2D Haar Wavelet Research Articles

Adaptive Ghost Imaging Based on 2D-Haar Wavelets

To improve the imaging speed of ghost imaging and ensure the accuracy of the images, an adaptive ghost imaging scheme based on 2D-Haar wavelets has been proposed. This scheme is capable of significantly retaining image information even under under-sampling conditions. By comparing the differences in light intensity distribution and sampling characteristics between Hadamard and 2D-Haar wavelet illumination patterns, we discovered that the lateral and longitudinal information detected by the high-frequency 2D-Haar wavelet measurement basis could be used to predictively adjust the diagonal measurement basis, thereby reducing the number of measurements required. Simulation and experimental results indicate that this scheme can still achieve high-quality imaging results with about a 25% reduction in the number of measurements. This approach provides a new perspective for enhancing the efficiency of computational ghost imaging.

Fast physic-informed mixer architecture for color Lensfree holographic reconstruction

Accurate color image reconstruction from multi-wavelength holograms is crucial in biomedical imaging applications. Current data-driven deep learning methods have made significant progress with promising reconstruction performance. Especially, untrained neural network methods have been developed to overcome data acquisition and the generalization issue. However, improving reconstruction quality requires more iterations, which can lead to longer convergence time. To address this challenge, we proposed an efficient complex-valued attention mixer (ECA-Mixer) architecture for fast and accurate physic-informed color holographic reconstruction. Our architecture consists of three core modules, an encoder, a nonlinear transformer and a decoder, each combining efficient attention mechanisms and Mixer layers for channel feature extraction and spatial information transformation. To preserve high-frequency information, we also introduced the use of 2D Haar wavelet and its inverse transform for encoding and decoding features. We then validate our method with extensive experiments on simulated and experimental samples and achieve state-of-art color reconstruction results in terms of computation time and image quality. Besides, we also demonstrate that our proposed lightweight network is capable of imaging large-size wide-field samples at a higher resolution in just a few minutes. The code is available and will be uploaded later at https://github.com/DeepPhysicVision/ECA-Mixer.git.

Hadamard-Haar (2D) dual domain ghost imaging

We propose a Hadamard-2D Haar transform computational ghost imaging scheme, which uses the rearranged Hadamard illumination pattern for sampling, and obtains the 2D-Haar wavelet coefficients directly by performing a low-order Hadamard transform on the acquired signal, and the information of the target object is obtained by the inverse transform. This scheme improves the problem of noise sensitivity of the computational ghost imaging based on Hadamard and the problem of weak illumination intensity in the high frequency region of 2D-Haar wavelet transform-based computational ghost imaging. Theoretical and experimental proofs show that the method is more robust to external noise and has more advantages in reconstructing images at low sampling rates thanks to the extraction property of 2D-Haar wavelet for edge information.

Blind image deblurring using GLCM and negans obtuse mono proximate distance

ABSTRACT Image deblurring is a challenging problem in computer vision, which aims to recover the sharp image from a blurred observation. This paper proposes the image deblurring algorithm based on Gray-Level Co-occurrence Matrix (GLCM) and Negans obtuse mono proximate distance to extract informative regions for better deblurring process without user guidance. The high-frequency layer is extracted from blurred image using 2D Haar wavelet, sparse approximation to estimate the sharper and more detailed high-frequency layer. From the high-frequency layer, rich edge region is extracted using GLCM along sliding window concepts after the canny edge detection. Finally, the extracted regions are applied for negans obtuse mono proximate distance. The proposed method avoids over-fitting data and reduces blurring. The proposed deblurring algorithm deblurs the blurred image by restoring image textures and details. The experiments performed are compared with existing deblurring algorithms to demonstrate the effectiveness of the proposed deblurring algorithm.

GPU based Image Compression with Scaling-Hard-Threshold Using HWT (Haar-Wavelet-Transform) + RL (Run-Length) Pair Encoding

In 5G MASSIVE MIMO the main problem for better video communication is of transmission bandwidth issues which in turn reflects in video conferencing, Mobile-learning, gaming, graphics applications etc. However, in regard to a versatile framework i.e. a computerized camera with web and correspondence office, at that point the transmission capacity for correspondence and additionally stockpiling are of genuine concern. Tremendous valuable data must be put away and recovered proficiently for down to earth purposes. This is the novel methodology that scaling technique has proposed for 2D Haar wavelet transform based compression of picture utilizing parameter CR- ratio of Compression with PSNR improvement, with maintaining picture quality, less bandwidth usage with better compression ratio which increase by increasing speed with the help of NVIDIA GPU.

