Discrete Wavelet Domain Research Articles

A Fast Intersection of Confidence Intervals Method-Based Adaptive Thresholding for Sparse Image Reconstruction Using the Matrix Form of the Wavelet Transform

One of the frequently used classes of sparse reconstruction algorithms is based on the iterative shrinkage/thresholding procedure, in which the thresholding parameter controls a trade-off between the algorithm’s accuracy and execution time. In order to avoid this trade-off, we propose using a fast intersection of confidence intervals method in order to adaptively control the threshold value throughout the iterations of the reconstruction algorithm. We have upgraded the two-step iterative shrinkage thresholding algorithm with a such procedure, improving its performance. The proposed algorithm, denoted as the FICI-TwIST, along with a few selected state-of-the-art sparse reconstruction algorithms, has been tested on the classical problem of image recovery by emphasizing the image sparsity in the discrete cosine and the discrete wavelet domain. Furthermore, we have derived a single wavelet transformation matrix which avoids wrapping effects, thereby achieving significantly faster execution times as compared to a more traditional function-based transformation. The obtained results indicate the competitive performance of the proposed algorithm, even in cases where all algorithm parameters have been individually fine-tuned for best performance.

Iterative histogram equalization using discrete wavelet transform in low-dynamic range

A progressive histogram equalization (HE) and contrast enhancement method is proposed in the frequency domain. This method has an iterative structure based on the 6-sigma rule in the low-dynamic range using discrete wavelet transform. The proposed method determines an automatic threshold for attenuating the high-frequency amplitude of a signal in the discrete wavelet domain, based on the standard deviation of the absolute power of the high-frequency components in the signal band generated from the probability density function (PDF). Then an iterative quantization procedure is used where the PDF values in the frequency domain are randomly quantized. Besides, the maximum Bhattacharyya coefficient, which matches the original input image’s PDF, is used as a cost function to optimize the histogram smoothing output. For the random number generation, a 32-bit pseudorandom generator is employed to produce the same result for the output image at each runtime. The quantization factor parameter enables a controlled contrast enhancement rate to receive balanced equalization results in images. In the experimental studies, the proposed iterative HE method is compared with the well-known global, local, and brightness preserving algorithms. Experimental studies quantitatively and qualitatively display promising and encouraging results in terms of various state-of-the-art quality assessment metrics such as mean squared error, peak signal-to-noise ratio, structural similarity index measurement, contrast improvement index, absolute mean brightness error, and quality-aware relative contrast measure.

Seismic data reconstruction using Bregman iterative algorithm based on compressed sensing and discrete orthonormal wavelet transform

AbstractDue to the limitations of the actual acquisition environment in the field, especially in ocean bottom seismometer (OBS) acquisition, the acquired seismic data are often irregular and incomplete, which affects the subsequent data imaging, interpretation and hydrocarbon‐bearing reservoir prediction. The interpolation reconstruction algorithm based on the compressive sensing theory can reconstruct the data without the limitation of Nyquist sampling interval. However, the reconstruction accuracy and effect are different for different sparse representations of the data. On the basis of compressed sensing theory, we propose a Bregman iterative seismic data reconstruction method based on the sparse decomposition of discrete orthonormal Coiflets and Symlets wavelet transforms. First, the discrete orthonormal matrix is constructed by using the above two wavelet functions to make the original seismic data sparse, then the Bregman iterative algorithm is used to reconstruct the sparse coefficients in the discrete wavelet domain, and finally the recovery matrix is used to reconstruct the seismic data. The discrete orthonormal Coiflets and Symlets wavelet transforms have good sparse representation ability and can compensate for the problem that discrete Fourier transform cannot well sparse representation of the data. After numerical experiments on horizontal‐layered model, Marmousi2 model and actual data, it is verified that the proposed method can reconstruct the missing seismic data under the regular observation system and under the irregular observation system with non‐uniform OBS distribution. Furthermore, this method can hardly bring the interference of random noise, and the reconstruction result is of high accuracy.

Seismic ground roll attenuation in DWT domain by split Bregman iteration algorithm

Noise reduction of seismic data is one of the most substantial steps in seismic signal processing. Goudarzi and Riahi presented wavelet domain ground roll analysis (WDGA), a technique based on the data. The results of this method showed a good improvement of the signal-to-noise ratio, but the WDGA did not work well in the data with a high level of random noise because this method uses a comparison-based search algorithm. This problem requires additional research to find a way to overcome this limitation. The wavelet domain split Bregman (WDSB) method presented in this paper is based on the use of the split Bregman algorithm in a discrete wavelet domain. The goal is to simultaneously use the capabilities of the F-K filter and the split Bregman iteration algorithm in the discrete wavelet domain, to overcome the problem of high levels of random noise in ground roll attenuation. The results of using WDSB for synthetic and real seismic data show improvement in ground roll attenuation while protecting seismic signals. The new algorithm is studied in time and wavelet domains.

