Haar Wavelet Decomposition Research Articles (Page 1)

Ship detection in complex environments presents challenges such as sea surface reflections, wave interference, variations in illumination, and a range of target scales. The interaction between symmetric ship structures and wave patterns challenges conventional algorithms, particularly in maritime wireless networks. This study presents YOLO-StarLS (You Only Look Once with Star-topology Lightweight Ship detection), a detection framework leveraging wavelet transforms and multi-scale feature extraction through three core modules. We developed a Wavelet Multi-scale Feature Extraction Network (WMFEN) utilizing adaptive Haar wavelet decomposition with star-topology extraction to preserve multi-frequency information while minimizing detail loss. We introduced a Cross-axis Spatial Attention Refinement module (CSAR), which integrates star structures with cross-axis attention mechanisms to enhance spatial perception. We constructed an Efficient Detail-Preserving Detection head (EDPD) combining differential and shared convolutions to enhance edge detection while reducing computational complexity. Evaluation on the SeaShips dataset demonstrated YOLO-StarLS achieved superior performance for both mAP50 and mAP50–95 metrics, improving by 2.21% and 2.42% over the baseline YOLO11. The approach achieved significant efficiency, with a 36% reduction in the number of parameters to 1.67 M, a 34% decrease in complexity to 4.3 GFLOPs, and an inference speed of 162.0 FPS. Comparative analysis against eight algorithms confirmed the superiority in symmetric target detection. This work enhances real-time ship detection and provides foundations for maritime wireless surveillance networks.

Aiming at the problems of leakage and misdetection caused by insufficient multi-scale feature extraction and an excessive amount of model parameters in bridge defect detection, this paper proposes the AMSF-Pyramid-YOLOv11n model. First, a Cooperative Optimization Module (COPO) is introduced, which consists of the designed multi-level dilated shared convolution (FPSharedConv) and a dual-domain attention block. Through the joint optimization of FPSharedConv and a CGLU gating mechanism, the module significantly improves feature extraction efficiency and learning capability. Second, the Unified Global-Multiscale Bottleneck (UGMB) multi-scale feature pyramid designed in this study efficiently integrates the FCGL_MANet, WFU, and HAFB modules. By leveraging the symmetry of Haar wavelet decomposition combined with local-global attention, this module effectively addresses the challenge of multi-scale feature fusion, enhancing the model’s ability to capture both symmetrical and asymmetrical bridge defect patterns. Finally, an optimized lightweight detection head (LCB_Detect) is employed, which reduces the parameter count by 6.35% through shared convolution layers and separate batch normalization. Experimental results show that the proposed model achieves a mean average precision (mAP@0.5) of 60.3% on a self-constructed bridge defect dataset, representing an improvement of 11.3% over the baseline YOLOv11n. The model effectively reduces the false positive rate while improving the detection accuracy of bridge defects.

This study explores integrating Haar wavelet decomposition techniques with convolutional neural networks for image classification on the MNIST dataset. The research demonstrates that without losing significant accuracy by applying the 1-level, 2-level, and 3-level decomposition techniques, the model can reduce the dimensionality and the number of parameters required by the convolutional neural network model. During the training, the 1-level Haar CNN results achieved optimal performance, demonstrating competitive accuracy and computational efficiency compared to the baseline CNN model. This approach highlights the potential of wavelet decomposition techniques to enhance CNN performance with limited computational resources.

