2D Discrete Wavelet Transform Research Articles

A Wavelet Shrinkage Mixed with a Single-level 2D Discrete Wavelet Transform for Image Denoising

The single-level 2D discrete wavelet transform method is a powerful technique for effectively removing Gaussian noise from natural images. Its effectiveness is attributed to its ability to capture a signal's energy at low energy conversion values, allowing for efficient noise reduction while preserving essential image details. The wavelet noise reduction method mitigates the noise present in the waveform coefficients produced by the discrete wavelet transform. In this study, three different wavelet families—Daubechies (db7), Coiflets (coif5), and Fejér-Korovkin (fk4)—were evaluated for their noise removal capabilities using the Bayes shrink method. This approach was applied to a set of images, and the performance was analyzed using the Mean Squared Error (MSE) and Peak Signal-to-Noise Ratio (PSNR) metrics. Our results demonstrated that among the wavelet families tested, the Fejér-Korovkin (fk4) wavelet consistently outperformed the others. The fk4 wavelet family yielded the lowest MSE values, indicating minimal reconstruction error, and the highest PSNR values, reflecting superior noise suppression and better image quality across all tested images. These findings suggest that the fk4 wavelet family, when combined with the Bayes shrink method, provides a robust framework for Gaussian noise reduction in natural images. The comparative analysis highlights the importance of selecting appropriate wavelet families to optimize noise reduction performance, paving the way for further research and potential improvements in image denoising techniques.

Image Segmentation Using 2D Discrete Wavelet Transform for Medical Image

Image Segmentation Using 2D Discrete Wavelet Transform for Medical Image

Optimizing Visual Sensor Node Image Compression for Resource-Constrained Environments

Abstract: An Approximate hybrid multiplier design is proposed to reduce the data-path width of lifting 2-D discrete wavelet transform (DWT) especially for wireless visual sensor node applications. The proposed multiplier design takes multiplier operand of size less by 3 bit and calculates full-width outputs with marginal loss of accuracy, which is significant. The proposed approximate 2-D DWT structure uses data-path DWT levels and produces reconstructed color images higher than the 70-dB peak-signal-to-noise ratio (PSNR). Compared with the existing fractional wavelet transform (FrWT)-based 2D DWT structures, the proposed structure has a smaller data-path width and free from overhead. Compared with the existing parallel structure

Genetic Algorithm Framework for 3D Discrete Wavelet Transform based Hyperspectral Image Classification

Genetic Algorithm Framework for 3D Discrete Wavelet Transform based Hyperspectral Image Classification

A new convolutional neural network based on combination of circlets and wavelets for macular OCT classification

Artificial intelligence (AI) algorithms, encompassing machine learning and deep learning, can assist ophthalmologists in early detection of various ocular abnormalities through the analysis of retinal optical coherence tomography (OCT) images. Despite considerable progress in these algorithms, several limitations persist in medical imaging fields, where a lack of data is a common issue. Accordingly, specific image processing techniques, such as time–frequency transforms, can be employed in conjunction with AI algorithms to enhance diagnostic accuracy. This research investigates the influence of non-data-adaptive time–frequency transforms, specifically X-lets, on the classification of OCT B-scans. For this purpose, each B-scan was transformed using every considered X-let individually, and all the sub-bands were utilized as the input for a designed 2D Convolutional Neural Network (CNN) to extract optimal features, which were subsequently fed to the classifiers. Evaluating per-class accuracy shows that the use of the 2D Discrete Wavelet Transform (2D-DWT) yields superior outcomes for normal cases, whereas the circlet transform outperforms other X-lets for abnormal cases characterized by circles in their retinal structure (due to the accumulation of fluid). As a result, we propose a novel transform named CircWave by concatenating all sub-bands from the 2D-DWT and the circlet transform. The objective is to enhance the per-class accuracy of both normal and abnormal cases simultaneously. Our findings show that classification results based on the CircWave transform outperform those derived from original images or any individual transform. Furthermore, Grad-CAM class activation visualization for B-scans reconstructed from CircWave sub-bands highlights a greater emphasis on circular formations in abnormal cases and straight lines in normal cases, in contrast to the focus on irrelevant regions in original B-scans. To assess the generalizability of our method, we applied it to another dataset obtained from a different imaging system. We achieved promising accuracies of 94.5% and 90% for the first and second datasets, respectively, which are comparable with results from previous studies. The proposed CNN based on CircWave sub-bands (i.e. CircWaveNet) not only produces superior outcomes but also offers more interpretable results with a heightened focus on features crucial for ophthalmologists.