Deep ResNet Based Remote Sensing Image Super-Resolution Reconstruction in Discrete Wavelet Domain

We present a single-image super-resolution (SR) method for Remote Sensing Image based on deep learning within Discrete Wavelet Domain in this paper. Our method is inspired Residual Learning. Firstly, an input image is decomposed by single level 2D Discrete wavelet transform to get four sub-bands. The four sub-bands coefficients are feeding into the Deep Learning Residual Network to predict correspondingly residual images; Adding four sub-band images and residual images as the new sub-bands of 2D wavelet transform; Finally, uses the inverse 2D Discrete wavelet transform to get the final output Super Resolution HR image. Our proposed method performs better than existing methods in accuracy and visual improvements in our results are easily noticeable.

An optimized blind watermarking scheme based on principal component analysis in redundant discrete wavelet domain

The frequency of digital data transmission or sharing online has heavily increased due to the number of people regularly accessing the internet. This guide explores how easily copyright can be breached on a large scale. Digital multimedia in the form of images, text, audio and video can easily be forged, faked and then shared for profit. To address this issue, digital watermarking has been introduced as a possible solution. In this guide, an optimized blind image watermarking approach based on principal component analysis (PCA) in redundant discrete wavelet (R-DW) domain is proposed. In addition, several attacks are applied to a watermarked image by extracting the message from the attacked image to show the robustness of the proposed PCA-R-DW scheme. Furthermore, an improved grey-wolf optimizer (IGWO) algorithm which has emerged as an efficient meta-heuristic optimization technique is utilized to optimize the performance of the proposed PCA-R-DW blind watermarking (BW) approach. Extensive comparison of test results with conventional BW approaches show the robustness of the proposed framework in terms of quality metrics such as normalized correlation coefficient (NCC), peak signal-to-noise ratio (PSNR), mean square error (MSE) and structural similarity (SSIM) index.

A Robust Watermarking Method for an Authentication of Video Surveillance Applications

The problem of authenticating the video content is the major role of any automated video surveillance systems (AVS). This research work delivers an approach to authenticate the surveillance video which can be used by attorneys to prove their clients using Digital Watermarking. The digital watermark gives an assurance that the provided video surveillance frame is not tampered. In this paper, we proposed a robust video watermarking approach for an authentication of video surveillance applications. The digital watermark is embedded into the Discrete Wavelet domain of the identified key frames using holoentropy. Here, the pixel map will be optimallygenerated for the watermarking and the image embedding using the proposed classifier using Moth – flame - Rider optimization based Neural Network (MF-ROA-based NN) will generate the optimal map prediction based on the fitness measure, such as wavelet coefficient, energy, entropy, loop coefficient, and standard deviation, respectively. This optimal map is used for both embedding and extraction. The experimental results proves that the proposed systems can authenticate the surveillance video frames against various attacks when compared to the existing systems.

Robust and blind watermarking using Arnold 4D cat map in discrete wavelet

Though watermarking got attention in the past decade, its robustness and security remain as a challenge to the researchers. Here, one new technique has been proposed to counter these problems using Arnold 4D cat map in discrete wavelet domain. The color watermark is decomposed into the RGB planes before the encryption process. Similarly, the cover image is decomposed to the RGB planes. Initially, the watermark planes are encrypted using Arnold 4D map followed by embedment in the wavelet coefficients of the respective cover image planes. The evaluation parameters, such as NPCR, PSNR and NC show a better performance of this proposed algorithm.

Multifocus image fusion based on coefficient significance of redundant discrete wavelet transform

PurposeThis study aims to obtain the more precise decision map to fuse the source images by Coefficient significance method. In the area of multifocus image fusion, the better decision map is very important the fusion results. In the processing of distinguishing the well-focus part with blur part in an image, the edge between the parts is more difficult to be processed. Coefficient significance is very effective in generating the better decision map to fuse the multifocus images.Design/methodology/approachThe energy of Laplacian is used in the approximation coefficients of redundant discrete wavelet transform. On the other side, the coefficient significance based on statistic property of covariance is proposed to merge the detail coefficient.FindingsDue to the shift-variance of the redundant discrete wavelet and the effectiveness of fusion rule, the presented fusion method is superior to the region energy in harmonic cosine wavelet domain, pixel significance with the cross bilateral filter and multiscale geometry analysis method of Ripplet transform.Originality/valueIn redundant discrete wavelet domain, the coefficient significance based on statistic property of covariance is proposed to merge the detail coefficient of source images.