Deblurring of Motion Blurred Images Using GLCM and Elastic Net Regularization

An image deburring algorithm consists of rich edge area mining with a gray-level co-occurring matrix and elastic net regularisation is proposed in this paper. First, the luminance channel of an image is removed from the blurred image. The frequency layer is highthat can be derived from the blurred image by converting the 2D haar wavelet in the luminance channel.By the way, measurements were made using area and the richest edge region information is then collected. Finally, the extracted rich edge field, instead full motion blurred image, approximate the blur kernel elastic net regularisation and the image is returned. A measurement of image mechanism and running time measures the proposed system. Result suggestedto recommended strategy would improve efficiency and ensure continuity in recovery.

Novel 4:2 Approximate Compressor Designs for Multimedia and Neural Network Applications

Low power dissipation in approximate arithmetic circuits has laid the foundation for area-efficient computational units for error resilient applications like image and signal processing. This paper proposes two novel low power high speed architectures for approximate 4:2 compressor that can be employed in multipliers for partial product summation. The two designs presented ([Formula: see text] and [Formula: see text]) have Error Distance (ED) of [Formula: see text] and Error Rate (ER) of 25%. The proposed [Formula: see text] and [Formula: see text] are able to achieve reduction in power and delay by (62.50%, 47.67%) and (83.13%, 60.20%), respectively, in comparison with the exact 4:2 compressor. To verify the effectiveness of the design, the proposed architectures are used to implement [Formula: see text] Dadda multiplier. The equal number of errors in positive and negative directions in the proposed designs aid in reducing the Mean Error Distance (MED) and Mean Relative Error Distance (MRED) of the multiplier. Multiplication of images and two-level decomposition of 2D Haar wavelets are implemented using the designed Dadda multiplier. The efficiency of the image processing applications is measured in terms of Mean Structural Similarity (MSSIM) index and Peak Signal-to-Noise Ratio (PSNR) and an average of 0.98 and 35[Formula: see text]dB, respectively, is obtained, which are in the acceptable range. In addition, a Convolutional Neural Network (CNN)-based LeNet-1 Handwritten Digit Recognition System (HDRS) is implemented using the proposed compressor-based multipliers. The proposed compressor-based architectures are able to achieve an average accuracy of 96.23%.

An accuracy improvement method for the topology measurement of an atomic force microscope using a 2D wavelet transform

The topology image is constructed from the 2D matrix (XY directions) of heights Z captured from the force-feedback loop controller. For small height variations, nonlinear effects such as hysteresis or creep of the PZT-driven Z nano scanner can be neglected and its calibration is quite straightforward. For large height variations, the linear approximation of the PZT-driven Z nano scanner fail and nonlinear behaviors must be considered because this would cause inaccuracies in the measurement image. In order to avoid such inaccuracies, an additional strain gauge sensor is used to directly measure displacement of the PZT-driven Z nano scanner. However, this approach also has a disadvantage in its relatively low precision. In order to obtain high precision data with good linearity, we propose a method of overcoming the low precision problem of the strain gauge while its feature of good linearity is maintained. We expect that the topology image obtained from the strain gauge sensor showing significant noise at high frequencies. On the other hand, the topology image obtained from the controller output showing low noise at high frequencies. If the low and high frequency signals are separable from both topology images, the image can be constructed so that it is represented with high accuracy and low noise. In order to separate the low frequencies from high frequencies, a 2D Haar wavelet transform is used. Our proposed method use the 2D wavelet transform for obtaining good linearity from strain gauge sensor and good precision from controller output. The advantages of the proposed method are experimentally validated by using topology images.

Solving Three Dimensional and Time Depending PDEs by Haar Wavelets Method

Haar wavelets are applied for solution of three dimensional partial differential equations (PDEs) or time depending two dimensional PDEs. The proposed method is mathematically simple and fast. Two techniques are used in numerical solution, the first based on 2D-Haar wavelets and the second based on 3D-Haar wavelets and we compare them. To demonstrate the efficiency of the method, two test problems (solution of the diffusion and Poisson equations) are discussed. Computer simulation showed that 3D-Haar wavelets are better and closer to the exact solution but it is need to more time from 2D-Haar wavelets.