A Machine Learning Approach for Simultaneous Classification of Material Types and Cracks

Exterior structures are susceptible to deformation, which can manifest as cracks on the surface. Deformations that occur on surfaces subjected to daily human use can exacerbate rapidly, potentially leading to irreversible structural damage. They have a potential to result in fatalities. Thus, continuous inspection of these deformations is of invaluable importance. In addition, the identification of the materials comprising the structures is essential to facilitate the implementation of appropriate precautionary measures. However, the inspections are hard to maintain with a solely human workforce. More advanced actions can be taken thanks to the developments in technology. Machine Learning methods could be used in this area where human workforce is ineffective. In this regard, an end-to-end Machine Learning approach was proposed in this study. The power of classical feature extraction methods and Artificial Neural Networks were combined to detect cracks and material of the surface simultaneously. The 2D Discrete Wavelet Transform and statistical properties gained from Gray Level Co-Occurrence Matrix were utilized in the feature extraction mechanism, and an ANN structure was designed. The findings of the study indicate that the proposed mechanism achieved an acceptable level of accuracy for recognizing the structural deformations, despite the challenges posed by the complexity of the problem.

An Improved Image Compression Algorithm Using 2D DWT and PCA with Canonical Huffman Encoding.

Of late, image compression has become crucial due to the rising need for faster encoding and decoding. To achieve this objective, the present study proposes the use of canonical Huffman coding (CHC) as an entropy coder, which entails a lower decoding time compared to binary Huffman codes. For image compression, discrete wavelet transform (DWT) and CHC with principal component analysis (PCA) were combined. The lossy method was introduced by using PCA, followed by DWT and CHC to enhance compression efficiency. By using DWT and CHC instead of PCA alone, the reconstructed images have a better peak signal-to-noise ratio (PSNR). In this study, we also developed a hybrid compression model combining the advantages of DWT, CHC and PCA. With the increasing use of image data, better image compression techniques are necessary for the efficient use of storage space. The proposed technique achieved up to 60% compression while maintaining high visual quality. This method also outperformed the currently available techniques in terms of both PSNR (in dB) and bit-per-pixel (bpp) scores. This approach was tested on various color images, including Peppers 512 × 512 × 3 and Couple 256 × 256 × 3, showing improvements by 17 dB and 22 dB, respectively, while reducing the bpp by 0.56 and 0.10, respectively. For grayscale images as well, i.e., Lena 512 × 512 and Boat 256 × 256, the proposed method showed improvements by 5 dB and 8 dB, respectively, with a decrease of 0.02 bpp in both cases.

Classification of 3D-DWT Features of Brain Tumours with SVM

Brain tumours are one of the most challenging medical conditions to diagnose and treat. Accurate and timely classification of brain tumours is critical for effective treatment planning and patient management. Machine learning algorithms have shown great promise in improving the accuracy of brain tumour classification. This study implemented high-grade glioma (HGG) and low-grade glioma (LGG) classification on four different 3D-MRI (magnetic resonance imaging) scans (FLAIR, T1, T1c, T2). By using four different scans, 15 different combinations were created for classification process. 3D Discrete Wavelet Transform was used to transform tumour images for feature extraction stage. 36 different wavelet types were used for image transformation. First Order Statistics (mean, variance, kurtosis, skewness, entropy, energy) were extracted from transformed images of 36 wavelet types. Support Vector Machines (SVM) algorithm classified the FOS features that were obtained on BraTS 2017 dataset. The 2-fold, 5-fold, and 10-fold cross-validations are implemented and six metrics (sensitivity, specificity, accuracy, precision, F1-score, AUC) evaluated the performance of proposed method. Consequently, proposed method achieved remarkable scores of 95.23% (sensitivity), 78.81% (specificity), 90.89% (accuracy), 92.59% (precision), 93.89% (F1-score), and 87.02% (AUC) for HGG/LGG classification of 3D brain MRI data on T1+T1c+T2 combination by 2-fold cross validation.