History Matching the Full Norne Field Model Using Seismic and Production Data

SummaryIn this paper, we use a combination of acoustic impedance and production data for history matching the full Norne Field. The purpose of the paper is to illustrate a robust and flexible work flow for assisted history matching of large data sets. We apply an iterative ensemble-based smoother, and the traditional approach for assisted history matching is extended to include updates of additional parameters representing rock clay content, which has a significant effect on seismic data. Further, for seismic data it is a challenge to properly specify the measurement noise, because the noise level and spatial correlation between measurement noise are unknown. For this purpose, we apply a method based on image denoising for estimating the spatially correlated (colored) noise level in the data. For the best possible evaluation of the workflow performance, all data are synthetically generated in this study. We assimilate production data and seismic data sequentially. First, the production data are assimilated using traditional distance-based localization, and the resulting ensemble of reservoir models is then used when assimilating seismic data. This procedure is suitable for real field applications, because production data are usually available before seismic data. If both production data and seismic data are assimilated simultaneously, the high number of seismic data might dominate the overall history-matching performance.The noise estimation for seismic data involves transforming the observations to a discrete wavelet domain. However, the resulting data do not have a clear spatial position, and the traditional distance-based localization schemes used to avoid spurious correlations and underestimated uncertainty (because of limited ensemble size), are not possible to apply. Instead, we use a localization scheme that is based on correlations between observations and parameters that does not rely on physical position for model variables or data. This method automatically adapts to each observation and iteration.The results show that we reduce data mismatch for both production and seismic data, and that the use of seismic data reduces estimation errors for porosity, permeability, and net-to-gross ratio (NTG). Such improvements can provide useful information for reservoir management and planning for additional drainage strategies.

Video Copyright Protection Using Chaotic Maps and Singular Value Decomposition in Wavelet Domain

This paper attempts to offer a new method for video copyright protection using Singular Value Decomposition (SVD) and chaotic maps in the discrete wavelet domain. To provide integrity to the watermark image, the singular values of watermark images are permuted using a hyper chaotic map and an authentication key. Based on the number of scene changes in the video, the permuted watermark image is partitioned into a number of blocks. Then the frame difference method is applied for selecting the key frames in each scene. In the embedding process, each frame in the group is transformed to single level DWT. The principal component (PC) of the watermark is embedded into the LL subband of each scene in the specific key frames and the corresponding permuted watermark PCs are added to the SVs of the scene followed by inverse SVD to obtain the watermarked scene. The suitable scaling factor is selected by a new mechanism in tune with rates of changes of PSNR and NCC. The proposed algorithm is robust against video processing attacks with better integrity of watermark data with lesser processing time. The proposed method also resolves the false-positive problem by embedding the principal component of the permuted watermark.

Illumination compensation for face recognition using adaptive singular value decomposition in the wavelet domain

Lighting variations are a challenge in face recognition. To overcome this problem, this paper proposes a novel illumination compensation method called adaptive singular value decomposition in the 2D discrete wavelet domain (ASVDW) to enhance face images. First, an efficient brightness detector based on the blue pixel values of the red green blue (RGB) color channels is used to classify the color face image into dark, normal, or bright before applying the corresponding Gaussian template. The RGB color channels of the face image are then transformed to the 2D discrete wavelet domain. The frequency subband coefficients of the three color channels are automatically adjusted by multiplying the singular value matrices of these frequency subband coefficient matrices with their corresponding compensation weight coefficients. An efficient image denoising model is then applied, and a 2D inverse discrete wavelet transform is applied to obtain the ASVDW-compensated color face images without the lighting effect. In addition, a region-based ASVDW method (RASVDW), which entails the application of the ASVDW algorithm in four regions of an image, is introduced to reduce the computing time. Experimental results validate the efficiency of the proposed methods.

