Discrete Cosine Harmonic Wavelet Research Articles

A secure and robust color image watermarking method using SVD and GAT in the multiresolution DCHWT domain

This paper introduces an innovative and robust watermarking technique for safeguarding the copyright of color digital images. The method operates within the domain of SVD-based multiresolution discrete cosine harmonic wavelet transforms. In this approach, the pre-processing phase employs successive generalized Arnold transforms to encrypt the RGB watermark layers, significantly enhancing the security of the watermarking algorithm. Subsequently, the blue layer of the host image undergoes R-level 2D-DCHWT processing. The encrypted watermark is embedded by altering the singular values of the host image's approximation coefficients. Additionally, a reliable extraction algorithm is devised to recover the watermark from potentially compromised watermarked images without requiring access to the original image. Through extensive experiments and comparisons with other relevant watermarking algorithms, the findings demonstrate that this scheme effectively embeds a color digital image watermark into the host image. This not only ensures high levels of invisibility but also establishes robustness, making it well-suited for the protection of digital image copyrights.

Performance comparison of different medical image fusion algorithms for clinical glioma grade classification with advanced magnetic resonance imaging (MRI)

Non-invasive glioma grade classification is an exciting area in neuroimaging. The primary purpose of this study is to investigate the performance of different medical image fusion algorithms for glioma grading purposes by fusing advanced Magnetic Resonance Imaging (MRI) images. Ninety-six subjects underwent an Apparent diffusion coefficient (ADC) map and Susceptibility-weighted imaging (SWI) MRI scan. After preprocessing, the different medical image fusion methods used to fuse ADC maps and SWI were Principal Component Analysis (PCA), Structure-Aware, Discrete Cosine Harmonic Wavelet Transform (DCHWT), Deep-Convolutional Neural network (DNN), Dual-Discriminator conditional generative adversarial network (DDcGAN), and Laplacian Re-Decomposition (LRD). The Entropy, standard deviation (STD), peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and Relative Signal Contrast (RSC) were calculated for qualitative and quantitative analysis. We found high fused image quality with LRD and DDcGAN methods. Further quantitative analysis showed that RSCs in fused images in Low-Grade glioma (LGG) were significantly higher than RSCs in High-Grade glioma (HGG) with PCA, DCHWT, LRD, and DDcGAN. The Receiver Operating Characteristic (ROC) curve test highlighted that LRD and DDcGAN have the highest performance for glioma grade classification. Our work suggests using the DDcGAN and LRD networks for glioma grade classification by fusing ADC maps and SWI images.

Interval type-2 fuzzy set based block-SBU for image fusion technique

Image fusion is the process of examining one or more obscure images, combining only the critical information in those images to make them a good quality image. Due to the large gap between the high dynamic range of landscape scenes and the low quality of consumer quality cameras, a single-shot image cannot record the information of a single set. A part of image processing called image fusion is used to overcome the above problem. In this method, authors propose a new technology for image fusion with intuitionistic fuzzy sets. During the processing, the given images are converted into fuzzy images and then intuitionistic fuzzy images (IFIs). Thus, a significant change occurs between the given image and IFIs. The resulting IFIs are converted into interval type-2 fuzzy images (IT2FIs) to overcome this problem. The proposed technique is compared to other procedures such as discrete cosine harmonic wavelet transform (DCHWT), multi-resolution single value decay (MSVD), primary component analysis (PCA), standard wavelet transform (SWT), two scale image fusion (TSIF), and wavelet transform (WT). The proposed method gives the best results based on performance analysis such as Entropy, standard deviation (STD), average gradient (AG), mutual information (MIF), and blind referenceless image spatial quality evaluator (BRISQUE). Using the proposed technique, one can obtain the best results for entropy, STD, AG, MIF, and BRISQUE respectively as 7.6241, 49.6745, 69.2100, 5.7276, and 3.3091. Hence it reveals that the proposed method performs better than other methods regarding overall visual quality and performance measurements.

Detection of epilepsy using discrete cosine harmonic wavelet transform-based features and neural network classifier

Epilepsy is a neurological disorder caused by the sudden hyper activity in certain parts of the brain. Electroencephalogram (EEG) is the commonly used cost effective modality for the detection of epilepsy. This paper presents a method to detect epilepsy using discrete cosine harmonic wavelet transform (DCHWT) and a neural network classifier. DCHWT is a harmonic wavelet transform (HWT) based on discrete cosine transform (DCT), which is proved to be a spectral estimation technique with reduced bias is used in this work. The proposed method involves decomposition of EEG signals into DCHWT sub-bands, extraction of features from sub-bands and classification using an artificial neural network (ANN) classifier. The main focus of this study is the automatic detection of epilepsy from interictal EEG. This is still a challenge to the researchers as interictal EEG looks like normal EEG which makes the detection difficult. The proposed method is giving classification accuracy of 93.33% to 100% for various classes.

