Discrete Cosine Transform Coefficients Research Articles

Secured steganographic scheme for highly compressed color image using weighted matrix through DCT

Due to the rapid growth of internet technology and the advent of various image processing tools, people started using digital media for hidden communication to protect valuable information which is important for multimedia commercials, health-care, medical and defense applications. On the other hand, image authentication and tamper detection are essential, especially when it is utilized for evidence of legal action. In this paper, a weighted matrix based steganographic scheme has been designed for highly compressed (Quality Factor (QF) 40) color image through discrete cosine transform (DCT) to maintain a good balance between payload and imperceptibility. Here, the AC components are collected from quantized DCT coefficient matrices of YCbCr channel. Then, a series of original matrices are formed to hide secret data. The collection of AC components is controlled by 128 bits shared secret key. A predetermined weighted matrix is employed to select the embedding position within a coefficient matrix of a cover image through the sum of the entry-wise multiplication operation. The proposed scheme provides good embedding capacity with the high visual quality compared to existing state-of-the-art methods. Finally, different steganographic analysis and attacks are carried out to observe its imperceptibility and robustness.

Reduced‐reference quality metric based on local sharpness measure for blurred images

A simple yet robust reduced-reference quality metric based on local sharpness measure for blurred images in discrete cosine transform (DCT) domain is introduced. As a single feature to represent the quantification of blur in an image, a global image sharpness is quantified from the local sharpness with a selected optimal subset of DCT coefficients in each overlapped block in the feature extraction process. Then, the final objective quality score is simply calculated by division by the reference value in the quality analysis process. The experimental results on three public quality assessment databases demonstrate the proposed method correlates highly with human subjective judgements and outperform other methods consistently in terms of prediction accuracy and monotonicity for a wide range of blurriness.

Image splicing forgery detection based on low-dimensional singular value decomposition of discrete cosine transform coefficients

Digital image forgery has significantly increased due to the rapid development of several tools of image manipulation. Based on the manipulation used to produce a tampered image, image forgery techniques can be characterized into three types: copy–move forgery, image splicing, and image retouching. Image splicing is achieved by adding regions from one image into another. This technique changes the content of the target image and causes variations in image features which are used to detect the forgery regions. In this study, an image splicing forgery detection method based on low-dimensional singular value decomposition of discrete cosine transform (DCT) coefficients has been presented. The suspicious input image is divided into multi-size blocks, and each block is transformed into 2D DCT. The DCT coefficients are calculated correspondingly to each block. The features from DCT are extracted using SVD algorithm. The roughness measure is calculated for the set of singular values obtained. Lastly, four types of statistical features—mean, variance, third-order moment skewness, and fourth-order moment kurtosis—are extracted from SVD features and are then arranged in a feature vector. Feature reduction has been applied by kernel principal component analysis. Finally, support vector machine is used to distinguish between the authenticated and spliced images. The proposed method was evaluated against three standard image datasets CASIA v1, DVMM v1, and DVMM v2. The proposed method shows an average detection accuracy of 97.15, 99.30, and 96.97 for DVMM v1, CASIA v1, and DVMM v2, respectively. These results outperform several current image splicing detection methods.

Analysis of the Reconstruction of Sparse Signals in the DCT Domain Applied to Audio Signals

Sparse signals can be reconstructed from a reduced set of signal samples using compressive sensing (CS) methods. The discrete cosine transform (DCT) can provide highly concentrated representations of audio signals. This property implies the DCT as a good sparsity domain for the audio signals. In this paper, the DCT is studied within the context of sparse audio signal processing using the CS theory and methods. The DCT coefficients of a sparse signal, calculated with a reduced set of available samples, can be modeled as random variables. It has been shown that the statistical properties of these variables are closely related to the unique reconstruction conditions. The main result of this paper is in an exact formula for the mean-square reconstruction error in the case of approximately sparse and nonsparse noisy signals reconstructed under the sparsity assumption. Based on the presented analysis, a simple and computationally efficient reconstruction algorithm is proposed. The presented theoretical concepts and the efficiency of the reconstruction algorithm are verified numerically, including examples with synthetic and recorded audio signals with unavailable or corrupted samples. Random disturbances and disturbances simulating clicks or inpainting in audio signals are considered. Statistical verification is done on a dataset with experimental signals. Results are compared with some classical and recent methods used in similar signal and disturbance scenarios.