Norm ratio-based audio watermarking scheme in DWT domain

In order to reach a balance between robustness, imperceptibility, and data payload, a novel blind audio watermarking scheme is proposed using the norm ratio of approximate coefficients in discrete wavelet domain (DWT). A chaotic sequence generated by Tent map is used to encrypt the watermark image and enhance the security of watermarking system. Firstly the original audio signal is segmented into non-overlapping frames and DWT is applied to each frame. Then, the approximate components are divided into two parts, and the norm ratio is calculated and modulated to embed the watermarks. Finally, the approximate components are scaled by optimizing the quality of the watermarked audio. Experimental results indicate that the proposed watermarking scheme is robust against different common attacks, such as noise addition, resampling, re-quantization, MP3 compression and amplitude scaling. The comparison analysis shows that the proposed scheme has high data payload and provides superior performance compared to the state-of-the-art watermarking schemes.

Image Watermarking using Singular Value Decomposition with integration of Particle Swarm Optimization in Discrete wavelet transform

This paper proposes an additive watermarking method by using an optimization technique which make use of singular value decomposition (SVD) and makes use of Particle swarm optimization in discrete wavelet domain to enhance the watermarking scheme.SVD based watermarking Is done to provide high capacity. In order to improve the quality of images and to achieve the imperceptibility without losing robustness, an optimal scheme for embedding the secret message derived from PSO. Meanwhile PSO as a popular optimization technique and has been used as a method to balance the imperceptibility and robustness it is because PSO serves the weighting factor inside of embedding process. The proposed technique takes an advantage of Arnold transformations that provide security after successful watermark extraction.DWT is applied on the original image and the value of scaling factors to insert the watermark are obtained using PSO. Result comparisons shows that this algorithm proposed outperforms the additive work as compared to the existing algorithm.

Effectiveness of steganalysis based on machine learning methods

Subject of Study.The paper presents comparative accuracy estimation of modern machine learning-based steganalytic methods. The paper deals with the most perspective methods in tasks of the passive counteraction to the information transfer channels using the discrete wavelet domain of static digital images. Methods. We have studied methods proposed by Gireesh Kumar, Hany Farid, Changxin Liu, Yun Q. Shi and the SPAM method. Basically the methods apply statistical moments obtained from wavelet bands LL, HL, LH and HH, as well as additional image features forming a support vector. BOWS2 image collection was used to estimate the effectiveness of methods. Steganographic impact was modeled by changing the least significant bits of coefficients for the each DWT band (LL, LH, HL and HH) with 5% and 20% of payload. The effectiveness of explored methods is estimated in view of obtained true positive, true negative, false positive and false negative image classification values. Main Results. The study has shown that all explored methods except for SPAM are effective in the task of detecting of embedding in HH band. As for the detection of the embedding in LH band, Yun Q. Shi is the most effective algorithm. In the task of the detecting in HL band, all explored methods except for SPAM have appeared to be comparatively effective under condition of big payload. When detecting the embedding in LL band, all methods have shown the effectiveness about 50% regardless the payload rate. It is established that the considered methods are not able to render effective counteraction to the hidden data channel, using the LH and HL region due to the fact that they use Haar wavelet transform. It is concluded that the application of the optimal wavelet transform makes it possible to reduce the intersection area of value histograms of the first statistical moment for the original images and steganoimages. Practical Relevance. The work results are useful to the specialists in the field of information security in the tasks of detection and combating the hidden data channels. The obtained results can be used in the development of steganalysis systems and improved methods of steganalysis as well.

Reversible Watermarking for Enhancing the Security and Storage of ECG Signal and EPR in DICOM Images

Hospital information system and picture archiving and communication system allow transfer of medical images via internet for sharing studies, getting second opinion from radiologist and physician etc. Storage and transmission of Medical Images is crucial as huge volumes are generated every day. Security of medical images is of greater concern for its role in clinical diagnostics. Digital image watermarking is a proven technique that addresses the security and storage issues concerned. The objective is to improve the storage of medical data by applying a reversible watermarking technique. This work presents a semi fragile watermarking technique which hides Electronic patient record and Electrocardiogram Signal (ECG) in the medical image. Embedding is done in discrete wavelet domain followed by singular value decomposition. Recursive dither modulation is used to embed the watermark consisting of EPR, ECG signal, Hash of Region of interest (ROI), vertices of ROI and Doctor Identification code (DIC). Security is provided by encrypting the watermark using Advanced Encryption Standard before embedding. Performance of the scheme is evaluated on DICOM images in different modalities using Peak Signal to noise ratio (PSNR), Mean Structural Similarity Index (MSSIM) and Normalized Cross Correlation (NCC). PSNR and MSSIM values obtained are above 57dB and 0.98 for the proposed technique. NCC value of 0.98 is obtained showing the robustness of the watermark. Thus the proposed work presents a technique for storing EPR and ECG signal in medical image offering better visual quality and security when compared to other techniques of this type.