Detection of epilepsy using discrete cosine harmonic wavelet transform-based features and neural network classifier

Epilepsy is a neurological disorder caused by the sudden hyper activity in certain parts of the brain. Electroencephalogram (EEG) is the commonly used cost effective modality for the detection of epilepsy. This paper presents a method to detect epilepsy using discrete cosine harmonic wavelet transform (DCHWT) and a neural network classifier. DCHWT is a harmonic wavelet transform (HWT) based on discrete cosine transform (DCT), which is proved to be a spectral estimation technique with reduced bias is used in this work. The proposed method involves decomposition of EEG signals into DCHWT sub-bands, extraction of features from sub-bands and classification using an artificial neural network (ANN) classifier. The main focus of this study is the automatic detection of epilepsy from interictal EEG. This is still a challenge to the researchers as interictal EEG looks like normal EEG which makes the detection difficult. The proposed method is giving classification accuracy of 93.33% to 100% for various classes.

Efficient analytic discrete cosine harmonic wavelet transform OFDM with denoising

The present wireless implementation needs efficient modulation methods and signal processing at physical layer to enhance system performance. Orthogonal Frequency Division Multiplexing (OFDM) is one such modulation and multiplexing method preferred for such implementation. OFDM implementation using harmonic wavelets has better performance and implementation simplicity. In this paper denoising is applied to Analytic Discrete Cosine Harmonic Wavelet Transform OFDM (ADCHWT OFDM) which is implemented in harmonic wavelet domain. An ADCHWT is simple and shift invariant as it does not involve explicit decimation, interpolation and associated filtering and delay compensation. The reduced leakage and computational simplicity offered by ADCHWT provide an interesting opportunity to explore its application for OFDM system. By application of denoising BER, the performance is further improved in shift invariant ADCHWT OFDM compared to its earlier version Discrete Cosine Harmonic Wavelet Transform (DCHWT OFDM). Further its peak to average power ratio (PAPR) performance is also improved over those of DFT OFDM and Haar WTOFDM.

Efficient analytic discrete cosine harmonic wavelet transform OFDM with denoising

The present wireless implementation needs efficient modulation methods and signal processing at physical layer to enhance system performance. Orthogonal Frequency Division Multiplexing (OFDM) is one such modulation and multiplexing method preferred for such implementation. OFDM implementation using harmonic wavelets has better performance and implementation simplicity. In this paper denoising is applied to Analytic Discrete Cosine Harmonic Wavelet Transform OFDM (ADCHWT OFDM) which is implemented in harmonic wavelet domain. An ADCHWT is simple and shift invariant as it does not involve explicit decimation, interpolation and associated filtering and delay compensation. The reduced leakage and computational simplicity offered by ADCHWT provide an interesting opportunity to explore its application for OFDM system. By application of denoising BER, the performance is further improved in shift invariant ADCHWT OFDM compared to its earlier version Discrete Cosine Harmonic Wavelet Transform (DCHWT OFDM). Further its peak to average power ratio (PAPR) performance is also improved over those of DFT OFDM and Haar WTOFDM.

Weighted Correction and Discrete Wavelet based Fusion for Aerial Images

Background/Objectives: The work introduces new image mixture method combining Aerial Images using improved discrete cosine harmonic wavelet transforms (DCHWT). Methods/Statistical Analysis: An innovative method is planned that provides better results. Firstly, the input histogram image is converted into many segments and then the proposed method is applied to every segment taken for fusion. The performance of the proposed method is evaluated on the basis of PSNR, SSIM and Execution Time. Findings: The method was found to be quite efficient, fast and accurate. Applications/ Improvements: Significant improvement in PSNR and SSIM values is observed resulting in improved quality of the Aerial images.