Soft Decision Based Gaussian‐Laplacian Combination Model for Noisy Speech Enhancement

One of the key issues of noisy speech enhancement technique is to achieve appropriate statistical distributions to model the clean speech and noise signals accurately. Most of the existing algorithms try to employ a sole model assumption in transform domain, which, however, has been proven to being contrary with the fact. To address this problem, the statistical properties of clean speech as well as several noise signals are analyzed using actual data in Discrete cosine transform (DCT) domain, and the study indicates the statistic of clean speech DCT coefficients tending to fall somewhere in between the Gaussian and Laplacian distribution. Based on the results, a novel speech enhancement algorithm is proposed using Gaussian-Laplacian combination model, whose core is employing a linear combination of Gaussian and Laplacian distribution to model the statistic of clean speech DCT coefficients. The corresponding weights of either distribution to the combination model are adaptively adjusted in terms of the probability of each hypothesis, which is estimated based on a soft decision technique by using Bayesian theorem. Through a number of objective and subjective tests, we compare the performance of the proposed algorithm with other recent model based approaches and have found that our algorithm is superior to the related approaches at all testing environments.

An Effective Watermarking Method Based on Energy Averaging in Audio Signals

Methods based on discrete cosine transform (DCT) have been proposed for digital watermarking of audio signals; however, the watermark is often vulnerable to data compression and signal processing. This paper presents an effective audio watermarking method by energy averaging of DCT coefficients such that an audio signal with watermark is robust to data processing. The method is to divide an audio signal into segments by three parameters defining the segment length, the segment sequence of watermark location, and the frequency range of DCT coefficients for watermark location. An error correcting code is also integrated to improve audio signal quality after watermarking. Experimental results show that the method is robust to data compression and many other kinds of signal processing. No original signal is required for decoding the watermark. Comparison of watermarking performance with a recent work validates that the watermarking method has better audio quality and higher robustness.

Text-image watermarking based on integer wavelet transform (IWT) and discrete cosine transform (DCT)

Text-images still have a great importance, despite the spread of electronic texts. Text-images are protected using digital watermarking. This paper proposes a watermarking method applied to text-images. This method integrates two transforms: integer wavelet transform (IWT) and discrete cosine transform (DCT). For the watermark embedding, IWT is performed on the cover image and DCT is applied to the low frequency sub-band LL. The watermark image is inserted in the lower to medium DCT coefficients to achieve a high degree of robustness and imperceptibility. Experiments using different Arabic text-images are performed to evaluate the proposed method in terms of imperceptibility and robustness. Results show that the proposed method has higher imperceptibility compared to other existing methods applied to Arabic text-images. Also, the proposed method provides good robustness results, especially against compression and noise.

Realization of Second-Order Structure of Recursive Algorithm for Discrete Cosine Transform

A computational and hardware-efficient second-order infinite impulse response filter structure is proposed in this paper. It can compute discrete cosine transform (DCT) with improved processing speed and is valid for N = 2r, where N is the length of the input sequence and r > 1. A new algorithm is also proposed in this paper which is an improvement over previously reported algorithms in the literature. The proposed algorithm reduces the total number of real multiplications and additions in comparison with the existing algorithms. Using the suggested algorithm, computational cycles required to compute a DCT coefficient are less which further reduces the truncation error while processing a long length of input data.