A robust video watermarking scheme using sparse principal component analysis and wavelet transform

The extension of internet facility profoundly eases the dissemination of all digital data such as audio, images and videos to the general public. This paper proposes a blind scheme for digital video watermarking. In this paper, a discrete wavelet domain watermarking is adopted for hiding a large amount of data with high security, good invisibility and no loss to the secret message. At first, dual tree complex wavelet transform (DTCWT) is applied on each frame decomposing it into a number of sub-bands. Then, holo entropy of each sub-band is calculated and the maximum entropy blocks are selected. The selected blocks are transformed using sparse principal component analysis (SPCA). The maximum coefficient of the SPCA blocks of each sub-band is quantised using quantisation index modulation (QIM). The proposed video watermarking scheme is analysed through various constraints such as the normalised correlation (NC) and the peak signal to noise ratio (PSNR).

A robust video watermarking scheme using sparse principal component analysis and wavelet transform

The extension of internet facility profoundly eases the dissemination of all digital data such as audio, images and videos to the general public. This paper proposes a blind scheme for digital video watermarking. In this paper, a discrete wavelet domain watermarking is adopted for hiding a large amount of data with high security, good invisibility and no loss to the secret message. At first, dual tree complex wavelet transform (DTCWT) is applied on each frame decomposing it into a number of sub-bands. Then, holo entropy of each sub-band is calculated and the maximum entropy blocks are selected. The selected blocks are transformed using sparse principal component analysis (SPCA). The maximum coefficient of the SPCA blocks of each sub-band is quantised using quantisation index modulation (QIM). The proposed video watermarking scheme is analysed through various constraints such as the normalised correlation (NC) and the peak signal to noise ratio (PSNR).

Denoising of magnetotelluric signals by polarization analysis in the discrete wavelet domain

Magnetotellurics (MT) is one of the prominent geophysical methods for underground deep exploration and, thus, appropriate for applications to petroleum and geothermal research. However, it is not completely reliable when applied in areas characterized by intense urbanization, as the presence of cultural noise may significantly affect the MT impedance tensor estimates and, consequently, the apparent resistivity values that describe the electrical behaviour of the investigated buried structures. The development of denoising techniques of MT data is thus one of the main objectives to make magnetotellurics reliably even in urban or industrialized environments. In this work we propose an algorithm for filtering of MT data affected by temporally localized noise. It exploits the discrete wavelet transform (DWT) that, thanks to the possibility to operates in both time and frequency domain, allows to detect transient components of the MT signal, likely due to disturbances of anthropic nature. The implemented filter relies on the estimate of the ellipticity of the polarized MT wave. The application of the filter to synthetic and field MT data has proven its ability in detecting and removing cultural noise, thus providing apparent resistivity curves more smoothed than those obtained by using raw signals.

Solving Enhanced Radar Imaging Inverse Problems: From Descriptive Regularization to Feature Structured Superresolution Sensing

Resolution enhancement (RE) and superresolution (SR) enhancement of the remote sensing imagery provided by conventional low-resolution (LR) coherent real aperture radar or fractional SAR sensors operating in real-world scenarios with the model data statistics unknown to the observer belong to a class of nonlinear uncertain inverse problems. The classical Bayesian statistical inference and modern compressed sensing-based approaches are not properly adapted to such inverse problems as the latter require robust spatially selective image despeckling adaptively balanced over RE with preservation of salient radar/SAR image features. In this paper, we propose to treat the RE/SR radar imaging inverse problems in a multistage descriptive experiment design regularization (DEDR) setting that logically unifies composite RE optimization tasks into a four-level structured DEDR framework. First, the conventional despeckled LR image formed via performing the matched spatial filtering of the recorded trajectory signals is considered as initial LR data for further feature enhanced processing. Second, the minimum risk inspired robust adaptive beamforming method is DEDR restructured and unified with the convergence guaranteed and sparsity promoting composite projections onto convex sets aimed at feature enhanced recovery of the high-resolution despeckled image. The third level suggests transition to the nested refined SR scales with preservation of the consistency space. Finally, the SR recovery of the fine image features is performed consequently in each nested refined image frame via discrete wavelet domain postprocessing-based sparsity promoting denoising with consistency preservation. The new multistage SR-DEDR technique conjugates excellent despeckling and SR enhancement performances corroborated via reported computer simulations.