Multi-Focus Image Fusion in Transform Domain using Steerable Pyramids

In optical lenses of conventional cameras, depth of field is restricted to a particular range. Therefore, only those objects that are at a particular distance from the camera captured clearly with proper focus whereas objects at other distances in front of or behind the focus plane remain defocused and blurred. However, for accurately interpreting and analyzing images, it is desired to obtain images with every object in focus. Multi-focus image fusion is an effective technique to solve this problem by combining two or more images of the same scene taken with different focus settings into a single all-in-focus image with extended depth of field, which is very useful for human or machine perception. The main drawbacks of pixel based fusion methods are misalignment of decision map with boundary of focused objects and wrong decision in sub-regions of the focused or defocused regions which produce undesirable artifacts in the final fused image. Therefore frequency domain methods are more preferred then spatial domain methods. In previous years, many kinds of multi-scale transforms have been proposed and adopted for image fusion such as pyramid decomposition, discrete wavelet transform (DWT) , dual-tree complex wavelet transform (DTCWT) , and discrete cosine harmonic wavelet transform (DCHWT). These transforms are widely used as wavelets become dominant filters in most of the techniques but they still have drawbacks. Wavelets are the lack of translation invariance, especially in twodimensional (2D) signals and the poor selectivity in orientation. This can be overcome by steerable pyramid transform as one can choose the orientation before applying the filters. We have applied this method to achieve multi-focus image fusion of images which have different focus areas while capturing them. Experimental results shows that the proposed method affectively carried out fusion process as performance of the technique has been evaluated by various parameters namely mutual information, QABF factor used for edge perservance measuring and entropy etc.

Analytic discrete cosine harmonic wavelet transform based OFDM system

An OFDM based on Analytic Discrete Cosine Harmonic Wavelet Transform (ADCHWT_OFDM) has been proposed in this paper. Analytic DCHWT has been realized by applying DCHWT to the original signal and to its Hilbert transform. ADCHWT has been found to be computationally efficient and very effective in improving Bit Error Rate (BER) and Peak to Average Power Ratio (PAPR) performance. Improvement compared to that of Haar-WT OFDM and DFT OFDM is achieved without employing Cyclic Prefix BER is 0.002 for ADCHWT OFDM compared to Haar WT, DFT OFDM which have BER of 0.06 and 0.4, respectively, at 15 dB SNR. PAPR is also reduced by 3 dB compared to DFT OFDM and 0.3 dB reduction compared to Haar WT OFDM.

A New OFDM System Based on Discrete Cosine Harmonic Wavelet Transform (DCHWT) for PSK and QAM

This paper proposes a new orthogonal frequency division multiplexing (OFDM) system, based on discrete cosine harmonic wavelet (DCHWT) for PSK and 16-QAM modulated signals. This system uses energy compaction property of discrete cosine transform (DCT) that provides low leakage in subcarriers. DCHWT based OFDM system provides improved performance in terms of bit error rate (BER) and reduction in the peak to average power ratio (PAPR) compared to conventional cyclic prefix (CP) based Fourier transform OFDM (DFT-OFDM). Application of $$\upmu $$μ-law companding to proposed system further improves the PAPR performance. The complementary cumulative distribution (CCDF) plots corroborate the same. BER performance is on par or better than that of Haar wavelet based OFDM in addition to improvement in PAPR. PAPR improved is in the range of 0.8---2.3 dB compared to Haar and DFT OFDM respectively, with remarkable improvement in BER. Proposed method is simple, does not require explicit decimation, interpolation, associated filtering and delay compensation for reconstruction, compared to other time domain wavelet transforms.

Orthogonal frequency division multiplexing peak‐to‐average power ratio reduction by best tree selection using coded discrete cosine harmonic wavelet packet transform

A new orthogonal frequency division multiplexing (OFDM) with reduced peak-to-average power ratio (PAPR) based on coded discrete cosine harmonic wavelet packet transform (DCHWPT), is proposed. In this method, tree pruning is done for the selection of a tree structure with minimum PAPR. To identify different tree structures, Gray code is used which is communicated as side information to the receiver. Also to improve bit error rate (BER) performance and reduce PAPR, Hadamard codes are employed. The proposed method based on DCHWPT exploits the desirable discrete cosine transform (DCT) properties like energy compaction/low leakage, better frequency resolution and its real nature, compared with those of discrete Fourier transform. Further, the harmonic wavelet employed has built in decimation without any associated antialiasing filters and easy reconstruction by concatenation of different scales in frequency (DCT) domain with no image rejection filters and complicated delay compensation makes the proposed wavelet packet simple in implementation. The proposed OFDM discrete cosine harmonic wavelet packet (DCHWP-OFDM) which leverages the advantages of DCHWPT has been used for BPSK modulated signals. The DCHWP-OFDM provides an improvement of PAPR reduction of 2.4 and 3.4 dB as compared with those of Haar and Daubechies-4 wavelet packet OFDM, respectively. This reduction in PAPR is with a BER performance in the range of 0.001-0.0001 at an signal-to-noise ratio of 10 dB.

