD outperformed all four CNN-based SE baseline algorithms (i.e., a CNN-based SE employing generic filters, a CNN-based SE without region-aware convolution, a CNN-based SE trained with complex spectrograms and a CNN-based SE processing in the time-domain) with an average of 0.95, 1.82 and 0.82 in short-time objective intelligibility (STOI), perceptual evaluation of speech quality (PESQ) and logarithmic spectral distance (LSD) scores, respectively, when tasked to denoise speech contaminated with NOISEX-92 noises at -5, 0 and 5 dB signal-to-noise ratios (SNRs).

Convolutional Neural Network Based on Diverse Gabor Filters for Deepfake Recognition

Media synthesis and manipulation has reached unprecedented levels of realism owing to the proliferation of deep learning. Deepfake has been the de-facto tool for media manipulation. Although this technology has potential in the entertainment industry, its threats include political manipulation and bypassing biometric security systems. As a result, deepfake detection has garnered widespread attention among research communities. The intuition is to use deep learning to fix the problems created by deep learning. Although convolutional neural networks have shown their dominance in the filed of pattern recognition, the receptive field-model size dilemma still persists along with the lack of interpretation for such models. While the traditional Gabor function was proposed to fix these problems, it can only generate limited linear Gabor filters which makes it optimal for limited data and applications. The contribution of this paper is quadruple: (i) proposing a unified Gabor function capable of generating linear, elliptical, and circular Gabor filters. (ii) leveraging the back-propagation learning framework to incorporate the proposed function in convolutional neural networks and generate adaptive Gabor filters. (iii) presenting a dual scale large receptive field network for deepfake image recognition. (iv) demonstrating where the proposed model stands in terms of performance and architecture size compared to state-of-the-art models. The proposed model is evaluated on four benchmark datasets: Celeb-DF (v2), DeepFake Detection Challenge Preview, FaceForensics++ and Wilddeepfake. Experimental results show that the proposed adaptive Gabor filters reduce the model size by 64.9% compared to adaptive weighted filters without performance reduction.

Adaptive Gabor convolutional networks

Despite the great breakthroughs that deep convolutional neural networks (DCNNs) have achieved on image representation learning in recent years, they lack the ability to extract invariant information from images. On the other hand, several traditional feature extractors like Gabor filters are widely used for invariant information learning from images. In this paper, we propose a new class of DCNNs named adaptive Gabor convolutional networks (AGCNs). In the AGCNs, the convolutional kernels are adaptively multiplied by Gabor filters to construct the Gabor convolutional filters (GCFs), while the parameters in the Gabor functions (i.e., scale and orientation) are learned alongside those in the convolutional kernels. In addition, the GCFs can be regenerated after updating the Gabor filters and convolutional kernels. We evaluate the performance of the proposed AGCNs on image classification using five benchmark image datasets, i.e., MNIST and its rotated version, SVHN, CIFAR-10, CINIC-10, and DogsVSCats. Experimental results show that the AGCNs are robust to spatial transformations and have achieved higher accuracy compared with the DCNNs and other state-of-the-art deep networks. Moreover, the GCFs can be easily embedded into any classical DCNN models (e.g., ResNet) and require fewer parameters than the corresponding DCNNs.

Emergence of Lie Symmetries in Functional Architectures Learned by CNNs.