Abstract. The use of autonomous underwater vehicles (AUVs) for surveying underwater infrastructure presents a potential cost saving in comparison to remotely operated vehicles (ROVs). One of the challenges when processing images of underwater structures captured by an AUV, is that vast number of images captured during the mission usually do not show the structure. For instance, images captured during the dive to the structure or of the sea floor, or of the deep sea facing away from the structure. Too many images captured, without relevant information for a 3D reconstruction of the structure, leads to increased processing time and issues during the reconstruction process. There are two solutions to reduce the images to only images showing the structure. Firstly, only images of the structure are captured in the first place or remove images that are not useful after the capture and before further processing. This study developed and evaluated techniques that would enable the first strategy to be applied in an AUV. To apply this strategy in an AUV, would require an on-board structure detection system to ensure that they are correctly orientated for capturing useful footage during a survey mission. However, the marine environment poses several challenges to image-based object detection. Furthermore, small AUVs have limited power and computational resources available while deployed on a mission. To investigate the suitability of creating a lightweight structure detection model for the purpose of image evaluation, three computationally efficient image feature extraction methods (colour moments, local binary patterns (LBP), and Haar wavelet decomposition) were evaluated for their ability to distinguish underwater structures from background areas using unsupervised k-means models. LBP was found to be an effective method for identifying underwater structures in open water conditions. For identifying a structure against the seabed, colour moments were identified as the most effective method.

Context. The high Reynolds number solar wind flow provides a natural laboratory for the study of turbulence in situ. Parker Solar Probe samples the solar wind between 0.17 AU and 1 AU, providing an opportunity to study how turbulence evolves in the expanding solar wind. Aims. We aim to obtain estimates of the scaling exponents and scale breaks of the power spectra of magnetohydrodynamic (MHD) turbulence at sufficient precision to discriminate between Kolmogorov and Iroshnikov-Kraichnan (IK) turbulence, both within each spectrum and across multiple samples at different distances from the Sun and at different plasma β. Methods. We identified multiple long-duration intervals of uniform solar wind turbulence, sampled by PSP/FIELDS and selected to exclude coherent structures, such as pressure pulses and current sheets, and in which the primary proton population velocity varies by less than 20% of its mean value. The local value of the plasma β for these datasets spans the range 0.14 < β < 4. All selected events span spectral scales from the approximately ‘1/f’ range at low frequencies, through the MHD inertial range (IR) of turbulence, and into the kinetic range, below the ion gyrofrequency. We estimated the power spectral density (PSD) using a discrete Haar wavelet decomposition, which provides accurate estimates of the IR exponents. Results. Within 0.3 AU of the Sun, the IR exhibits two distinct ranges of scaling. The inner, high-frequency range has an exponent consistent with that of IK turbulence within uncertainties. The outer, low-frequency range is shallower, with exponents in the range from –1.44 to –1.23. Between 0.3 and 0.5 AU, the IR exponents are closer to, but steeper than, that of IK turbulence and do not coincide with the value –3/2 within uncertainties. At distances beyond 0.5 AU from the Sun, the exponents are close to, but mostly steeper than, that of Kolmogorov turbulence, –5/3: uncertainties inherent in the observed exponents exclude the value –5/3. Between these groups of spectra we find examples, at 0.26 AU and 0.61 AU, of two distinct ranges of scaling within the IR with an inner, high-frequency range with exponents ∼ − 1.4, and a low-frequency range with exponents close to the Kolmogorov value of –5/3. Conclusions. Since the PSD-estimated scaling exponents are a central predictor in turbulence theories, these results provide new insights into our understanding of the evolution of turbulence in the solar wind.

A growing number of services and applications are developed using multimedia sensing low-cost wireless devices, thus creating the Internet of Multimedia Things (IoMT). Nevertheless, energy efficiency and resource availability are two of the most challenging issues to overcome when developing image-based sensing applications. In depth, image-based sensing and transmission in IoMT significantly drain the sensor energy and overwhelm the network with redundant data. Event-based sensing schemes can be used to provide efficient data transmission and an extended network lifetime. This paper proposes a novel approach for distributed event-based sensing achieved by a cluster of processing nodes. The proposed scheme aims to balance the processing load across the nodes in the cluster. This study demonstrates the adequacy of distributed processing to extend the lifetime of the IoMT platform and compares the efficiency of Haar wavelet decomposition and general Fourier descriptors (GFDs) as a feature extraction module in a distributed features-based target recognition system. The results show that the distributed processing of the scheme based on the Haar wavelet transform of the image outperforms the scheme based on a general Fourier shape descriptor in recognition accuracy of the target as well as the energy consumption. In contrast to a GFD-based scheme, the recognition accuracy of a Haar-based scheme was increased by 26%, and the number of sensing cycles was increased from 40 to 70 cycles, which attests to the adequacy of the proposed distributed Haar-based processing scheme for deployment in IoMT devices.