Semi-parametric joint detection and estimation for speech enhancement based on minimum mean square error

We propose a novel estimator for estimating the amplitude of speech coefficients in the time-frequency domain. In order to avoid a phase spectrum estimator of complex coefficients when using the Fourier transform, we consider the discrete cosine transform (DCT). This estimator aims at minimizing the mean square error of the absolute values of the speech DCT coefficients. In order to take advantage of both parametric and non-parametric approaches, the proposed method combines block shrinkage and Bayesian statistical estimation. First, the absolute value of the clean coefficient is estimated by block smoothed sigmoid-based shrinkage (Block-SSBS). The block size required by the Block-SSBS is obtained by statistical optimization. This step enables us to reduce the negative impact on speech intelligibility of classical denoising methods similarly to smoothed binary masking. Second, for refining the estimation, an optimal statistical estimator is added to handle musical noise. For evaluating the performance of the proposed method, objective criteria are used. The experiments enhance the relevance of the approach, in terms of speech quality and intelligibility.

Classification of natural circulation two-phase flow image patterns based on self-organizing maps of full frame DCT coefficients

Many of the recent nuclear power plant projects use natural circulation as heat removal mechanism. The accuracy of heat transfer parameters estimation has been improved through models that require precise prediction of two-phase flow pattern transitions. Image patterns of natural circulation instabilities were used to construct an automated classification system based on Self-Organizing Maps (SOMs). The system is used to investigate the more appropriate image features to obtain classification success. An efficient automated classification system based on image features can enable better and faster experimental procedures on two-phase flow phenomena studies. A comparison with a previous fuzzy inference study was foreseen to obtain classification power improvements.In the present work, frequency domain image features were used to characterize three different natural circulation two-phase flow instability stages to serve as input to a SOM clustering algorithm. Full-Frame Discrete Cosine Transform (FFDCT) coefficients were obtained for 32 image samples for each instability stage and were organized as input database for SOM training. A systematic training/test methodology was used to verify the classification method. Image database was obtained from two-phase flow experiments performed on the Natural Circulation Facility (NCF) at Instituto de Pesquisas Energéticas e Nucleares (IPEN/CNEN), Brazil.A mean right classification rate of 88.75% was obtained for SOMs trained with 50% of database. A mean right classificationrate of 93.98% was obtained for SOMs trained with 75% of data. These mean rates were obtained through 1000 different randomly sampled training data. FFDCT proved to be a very efficient and compact image feature to improve image-based classification systems. Fuzzy inference showed to be more flexible and able to adapt to simpler statistical features from only one image profile. FFDCT features resulted in more precise results when applied to a SOM neural network, though had to be applied to the full original grayscale matrix for all flow images to be classified.

JPEG image width estimation for file carving

Image width is an important factor for making the partially recovered data perceptually meaningful in image file carving. The authors conduct a comprehensive comparison of the performance of the representative methods for estimating the JPEG image width. Experimental results show that the best methods based on pixels are always better than the best methods based on quantised discrete cosine transform (DCT) coefficients. To keep the good performance of the pixel-based methods when the correct quantisation tables are unavailable, the authors replace the correct quantisation tables with the standard ones. Experimental results certify that such a replacement has only a little effect on the performance of the pixel-based methods, the best of which still outperform the best methods based on quantised DCT coefficients. The two results indicate that it may be enough to just focus on the pixel-based methods for future work. Finally, they propose a pixel-based method, which derives the candidate image widths from the most likely adjacent minimum coded unit (MCU) pairs in the vertical direction. The candidate width which appears most frequently is chosen as the estimated image width. Experimental results show that the proposed method usually has the best performance when most MCUs of an image are recovered.

A novel reversible data hiding scheme with two-dimensional histogram shifting mechanism

In this paper, we propose a novel reversible data hiding technique based on two-dimensional histogram shifting for quantized discrete cosine transformation coefficients (QDCT). In the proposed scheme, a two-dimensional histogram is constructed by QDCT coefficients blocks with the size of 8 × 8 of the left image and the right image. Once most of the QDCT coefficients are located at the top-right corner of the two-dimensional histogram, the QDCT coefficients are selected for embedding data to achieve high embedding capacity. In the embedding procedure, the three main steps, i.e., expanding, shifting, and embedding, are only used for QDCT coefficients in this corner not only to gain embedding capacity, but also to maintain good visual quality of stego images. The experimental results demonstrated that the proposed scheme is superior to the previous schemes in terms of embedding capacity and image quality.