In this paper we study the spontaneous development of symmetries in the early layers of a Convolutional Neural Network (CNN) during learning on natural images. Our architecture is built in such a way to mimic some properties of the early stages of biological visual systems. In particular, it contains a pre-filtering step ℓ0 defined in analogy with the Lateral Geniculate Nucleus (LGN). Moreover, the first convolutional layer is equipped with lateral connections defined as a propagation driven by a learned connectivity kernel, in analogy with the horizontal connectivity of the primary visual cortex (V1). We first show that the ℓ0 filter evolves during the training to reach a radially symmetric pattern well approximated by a Laplacian of Gaussian (LoG), which is a well-known model of the receptive profiles of LGN cells. In line with previous works on CNNs, the learned convolutional filters in the first layer can be approximated by Gabor functions, in agreement with well-established models for the receptive profiles of V1 simple cells. Here, we focus on the geometric properties of the learned lateral connectivity kernel of this layer, showing the emergence of orientation selectivity w.r.t. the tuning of the learned filters. We also examine the short-range connectivity and association fields induced by this connectivity kernel, and show qualitative and quantitative comparisons with known group-based models of V1 horizontal connections. These geometric properties arise spontaneously during the training of the CNN architecture, analogously to the emergence of symmetries in visual systems thanks to brain plasticity driven by external stimuli.

Learning 2D Gabor filters by infinite kernel learning regression

Gabor functions have wide-spread applications both in analyzing the visual cortex of mammalians and in designing machine vision algorithms. It is known that the receptive field of neurons of V1 layer in the visual cortex can be accurately modeled by Gabor functions. In addition, Gabor functions are extensively used for feature extraction in machine vision tasks. In this paper, we prove that Gabor functions are translation-invariant positive-definite kernels and show that the problem of image representation with Gabor functions can be formulated as infinite kernel learning regression. Specifically, we use the stabilized infinite kernel learning regression algorithm that has already been introduced for learning translation-invariant positive-definite kernels and has enough flexibility and generality to embrace the class of Gabor kernels. The algorithm yields a representation of the image as a support vector expansion with a compound kernel that is a finite mixture of Gabor functions. The problem with this representation is that all Gabor functions are present at all support vector pixels. Using LASSO, we propose a method for sparse representation of an image with Gabor functions in which each Gabor function is positioned at a very sparse set of pixels. As a practical application, we introduce a novel method for learning a dataset-specific set of Gabor filters that can be used subsequently for feature extraction. Our experiments on CMU-PIE and Extended Yale B datasets show that use of the learned Gabor filters significantly improves the recognition accuracy of a recently introduced face recognition algorithm.

Transfer learning for denoising the echolocation clicks of finless porpoise (Neophocaena phocaenoides sunameri) using deep convolutional autoencoders.

Ocean noise has a negative impact on the acoustic recordings of odontocetes' echolocation clicks. In this study, deep convolutional autoencoders (DCAEs) are presented to denoise the echolocation clicks of the finless porpoise (Neophocaena phocaenoides sunameri). A DCAE consists of an encoder network and a decoder network. The encoder network is composed of convolutional layers and fully connected layers, whereas the decoder network consists of fully connected layers and transposed convolutional layers. The training scheme of the denoising autoencoder was applied to learn the DCAE parameters. In addition, transfer learning was employed to address the difficulty in collecting a large number of echolocation clicks that are free of ambient sea noise. Gabor functions were used to generate simulated clicks to pretrain the DCAEs; subsequently, the parameters of the DCAEs were fine-tuned using the echolocation clicks of the finless porpoise. The experimental results showed that a DCAE pretrained with simulated clicks achieved better denoising results than a DCAE trained only with echolocation clicks. Moreover, deep fully convolutional autoencoders, which are special DCAEs that do not contain fully connected layers, generally achieved better performance than the DCAEs that contain fully connected layers.

Task-specific efficient channel selection and bias management for Gabor function channelized Hotelling observer model for the assessment of x-ray angiography system performance.