Multifocus and multispectral image fusion based on pixel significance using discrete cosine harmonic wavelet transform

The energy compaction and multiresolution properties of wavelets have made the image fusion successful in combining important features such as edges and textures from source images without introducing any artifacts for context enhancement and situational awareness. The wavelet transform is visualized as a convolution of wavelet filter coefficients with the image under consideration and is computationally intensive. The advent of lifting-based wavelets has reduced the computations but at the cost of visual quality and performance of the fused image. To retain the visual quality and performance of the fused image with reduced computations, a discrete cosine harmonic wavelet (DCHWT)-based image fusion is proposed. The performance of DCHWT is compared with both convolution and lifting-based image fusion approaches. It is found that the performance of DCHWT is similar to convolution-based wavelets and superior/similar to lifting-based wavelets. Also, the computational complexity (in terms of additions and multiplications) of the proposed method scores over convolution-based wavelets and is competitive to lifting-based wavelets.

A Dual Tree Complex Discrete Cosine Harmonic Wavelet Transform (ADCHWT) and Its Application to Signal/Image Denoising

A new simple and efficient dual tree analytic wavelet transform based on Discrete Cosine Harmonic Wavelet Transform DCHWT (ADCHWT) has been proposed and is applied for signal and image denoising. The analytic DCHWT has been realized by applying DCHWT to the original signal and its Hilbert transform. The shift invariance and the envelope extraction properties of the ADCHWT have been found to be very effective in denoising speech and image signals, compared to that of DCHWT.

A Discrete Cosine Adaptive Harmonic Wavelet Packet and Its Application to Signal Compression

A new adaptive Packet algorithm based on Discrete Cosine harmonic wavelet transform (DCHWT), (DCAHWP) has been proposed. This is realized by the Discrete Cosine Harmonic Wavelet transform (DCHTWT) which exploits the good properties of DCT viz., energy compaction (low leakage), frequency resolution and computational simplicity due its real nature, compared to those of DFT and its harmonic wavelet version. Hence the proposed wavelet packet is advantageous both in terms of performance and computational efficiency compared to those of existing DFT harmonic wavelet packet. Further, the new DCAHWP also enjoys the desirable properties of a Harmonic wavelet transform over the time domain WT, viz., built in decimation without any explicit antialiasing filtering and easy interpolation by mere concatenation of different scales in frequency (DCT) domain with out any image rejection filter and with out laborious delay compensation required. Further, the compression by the proposed DCAHWP is much better compared to that by adaptive WP based on Daubechies-2 wavelet (DBAWP). For a compression factor (CF) of 1/8, the ratio of the percentage error energy by proposed DCAHWP to that by DBAWP is about 1/8 and 1/5 for considered 1-D signal and speech signal, respectively. Its compression performance is better than that of DCHWT, both for 1-D and 2-D signals. The improvement is more significant for signals with abrupt changes or images with rapid variations (textures). For compression factor of 1/8, the ratio of the percentage error energy by DCAHWP to that by DCHWT, is about 1/3 and 1/2, for the considered 1-D signal and speech signal, respectively. This factor for an image considered is 2/3 and in particular for a textural image it is 1/5.

Discrete cosine harmonic wavelet transform and its application to signal compression and subband spectral estimation using modified group delay

This paper proposes a new harmonic wavelet transform (HWT) based on discrete cosine transform (DCTHWT) and its application for signal or image compression and subband spectral estimation using modified group delay (MGD). Further, the existing DFTHWT has also been explored for image compression. The DCTHWT provides better quality decomposed decimated signals, which enable improved compression and MGD processing. For signal/image compression, compared to the HWT based on DFT (DFTHWT), the DCTHWT reduces the reconstruction error. Compared to DFTHWT for the speech signal considered for a compression factor of 0.62, the DCTWHT provides a 30% reduction in reconstruction error. For an image, the DCTHWT algorithm due to its real nature, is computationally simple and more accurate than the DFTHWT. Further compared to Cohen–Daubechies–Feauveau 9/7 biorthogonal symmetric wavelet, the DCTHWT, with its computational advantage, gives a better or comparable performance. For an image with 6.25% coefficients, the reconstructed image by DFTHWT is significantly inferior in appearance to that by DCTHWT which is reflected in the error index as its values are 3.0 and 2.65%, respectively. For spectral estimation, DCTHWT reduces the bias both in frequency (frequency resolution) and spectral magnitude. The reduction in magnitude bias in turn improves the signal detectability. In DCTHWT, the improvement in frequency resolution and the signal detectability is not only due to good quality DCT subband signals but also due to their stretching (decimation) in the wavelet transform. The MGD reduces the variance while preserving the frequency resolution achieved by DCT and decimation. In view of these, the new spectral estimator facilitates a significant improvement both in magnitude and frequency bias, variance and signal detection ability; compared to those of MGD processing of both DFT and DCT fullband and DFT subband signals.