An Analysis of Periodogram Based on a Discrete Cosine Transform for Spectrum Sensing

One of the complex problems nowadays in communication systems is the lack of frequency spectrum. To solve this problem, cognitive radio is considered the best candidate that can opportunistically exploit the spectrum. The periodogram based spectrum sensing technique can be used to detect the spectrum in cognitive radio. It is a useful technique since does not need to prior information about the primary signal. In this paper, a new periodogram is presented using the Discrete Cosine Transform (DCT). Results are analyzed and compared with the current raw periodogram. It is observed that the DCT periodogram outperforms the raw technique in terms of probabilities of false alarm and detection, variance, and complexity. In addition, the lowest power of DCT coefficients can be removed without compromising the sensing performance. The proposed system shows high probability of detection with low probability of false alarm even in the case of low Signal-to-Noise Ratio (SNR).

Adaptive Histogram Equalization Based Image Forensics Using Statistics of DC DCT Coefficients

The vulnerability of digital images is growing towards manipulation. This motivated an area of research to deal with digital image forgeries. The certifying origin and content of digital images is an open problem in the multimedia world. One of the ways to find the truth of images is finding the presence of any type of contrast enhancement. In this work, novel and simple machine learning tool is proposed to detect the presence of histogram equalization using statistical parameters of DC Discrete Cosine Transform (DCT) coefficients. The statistical parameters of the Gaussian Mixture Model (GMM) fitted to DC DCT coefficients are used as features for classifying original and histogram equalized images. An SVM classifier has been developed to classify original and histogram equalized image which can detect histogram equalized image with accuracy greater than 95% when false rate is less than 5%.

Dual image watermarking by exploiting the properties of selected DCT coefficients with JND modeling

The distinctive properties of partly sign-altered (PSA) coefficients in discrete cosine transform (DCT) domain are explored to achieve effective dual blind image watermarking. A host image is divided into non-overlapped blocks, each of which is then converted to a DCT representation separately. For each block, low-frequency DCT coefficients are selected for dual binary watermarking. The first binary bit is applied to the mean value of the PSA coefficients. Our formulation takes into account of human psychovisual characteristics. A stair-like quantization function is designed to not only regulate embedding strength but accommodate extra embedding for blocks with high contrast masking. In case second watermarking is requested, we tactically adjust the standard deviation of the PSA coefficients while keeping the PSA mean intact. The embedding strengths with respect to the involved parameters in the first and second watermarking are analytically examined. Experiment results indicate that the proposed scheme is capable of achieving excellent robustness at a peak signal-to-noise ratio (PSNR) around 38.7 dB. In particular, the exploitation of just noticeable distortion helps to enhance the robustness of the first watermark without causing noticeable quality degradation. The secondary watermark is embedded at the cost of approximately 1 dB PSNR. Yet the resultant performance is comparable with other compared methods in terms of bit error rates.

Reversible data hiding in JPEG image based on DCT frequency and block selection

The joint photographic experts group (JPEG) is the most popular format of digital image. In this paper, a novel reversible data hiding scheme based on JPEG image is proposed. In JPEG image, quantified DCT (discrete cosine transform) coefficients with different frequencies will yield different capacities and embedding distortions. To reduce the total distortion for the marked image, we select coefficients from frequencies yielding less distortions for embedding, and then an advanced block selection strategy is applied to always modify the block yielding less simulated distortion firstly until the given payloads are completely embedded. Experimental results show that the proposed method can keep good visual quality with small bitstream expansion.