The study of the properties and variations of planetary boundaries such as magnetosheaths and bow shocks is an important subject for magnetospheric dynamics and interaction with solar wind. The identification of these boundaries is important for those studies. Thus, the Haar wavelet decomposition technique is used to detect the planetary magnetosphere boundaries and discontinuities. We use the magnetometer data from the CASSINI and MESSENGER spacecraft to identify the abrupt changes in the magnetic field when the spacecraft crossed the magnetospheric bow shocks and magnetopauses of Saturn and Mercury, respectively. The methodology based on variance obtained by scale and edge identifications was shown to be a simple tool to perform this task. The results confirm that the Haar transform can efficiently identify the planetary magnetosphere boundaries characterized by the abrupt magnetic field changes. Due to this wavelet function to be a discrete function it promotes the abrupt and sharp identification of the boundaries. It is suggested that this technique can be applied to detect the planetary boundaries as well as the discontinuities such as the shock waves in the interplanetary space.

Using frequency splitting, two energy management strategies (EMS) based on Haar wavelet decomposition and Fourier analysis for fuel cell hybrid vehicle (FCHV) are proposed to manage efficiently the power flow between components. The paper aims to discuss the performances of the proposed EMS in terms of dynamic behavior, robustness operation, real time application and fuel economy. For apply this methodology, two EMS approaches are elaborated and successfully tested for parallel Fuel Cell/UC: conventional approach using Fourier Transform analysis (FT) and Wavelet analysis approach allowing natural frequency splitting. Finally, and to evaluate the performance and relevance of the developed approach, a comparison analysis were conducted. The simulation results exhibit the effectiveness of both strategies. Indeed, Wavelet analysis leads to better results in terms of energy flow and dynamic behavior, excellent robustness and stability of system, as well as energy economy improvement. A very relevant strategy is proposed based on Wavelet analysis using digital filtering techniques, which enables a natural frequency splitting to ensure the best global performances. In addition, the approach remains simple and suitable for real time operation.

Convolutional neural networks (CNNs) are widely utilized in hyperspectral image (HSI) classification due to their powerful capability to automatically learn features. However, ordinary CNN mainly captures the spatial characteristics of HSI and ignores the spectral information. To alleviate the issue, this work proposes a CNN-enhanced multi-level Haar wavelet features fusion network (CNN-MHWF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> N), which combines the spatial features obtained through 2-D-CNN with the Haar wavelet decomposition features to obtain sufficient spectral–spatial features. Specifically, factor analysis is first used to reduce the HSI dimension. Then, four-level decomposition features are obtained through the Haar wavelet decomposition algorithm, which of them are, respectively, concatenated with four-layer convolution features for combining spatial with spectral information. In this way, spectral–spatial features achieve better information interaction. Besides, a double filtrating feature fusion module is designed, which is operated following each level spectral–spatial features to obtain finer characteristics. Finally, those recognizable features are merged via a fusion operator. The whole designed model is conducive to enhancing the final HSI classification performance. In addition, experiments also reveal that the designed model is superior on three benchmark databases compared with the state-of-the-art approaches.