Iris recognition model based on Principal Component analysis and 2 level Haar wavelet transform: Case study CUHK and UTIRIS iris databases

A biometric recognition system provide automatic identification of human being based on some special and unique physical or behavioral features of the individual. One of the most reliable identification system is iris recognition system. This work aim to recognize and identify iris among many of images that have been save in databases. Each one of database that used manipulating in many steps starting with enhance the details of iris and segment the iris and pupil then extract the raw features based on 2D Haar wavelet transform to capture both global and local features of iris image. After that by Appling reduction step to select only the useful and unique features that belong to each person. In this work PCA used as a reduction method. Finally the minimum distance are used to check the similarity between the database’s features training set and input image, also three similarity techniques are used between input iris image and the template that save in database. Weighted Euclidean distance, Hamming distance and Cosine distance. Cosine method achieve good result than other method by using reduction and without reduction.

Numerical Solution of Fractional Partial Differential Equation of Parabolic Type With Dirichlet Boundary Conditions Using Two-Dimensional Legendre Wavelets Method

In this paper, the numerical solution for the fractional order partial differential equation (PDE) of parabolic type has been presented using two dimensional (2D) Legendre wavelets method. 2D Haar wavelets method is also applied to compute the numerical solution of nonlinear time-fractional PDE. The approximate solutions of nonlinear fractional PDE thus obtained by Haar wavelet method and Legendre wavelet method are compared with the exact solution obtained by using homotopy perturbation method (HPM). The present scheme is simple, effective, and expedient for obtaining numerical solution of the fractional PDE.

URL query string anomaly sensor designed with the bidimensional Haar wavelet transform

In this paper, the 2D Haar wavelet transform is the proposed analysis technique for HTTP traffic data. Web attacks are detected by two threshold operations applied to the wavelet coefficients of th...

Eye detection using discriminatory Haar features and a new efficient SVM

This paper presents an accurate and efficient eye detection method using the discriminatory Haar features (DHFs) and a new efficient support vector machine (eSVM). The DHFs are extracted by applying a discriminating feature extraction (DFE) method to the 2D Haar wavelet transform. The DFE method is capable of extracting multiple discriminatory features for two-class problems based on two novel measure vectors and a new criterion in the whitened principal component analysis (PCA) space. The eSVM significantly improves the computational efficiency upon the conventional SVM for eye detection without sacrificing the generalization performance. Experiments on the Face Recognition Grand Challenge (FRGC) database and the BioID face database show that (i) the DHFs exhibit promising classification capability for eye detection problem; (ii) the eSVM runs much faster than the conventional SVM; and (iii) the proposed eye detection method achieves near real-time eye detection speed and better eye detection performance than some state-of-the-art eye detection methods.

Iris Feature Extraction based on Haar Wavelet Transform

To improve the accuracy of iris recognition system, we propose an efficient algorithm for iris feature extraction based on 2D Haar wavelet. Firstly, the iris image is decomposed by the 2D Haar wavelet three times, and then a 375-bit iris code is obtained by quantizing all the high-frequency coefficients at third lever. Finally we use similarity degree function as matching scheme. Experimental results on CASIA iris database show that our algorithm has the encouraging correct recognition rate (CRR) which is only 99.18%, accompanying with very low equal error rate (EER) 0.54%.

Maximum Entropy Threshold Segmentation for Target Matching Using Speeded-Up Robust Features

This paper proposes a 2-dimensional (2D) maximum entropy threshold segmentation (2DMETS) based speeded-up robust features (SURF) approach for image target matching. First of all, based on the gray level of each pixel and the average gray level of its neighboring pixels, we construct a 2D gray histogram. Second, by the target and background segmentation, we localize the feature points at the interest points which have the local extremum of box filter responses. Third, from the 2D Haar wavelet responses, we generate the 64-dimensional (64D) feature point descriptor vectors. Finally, we perform the target matching according to the comparisons of the 64D feature point descriptor vectors. Experimental results show that our proposed approach can effectively enhance the target matching performance, as well as preserving the real-time capacity.