Compression of signs of DCT coefficients for additional lossless compression of JPEG images

One of the main approaches to additional lossless compression of JPEG images is decoding of quantized values of discrete cosine transform (DCT) coefficients and further more effective recompression of the coefficients. Values of amplitudes of DCT coefficients are highly correlated and it is possible to effectively compress them. At the same time, signs of DCT coefficients, which occupy up to 20% of compressed image, are often considered unpredictable. In the paper, a new and effective method for compression of signs of quantized DCT coefficients is proposed. The proposed method takes into account both correlation between DCT coefficients of the same block and correlation between DCT coefficients of neighbor blocks. For each of 64 DCT coefficients, positions of 3 reference coefficients inside the block are determined and stored in the compressed file. Four reference coefficients with fixed positions are used from the neighbor blocks. For all reference coefficients, 15 frequency models to predict signs of a given coefficient are used. All 7 probabilities (that the sign is negative) are mixed by logistic mixing. For test set of JPEG images, we show that the proposed method allows compressing signs of DCT coefficients by 1.1 ... 1.3 times, significantly outperforming nearest analogues.

Blind estimation of white Gaussian noise variance in highly textured images

In the paper, a new method of blind estimation of noise variance in a single highly textured image is proposed. An input image is divided into 8x8 blocks and discrete cosine transform (DCT) is performed for each block. A part of 64 DCT coefficients with lowest energy calculated through all blocks is selected for further analysis. For the DCT coefficients, a robust estimate of noise variance is calculated. Corresponding to the obtained estimate, a part of blocks having very large values of local variance calculated only for the selected DCT coefficients are excluded from the further analysis. These two steps (estimation of noise variance and exclusion of blocks) are iteratively repeated three times. For the verification of the proposed method, a new noise-free test image database TAMPERE17 consisting of many highly textured images is designed. It is shown for this database and different values of noise variance from the set {25, 49, 100, 225}, that the proposed method provides approximately two times lower estimation root mean square error than other methods.

Multiple Watermarking for Healthcare Applications

AbstractIn this paper, an algorithm for multiple digital watermarking based on discrete wavelet transform (DWT), discrete cosine transform (DCT), and singular value decomposition (SVD) was proposed for healthcare applications such as tele-ophthalmology, tele-medicine, tele-diagnosis, and tele-consultancy services. Multiple watermarks were used in this algorithm to reduce the consequences of medical identity thefts. In the embedding process, the cover medical image was decomposed into third-level DWT. Low-frequency bands (LH2 and LL3) were transformed by DCT, and then SVD was applied to DCT coefficients. Two watermarks in the form of images were also transformed by DCT and then SVD. The singular values of the watermark information were embedded in the singular value of the cover medical image. Watermarks were extracted using an extraction algorithm. In order to enhance the robustness performance of the image watermarks, back-propagation neural network was applied to the extracted watermarks to reduce the effects of different noise applied on the watermarked image. Results were obtained by varying the gain factor and the different cover image modalities. Experimental results were provided to illustrate that the proposed method is able to withstand a variety of signal processing attacks, and has been found to give excellent performance in terms of robustness and imperceptibility. The performance of the method was also compared with other reported techniques. Further, the visual quality of the proposed method was also evaluated by a subjective method.

Color image interpolation in the DCT domain using a wavelet-based differential value

We propose a new image-interpolation technique using a combination of an adaptive directional wavelet transform (ADWT) and discrete cosine transform (DCT). In the proposed method, we use ADWT to decompose the low-resolution image into different frequency subband images. The high-frequency subband images are further transformed to DCT coefficients, and the zero-padding method is used for interpolation. Simultaneously, the low-frequency subband image is replaced by the original low-resolution image. Finally, we generate the interpolated image by combining the original low-resoultion image and the interpolated subband images by using inverse DWT. Experimental results demonstrate that the proposed algorithm yields better quality images in terms of subjective and objective quality metrics compared to the other methods considered in this paper.