This study addresses the application of signal processing in the evaluation of meteorological drought associated with monthly precipitation time series. Several drought indices and a Haar wavelet decomposition (WD) with ten components are implemented in the evaluation of the monthly precipitation of a mountainous region called Mount Uludag in Turkey. Monthly precipitation time series in three meteorological stations at the summit and foothills are used. The Standardized Precipitation Index (SPI) is used at monthly, annual, and 12- and 48-month moving average time frames as the benchmark to investigate the drought patterns. The results obtained by the WD and SPI are then confirmed using the Z-score index (ZSI) at monthly and annual scales, together with the modified China Z-index (MCZI) and rainfall anomaly index (RAI) at a monthly scale. Changes in the moments of the distribution, correlation analysis, mutual information, and power spectrum are applied to investigate the nature of the relationship between the sequences of precipitation events in time and space. The temporal correlation analysis, together with the mutual information, showed that the system has a short-term memory with strong seasonality. Similarly, the power spectra depicted major seasonality at 1, 3, 5, 6, 12, 22, and 60 months in the precipitation time series. It is concluded that the recent drought events have an infrequent nature, which altered the sinusoidal patterns of the large-scale events. The SPI-48 and the WD showed that declines are strongly related to the large-scale cycles, but the decline patterns are more related to the station located at the mountain summit.

Traditional deep learning detection network has poor effect on the detection of infrared dim and small targets on the sea in the case of interference or bad weather. In this paper, an improved dim and small infrared ship detection network based on Haar wavelet is proposed. The HaarConv module is designed based on the high-frequency features obtained by Haar wavelet decomposition, which further increases the feature extraction ability of the backbone network for small targets. Meanwhile, the HaarUp-HaarDown module is designed by using Haar forward and inverse transform, replacing the up-sampling layer of the feature pyramid network and the down-sampling layer of backbone network to retain smaller target features. Furthermore, the pseudo-label-based method enables the network to conduct semi-supervised learning, which reduces the labeling cost and improves detection accuracy while expanding the amount of training data. The above method is applied to the YOLOv5-s lightweight network and 11278 infrared images (3352 labeled) of dim and small ships are collected as a dataset. The results show that the introduction of semi-supervised training method effectively expands the training dataset, and the mAP@.5:.95 increases by 23.5%. The proposed Haar wavelet improvement method can effectively improve the detection accuracy of dim and small infrared ship targets by more than 2%, and the number of parameters increases by only about 0.02M. Compared with existing methods, the proposed method reaches the state-of-the-art result and has good generalization performance.

Electroencephalogram (EEG) measures electrical activity of the brain and proffers valuable insight of the brain dynamics. Accurate and careful analysis of EEG signal plays a prominent role in the diagnosis of brain diseases like epilepsy, brain tumor. EEG is the most significant method used for epilepsy monitoring, diagnosis and rehabilitation. A patient-specific seizure detection model has been developed using Haar wavelet and Artificial Neural Network. HAAR Wavelet decomposition of multi-channel EEG with five scales is made and three frequency bands of EEG selected for the consequent process. The conventional Haar wavelet transform (HWT) is replaced by a modified Haar wavelet transform whereas the number of multiplications and additions are reduced. The Haar wavelet reduces computational complexity from the existing Haar wavelet structure which consumes only 1–3 ms based on the decomposition level to detect epilepsy.

Palm vein recognition is motivated by the advantages of high security and liveness detection, but its popularity is prevented by the cost of palm vein capture devices. This study proposes a low-cost and practical palm vein recognition system. First, the authors' system captures near-infrared (NIR) palm vein image with complementary metal-oxide-semiconductor camera in lieu of an NIR charge-coupled device camera. The goal is to reduce the cost of palm vein capture devices greatly. Second, this study adopts thenar area on the palm as the region of interest (ROI) for further palm vein recognition. The goal is to get the rich vessel and avoid the effect of palmprint. Finally, the discriminate palm vein features are extracted based on Haar-wavelet decomposition and partial least squares algorithm on the ROI image. The goal is to increase the recognition accuracy, though the resolution of the image is low. A database with 1500 palm vein images from 250 samples is setup with the capture device. Experiments in the self-built database and a public database show the effectiveness of the scheme.