Coronavirus disease identification using Multi-subband feature analysis in DWT domain

Coronavirus disease early identification and differentiating it with other lung infections is a complex and time-consuming task. At present RT-PCR and Antigen tests are used for diagnosis, but the whole process is tedious, time exhausting and sometimes gives inaccurate results. Radiological scans like CT scan and X-rays are often considered for confirmation of infection, as it contains vital information about region of infection, disease state and severity, texture, size and opacity of infection. Automated machine learning techniques along with CXR (Chest X-ray) images can serve as alternative approach for Covid-19 diagnosis and differentiating it with other health conditions. In this work, Covid-19 disease identification is performed based on multi-subband feature extraction using 2D Discrete Wavelet Transform (DWT) on CX-Ray images. The CX-ray images are decomposed into multi-subbands of frequencies using DWT. The quarter-sized decomposed low and high frequency components are concatenated into single feature vector. In order to find suitable wavelet filter for extracting features from CX-ray images, a rigorous experimentation is carried out among various wavelet families such as Haar, Daubechies, Symlets, Biorthogonal and their respective members that have different vanishing moment and regularity properties. The feature vector is then used for training machine learning model based on support vector machine classifier. Experimental result shows that the classification model based on Haar wavelet feature extraction performs better as compared to other wavelet families with classification accuracy of 100%.

Analysis of ECG-based arrhythmia detection system using machine learning

The 3D Discrete Wavelet Transform (DWT) and Support Vector Machine (SVM) are used in this study to analyze and characterize Electrocardiogram (ECG) signals. This technique consists of three stages: ECG signal preprocessing, feature extraction, and ECG signal order. The 3D wavelet transform is a signal preprocessing technique, de-noising, along with wavelet coefficient extraction.•SVM is used to categorize the ECG through each of the nine heartbeat types recognized by the various classifiers. For this work, around 6400 ECG beats were looked at over the China Physiological Signal Challenge (CPSC) 2018 arrhythmia dataset.•The best degree of exactness was acquired when level 4 rough constants with Symlet-8 (Sym8) channel were utilized for arrangement. Utilizing the ECG signals from CPSC 2018 data set, the SVM classifier has a normal precision of 99.02%, which is much better than complex support vector machine (CSVM) 98.5%, and weighted support vector machine (WSVM) 99%.•The suggested approach is far superior to others in terms of accuracy, and classification of several diseases of arrhythmia.

Classification of microscopic cervical blood cells using inception ResNet V2 with modified activation function

Cervical cancer is the most frequent and fatal malignancy among women worldwide. If this tumor is detected and treated early enough, the complications it causes can be minimized. Deep learning demonstrated significant promise when imposed on biomedical difficulties such as medical image processing and disease prognostication. Therefore, in this paper, an automatic cervical cell classification approach named IR-PapNet is developed based on Inception-ResNet which is an optimized version of Inception. The learning model’s conventional ReLu activation is replaced with the parametric-rectified linear unit (PReLu) to overcome the nullification of negative values and dying ReLu. Finally, the model loss function is minimized with the SGD optimization model by modifying the attributes of the neural network. Furthermore, we present a simple but efficient noise removal technique called 2D-Discrete Wavelet Transform (2D-DWT) algorithm for enhancing image quality. Experimental results show that this model can achieve a top-1 average identification accuracy of 99.8% on the pap smear cervical Herlev datasets, which verifies its satisfactory performance. The restructured Inception-ResNet network model can obtain significant improvements over most of the state-of-the-art models in 2-class classification, and it achieves a high learning rate without experiencing dead nodes.

An Adaptive Enhanced Technique for Locked Target Detection and Data Transmission over Internet of Healthcare Things

The incredible advancements in data transmission technology have opened up more potentials for data security than ever before. Numerous methods for data protection have been developed during the previous decades, including steganography and cryptography. The security and integrity of medical data have emerged as major barriers for healthcare service systems as the Internet of Things has evolved dramatically in the healthcare business. Communication between two devices securely is a difficult problem. Numerous cryptographic algorithms are already available, including data encryption standard (DES), Rivest–Shamir–Adleman (RSA), and advanced encryption standard (AES). In this paper, we present a hybrid security model for the protection of diagnostic text data contained in medical photographs. The proposed model is built by combining a proposed hybrid encryption system with either a 2D Discrete Wavelet Transform 1 Level (2D-DWT-1L) or a 2D Discrete Wavelet Transform 2 Level (2D-DWT-2L) steganography technique. The suggested model encrypts secret data and hides them using 2D-DWT-3L. As text covers, color and grayscale images are employed. The suggested system’s performance was tested using PSNR, SSIM, MSE, and Correlation. Associated to state-of-the-art approaches, the proposed model masked personal patient data with high capacity, imperceptibility and minimum deterioration in the received stego-image. We use MATLAB to build the proposed mechanism, and measures such as throughput and execution time are used to assess performance.

Wind-Direction Estimation from Single X-Band Marine Radar Image Improvement by Utilizing the DWT and Azimuth-Scale Expansion Method.