Channelized Hotelling observer (CHO) models have been implemented to assess imaging performance in x-ray angiography systems. While current methods are appropriate for assessing unprocessed images of moving test objects upon uniform-exposure backgrounds, they are inadequate for assessing conditions which more appropriately mimic clinical imaging conditions including the combination of moving test objects, complex anthropomorphic backgrounds, and image processing. In support of this broad goal, the purpose of this work was to develop theory and methods to automatically select a subset of task-specific efficient Gabor channels from a task-generic Gabor channel base set. Also, previously described theory and methods to manage detectability index (d') bias due to nonrandom temporal variations in image electronic noise will be revisited herein. Starting with a base set of 96 Gabor channels, backward elimination of channels was used to automatically identify an "efficient" channel subset which reduced the number of channels retained in the subset while maintaining the magnitude of the d' estimate. The concept of a pixelwise Hotelling observer (PHO) model was introduced and similarly implemented to assess the performance of the efficient-channel CHO model. Bias in d' estimates arising from temporally variable nonstationary noise was modeled as a bivariate probability density function for normal distributions, where one variable corresponds to the signal from the test object and the other variable corresponds to the signal from temporally variable nonstationary noise. Theory and methods were tested on uniform-exposure unprocessed angiography images with detector target dose (DTD) of 6, 18, and 120nGy containing static disk-shaped test objects with diameter in the range of 0.5 to 4mm. Considering all DTD levels and test object sizes, the proposed method reduced the number of Gabor channels in the final subset by 63-82% compared to the original 96 Gabor channel base set, while maintaining a mean relative performance ( ) of 95% 4% with respect to the reference PHO model. Experimental results demonstrated that the bivariate approach to account for bias due to temporally variable nonstationary noise resulted in improved correlation between the CHO and PHO models as compared to a previously proposed univariate approach. Computationally efficient backward elimination can be used to select an efficient subset of Gabor channels from an initial channel base set without substantially compromising the magnitude of the d' estimate. Bias due to temporally variable nonstationary noise can be modeled through a bivariate approach leading to an improved unbiased estimate of d'.

Cable reverberations during wireline distributed acoustic sensing measurements: their nature and methods for elimination

ABSTRACTThe application of distributed acoustic sensing in borehole measurements allows for the use of fibre optic cables to measure strain. This is more efficient in terms of time and costs compared with the deploying of conventional borehole seismometers. Nevertheless, one known drawback for temporary deployment is represented by the freely hanging wireline cable slapping and ringing inside the casing, which introduces additional coherent coupling noise to the data. The present study proposes an explanation for the mechanism of noise generation and draws an analogy with similar wave propagation processes and phenomena, such as ghost waves in marine seismics. This observation allows to derive a ringing noise filter function, to study its behaviour and to consider known effects of the gauge length filter. After examining existing methods aimed at eliminating ringing noise and results of their application, we propose a two‐step approach: (1) developing a denoising method based on a matching pursuit decomposition with Gabor atoms and (2) subtracting the noise model for imaging improvement. The matching pursuit method focuses on decomposing the original input signal into a weighted sum of Gabor functions. Analysing Gabor atoms properties for frequency, amplitude and position in time provides the opportunity to distinguish parts of the original signal denoting noise caused by the vibrating cable. The matching pursuit decomposition applied to the distributed acoustic sensing‐vertical seismic profiling data at the geothermal test site Groß Schönebeck provides a versatile processing instrument for noise suppression.

Applying Ateb–Gabor Filters to Biometric Imaging Problems

This article presents a new method of image filtering based on a new kind of image processing transformation, particularly the wavelet-Ateb–Gabor transformation, that is a wider basis for Gabor functions. Ateb functions are symmetric functions. The developed type of filtering makes it possible to perform image transformation and to obtain better biometric image recognition results than traditional filters allow. These results are possible due to the construction of various forms and sizes of the curves of the developed functions. Further, the wavelet transformation of Gabor filtering is investigated, and the time spent by the system on the operation is substantiated. The filtration is based on the images taken from NIST Special Database 302, that is publicly available. The reliability of the proposed method of wavelet-Ateb–Gabor filtering is proved by calculating and comparing the values of peak signal-to-noise ratio (PSNR) and mean square error (MSE) between two biometric images, one of which is filtered by the developed filtration method, and the other by the Gabor filter. The time characteristics of this filtering process are studied as well.