An efficient wavelet-based algorithm to reconstruct non-square/non-cubic signals from gradient data is proposed. This algorithm is motivated by applications such as image or video processing in the gradient domain. In some earlier approaches, the non-square/non-cubic gradients were extended to enable a square/cubic Haar wavelet decomposition and the coarsest resolution subband was derived from the mean value of the signal. In this paper, a non-square/non-cubic wavelet decomposition is obtained directly without extending the gradient data. The challenge comes from finding the coarsest resolution subband of the wavelet decomposition and an algorithm to compute this is proposed. The performance of the algorithm is evaluated in terms of accuracy and computation time, and is shown to outperform the considered earlier approaches in a number of cases. Further, a closer look on the role of the coarsest resolution subband coefficients reveals a trade-off between errors in reconstruction and visual quality which has interesting implications in image and video processing applications.

A Haar wavelet-based perceptual similarity index for image quality assessment

In this paper, two compression mechanisms based on 3D-discrete wavelet transform (DWT) and 2D embedded zero wavelet (EZW) are proposed and compared depending on the mathematical parameters, i.e., peak signal-to-noise ratio (PSNR) and compression ratio (CR). In this paper, we are using Haar wavelet decomposition for compression, as it has shown improved compression in recent years when used along with the techniques like EZW, SPIHT, etc. Haar wavelet is chosen because of its ease implementation and has inherent properties and EZW is chosen for compression. We apply EZW with frame-by-frame basis on the encoded video as EZW is meant for 2D-data only. Here we are adding the extra blocks for video encoding and decoding before and after the existing compression technique, i.e., EZW. So, these mechanisms are very easy to implement by just adding the extra blocks of encoding and decoding.

In this paper, two compression mechanisms based on 3D-discrete wavelet transform (DWT) and 2D embedded zero wavelet (EZW) are proposed and compared depending on the mathematical parameters, i.e., peak signal-to-noise ratio (PSNR) and compression ratio (CR). In this paper, we are using Haar wavelet decomposition for compression, as it has shown improved compression in recent years when used along with the techniques like EZW, SPIHT, etc. Haar wavelet is chosen because of its ease implementation and has inherent properties and EZW is chosen for compression. We apply EZW with frame-by-frame basis on the encoded video as EZW is meant for 2D-data only. Here we are adding the extra blocks for video encoding and decoding before and after the existing compression technique, i.e., EZW. So, these mechanisms are very easy to implement by just adding the extra blocks of encoding and decoding.

In order to address the problems of discontinuity and block effect for the dehazing method based on dark channel prior, we improved this method using wavelet decomposition, fast kernel regression model, and bicubic interpolation. First, spatial resolution of the hazy image was reduced by the downsampling method with Haar wavelet decomposition. Second, the fast kernel regression model was proposed to smooth the central transmission with local neighbor transmissions. Last, the smoothed transmission for the approximation image was resized to the hazy image by the bicubic interpolation method. Experiments were carried out on synthetic hazy images with known ground truth and real-world hazy images without ground truth. The regions of sudden change of depth in the dehazed images by our method were more smooth and continuous than those of several state-of-the-art methods, and contrast of our method was higher than that of other methods. Indexes based on the concept of visibility level, mean squared error, and structural similarity of our method were better than those of other methods.

Automatic detection of sea-sky horizon line and small targets in maritime infrared imagery

In this paper, we investigate the existence of W1,p-extension operators for a class of bidimensional ramified domains with a self-similar fractal boundary previously studied by Mandelbrot and Frame. When the fractal boundary has no self-contact, the domains have the (E , δ)-property, and the extension results of Jones imply that there exist such extension operators for all 1 6 p 6 1. In the case where the fractal boundary self-intersects, this result does not hold. In this work we construct extension operators for 1 < p < p?, where p? depends only on the dimension of the self-intersection of the boundary. The construction of the extension operators is based on a Haar wavelet decomposition on the fractal part of the boundary. It relies mainly on the self-similar properties of the domain. The result is sharp in the sense that W1,p-extension operators fail to exist when p > p?.