In this study, a method based on the discrete wavelet transform (DWT) and azimuth-scale expansion is presented to retrieve the sea-surface wind direction from a single X-band marine radar image. The algorithm first distinguishes rain-free and rain-contaminated radar images based on the occlusion zero-pixel percentage and then discards the rain-contaminated images. The radar image whose occlusion areas have been removed is decomposed into different low-frequency sub-images by the 2D DWT, and the appropriate low-frequency sub-image is selected. Images collected with a standard marine HH-polarized X-band radar operating at grazing incidence display a single intensity peak in the upwind direction. To overcome the influence of the occlusion area, before determining the wind direction, the data near the ship bow are shifted to expand the azimuth scale of the data. Finally, a harmonic function is least-square-fitted to the range-averaged radar return of the low-frequency sub-image as a function of the antenna look azimuth to determine the wind direction. Different from the wind-direction retrieval algorithms previously presented, this method is more suitable for sailing ships, as it functions well even if the radar data are heavily blocked. The results show that compared with the single-curve fitting algorithm, the algorithm based on DWT and azimuth-scale expansion can improve the wind-direction results in sailing ships, showing a reduction of 7.84° in the root-mean-square error with respect to the reference.

Optimization of Discrete Anamorphic Stretch Transform and Phase Recovery for ECG Signal Compression

An ECG signal compression scheme using both Discrete Anamorphic Stretch Transform (DAST) and Discrete wavelet transform (DWT) is reported in the literature. In this scheme, a linear filter is used for the recovery of the phase of the DAST for the computation of inverse DAST. However, at a higher compression ratio, the phase recovered and the reconstructed signal became increasingly inaccurate. To overcome this problem, a phase recovery technique that uses only an adder with fixed offset is proposed in this paper. A scheme for optimizing the DAST kernels to increase the compression ratio is also proposed. To evaluate their effectiveness, the ECG signals of the MIT-BIH Arrhythmia database are compressed using 6 level 1D DWT and run-length encoding with and without DAST pre-compressor and their performances are compared. The phase of DAST of the ECG signals recovered using both linear filter and adder are computed and compared for different kernels. The proposed phase recovery scheme with the optimized sublinear and linear kernels provides a 12.2% and 10.91% increase in data compression ratio and 24.63% and 28.73% decrease in percentage root mean square difference (PRD) with 99.9% of energy packing efficiency (EPE) compared to the scheme using the filter. The compression scheme using DAST provides a 2.81 times higher compression ratio compared to that without DAST. The proposed compression scheme yields a higher Compression Ratio and lower PRD than those reported in the literature. It can be used as pre-compressor for the real time transmission of ECG signal with lower bandwidth.

Lossy Image Compression Techniques

In recent years, domain image processing plays a most significant role in realtime applications. Due to reserved bandwidth and capacity, images are needed to be compressed, enhance, and noise-free to reduce the storage space as well as the transmission time. Compression overcomes the problem such as insufficient bandwidth of network and storage of memory device. Nowadays, many techniques are used to compress an image with a good quality. In this paper, I briefly discuss the concept of image compression and review the techniques which are used in loss image compression. This technique losses some data by using transform codes. Two codes are used to compress an image such as wavelet and fractal. The techniques scalar and vector quantization are used to quantize an input and partition into sub-images. I briefly discussed about the 2D-Discrete wavelet transform codes with examples which were done by Mat lab software.

Defining of the Minimum Wavelet Filter Coefficients Bit-Width for 3D Medical Imaging

Medical imaging uses a variety of modalities to provide visual information about a patient. Various methods are used to process this data. Many of them are based on discrete wavelet transform (DWT). Its use will allow effective denoising and compression of 2D and 3D images. This paper proposes a new approach to linear time-invariant wavelet filtering using quantized filter coefficients when using which the computational errors have different signs and allow to partially compensate each other as a result of which the processed image is of high quality. The analysis of the quantization noise of the direct multilevel DWT filter coefficients is carried out. The derived formulas demonstrate the relationship between the quantization accuracy of these coefficients and the processing quality of digital 3D images. The derived formulas for calculating the minimum accuracy of the wavelet filter coefficients representation in the computing devices memory allow minimizing the effect of quantization noise on the result of 3D images processing. Modelling of 3D medical tomographic images DWT processing showed that a decrease in the ratio of the average voxel brightness to the maximum allowable value with increasing color depth of images leads to faster achievement of high quality compared to the results of theoretical analysis with an increase in the value of the scaling degree of the wavelet filter coefficients. The obtained theoretical and practical results open up the possibility for reducing the computational complexity of software and hardware implementation of wavelet processing of 3D medical visual data on modern microelectronic devices (field-programmable gate arrays, application-specific integrated circuits, etc.).