Fingerprint Image Segmentation Using Haar Wavelet and Self Organizing Map

Fingerprint image segmentation is one of the important preprocessing steps in Automatic Fingerprint Identification Systems (AFIS). Segmentation separates image background from image foreground, removing unnecessary information from the image. This paper proposes a new fingerprint segmentation method using Haar wavelet and Kohonen’s Self Organizing Map (SOM). Fingerprint image was decomposed using 2D Haar wavelet in two levels. To generate features vectors, the decomposed image was divided into nonoverlapping blocks of 2x2 pixels and converted into four elements vectors. These vectors were then fed into SOM network that grouped them into foreground and background clusters. Finally, blocks in the background area were removed based on indexes of blocks in the background cluster. From the research that has been carried out, we conclude that the proposed method is effective to segment background from fingerprint images.

Two-dimensional wavelets for numerical solution of integral equations

Purpose: In this paper, we shall investigate the numerical solution of two-dimensional Fredholm integral equations (2D-FIEs). Methods: In this work, we apply two-dimensional Haar wavelets, to solve linear two dimensional Fredholm integral equations (2D-FIEs). Using 2D Haar wavelets and their properties, 2D-FIEs of the second kind reduce to a system of algebraic equations. Results: The numerical examples illustrate the efficiency and accuracy of the method. Conclusions: In comparison with other bases (for example, polynomial bases), one of the advantages of this method is, although the involved matrices have a large dimension, they contain a large percentage of zero entries, which keeps computational effort within reasonable limits.

Image similarity based on Discrete Wavelet Transform for robots with low-computational resources

This paper describes a similarity measure for images which can be used in image-based topological localization and topological SLAM problems by autonomous robots with low computational resources. Instead of storing the images in the robot’s memory, we propose a compact signature to be extracted from the images. The signature is based on the calculation of the 2D Haar Wavelet Transform of the gray-level image and its size is only 170 bytes. We called this signature the DWT-signature. We exploit the frequency and space localization property of the wavelet transform to match the images grabbed by the perspective camera mounted on board the robot and the reference panoramic images built using an automatic image stitching procedure. The proposed signature allows, at the same time, memory saving and fast and efficient similarity calculation. For the topological SLAM problem we also present a simple implementation of a loop-closure detection based on the proposed signature. We report experiments showing the effectiveness of the proposed image similarity measure using two kinds of small robots: an AIBO ERS-7 robot of the RoboCup Araibo Team of the University of Tokyo and a Kondo KHR-1HV humanoid robot of the IAS-Lab of the University of Padua.

A New Spatial-Scale Decomposition of the Brier Score: Application to the Verification of Lightning Probability Forecasts

Abstract A new scale decomposition of the Brier score for the verification of probabilistic forecasts defined on a spatial domain is introduced. The technique is illustrated on the Canadian Meteorological Centre (CMC) lightning probability forecasts. Probability forecasts of lightning occurrence in 3-h time windows and 24-km spatial resolution are verified against lightning observations from the North American Lightning Detection Network (NALDN) on a domain encompassing Canada and the northern United States. Verification is performed for lightning occurrences exceeding two different thresholds, to assess the forecast performance both for modest and intense lightning activity. Observation and forecast fields are decomposed into the sum of components on different spatial scales by performing a discrete 2D Haar wavelet decomposition. Wavelets, rather than Fourier transforms, were chosen because they are locally defined, and therefore more suitable for representing discontinuous spatial fields characterized by the presence of a few sparse nonzero values, such as lightning. Verification at different spatial scales is performed by evaluating Brier score and Brier skill score for each spatial-scale component. Reliability and resolution are also evaluated on different scales. Moreover, the bias on different scales is assessed, along with the ability of the forecasts to reproduce the observed-scale structure.

A multi-expert approach for robust face detection

Both detection accuracy and speed are of major concerns in developing a robust face detection system for real-world applications. To this end, we propose a robust face detection approach by combining multiple experts in both cascade and parallel manner. We design three detection experts which employ different feature representation schemes of local images: 2D Haar wavelet, gradient direction, and Gabor filter. The three features are classified using the same classification model, namely, a polynomial neural network (PNN) on reduced feature subspace. The detection experts are used in multiple stages with simple ones in proceeding stages and complex ones in succeeding stages for improving detection speed. Meanwhile, the output of each expert is combined with the outputs of its preceding experts to improve detection accuracy. The effectiveness of the multi-expert approach has been demonstrated in experiments on a large number of images. The obtained detection results are superior to the best individual expert and state-of-the-art approaches while the detection speed is fast.