Real Time Implementation of Video Compression Based on DWT

In this paper highly efficient 3D Discrete Wavelet Transform architecture is designed and implemented on seven series FPGA. The throughput is analyzed and its performance matrices are compared with different video file format. Today top of the line high-end image and video consume huge amount of memory. The designed architecture of DWT based video compression is again executed in parallel processing mode and its execution time is tabulated demonstrates reduced the processing or execution time. This paper demonstrates the superiority of the designed architecture both in normal mode of execution and parallel processing mode of execution .We know that higher the throughput of the video processing design results in Low power consumption. The Internal Architecture of the design is explained in brief and is synthesized in Xilinx Vivado 17.4 and implemented on Zed board. Based on the experimental results of the design being implemented on FPGA, demonstrates the memory saving capabilities and superiority of this architecture. The resultant architecture has drastically reduced latency and has enhanced the speed of operation.

Hybrid data encryption model integrating multi-objective adaptive genetic algorithm for secure medical data communication over cloud-based healthcare systems

The exponential rise in the development of cloud computing environments in the healthcare field, the protection and confidentiality of the medical records become a primary concern for healthcare services applications. Today, health data stored in the cloud is highly confidential information concealed to avoid unauthorized access to protect the patient’s information. As cloud-based medical data transmission becomes more common, it receives growing attention from researchers and academics. Despite the potential for misuse, medical data transmitted through unreliable networks can be manipulated or compromised. The current cryptosystems alone are not sufficient to deal with these issues, and hence this paper introduces a new hybridization of data encryption model to shelter the diagnosis data in medical images. The proposed model is developed by combining either 2D Discrete Wavelet Transform 1 Level (2D-DWT-1 L) or 2D Discrete Wavelet Transform 2 Level (2D-DWT-2 L) steganography with the proposed hybrid encryption scheme. The hybrid encryption scheme is built by strategically applying Advanced Encryption Standard (AES) and Rivest–Shamir–Adleman (RSA) algorithms to secure diagnosis data to be embedded with the RGB channels of medical cover image. One of the key novelties is the use of an Adaptive Genetic Algorithm for Optimal Pixel Adjustment Process (AGA-OPAP) that enriches data hiding ability as well as imperceptibility features. To evaluate the efficiency of the proposed model, numerical tests are performed. The results show that the proposed algorithm is capable of safely transmitting medical data. Comparison of results is carried out concerning the datasets with the state-of-the-art algorithm. In terms of various statistical measures, the results showed the superiority of the proposed algorithm, such as peak signal to noise ratio (PSNR), correlation, structural content (SC), structure similarity (SSIM), entropy, histogram, NPCR, UACI and embedding capacity. The proposed model can also prevent attacks, such as steganalysis or RS attacks.

Lossy Image Compression Techniques

In recent years, domain image processing plays a most significant role in realtime applications. Due to reserved bandwidth and capacity, images are needed to be compressed, enhance, and noise-free to reduce the storage space as well as the transmission time. Compression overcomes the problem such as insufficient bandwidth of network and storage of memory device. Nowadays, many techniques are used to compress an image with a good quality. In this paper, I briefly discuss the concept of image compression and review the techniques which are used in loss image compression. This technique losses some data by using transform codes. Two codes are used to compress an image such as wavelet and fractal. The techniques scalar and vector quantization are used to quantize an input and partition into sub-images. I briefly discussed about the 2D-Discrete wavelet transform codes with examples which were done by Mat lab software.

A Novel Image Encryption Scheme Based on 2D Fractional Chaotic Map, DWT and 4D Hyper-chaos

In this paper, a novel image encryption scheme based on a fractional-order Henon chaotic map, a two-dimensional (2D) Discrete Wavelet Transform (DWT) and a four-dimensional (4D) hyperchaotic system is proposed. Firstly, the original image is transformed and scrambled by the 2D DWT, and then the image is shuffled with the fractional-order Henon chaotic time series. Finally, the shuffled image is diffused and encrypted by the 4D hyperchaos system. Through the application of DWT and high-low dimensional chaotic systems, the encryption effect of this algorithm is better than those done by single or ordinary chaotic encryption algorithm, and it has a larger key space and higher security. The experimental tests show that the system has good statistical characteristics, such as histogram analysis, correlation coefficient analysis, key space and key sensitivity, information entropy analysis and so on. The encryption algorithm also passes the relevant security attack tests with good security.