Discrete Cosine Research Articles

On Block g-Circulant Matrices with Discrete Cosine and Sine Transforms for Transformer-Based Translation Machine

On Block g-Circulant Matrices with Discrete Cosine and Sine Transforms for Transformer-Based Translation Machine

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.

Regression of the Rician Noise Level in 3D Magnetic Resonance Images from the Distribution of the First Significant Digit

This paper investigates the distribution characteristics of Fourier, discrete cosine, and discrete sine transform coefficients in T1 MRI images. This paper reveals their adherence to Benford’s law, characterized by a logarithmic distribution of first digits. The impact of Rician noise on the first digit distribution is examined, which causes deviations from the ideal distribution. A novel methodology is proposed for noise level estimation, employing metrics such as the Bhattacharyya distance, Kullback–Leibler divergence, total variation distance, Hellinger distance, and Jensen–Shannon divergence. Supervised learning techniques utilize these metrics as regressors. Evaluations on MRI scans from several datasets coming from a wide range of different acquisition devices of 1.5 T and 3 T, comprising hundreds of patients, validate the adherence of noiseless T1 MRI frequency domain coefficients to Benford’s law. Through rigorous experimentation, our methodology has demonstrated competitiveness with established noise estimation techniques, even surpassing them in numerous conducted experiments. This research empirically supports the application of Benford’s law in transforms, offering a reliable approach for noise estimation in denoising algorithms and advancing image quality assessment.

Fast Generalized Sliding Sinusoidal Transforms

Discrete cosine and sine transforms closely approximate the Karhunen–Loeve transform for first-order Markov stationary signals with high and low correlation coefficients, respectively. Discrete sinusoidal transforms can be used in data compression, digital filtering, spectral analysis and pattern recognition. Short-time transforms based on discrete sinusoidal transforms are suitable for the adaptive processing and time–frequency analysis of quasi-stationary data. The generalized sliding discrete transform is a type of short-time transform, that is, a fixed-length windowed transform that slides over a signal with an arbitrary integer step. In this paper, eight fast algorithms for calculating various sliding sinusoidal transforms based on a generalized solution of a second-order linear nonhomogeneous difference equation and pruned discrete sine transforms are proposed. The performances of the algorithms in terms of computational complexity and execution time were compared with those of recursive sliding and fast discrete sinusoidal algorithms. The low complexity of the proposed algorithms resulted in significant time savings.

Application of Principal Component Analysis to advancing digital phenotyping of plant disease in the context of limited memory for training data storage

Despite its widespread employment as a highly efficient dimensionality reduction technique, limited research has been carried out on the advantage of Principal Component Analysis (PCA)–based compression/reconstruction of image data to machine learning-based image classification performance and storage space optimization. To address this limitation, we designed a study in which we compared the performances of two Convolutional Neural Network-Random Forest Algorithm (CNN-RF) guava leaf image classification models developed using training data from a number of original guava leaf images contained in a predefined amount of storage space (on the one hand), and a number of PCA compressed/reconstructed guava leaf images contained in the same amount of storage space (on the other hand), on the basis of four criteria – Accuracy, F1-Score, Phi Coefficient and the Fowlkes–Mallows index. Our approach achieved a 1:100 image compression ratio (99.00% image compression) which was comparatively much better than previous results achieved using other algorithms like arithmetic coding (1:1.50), wavelet transform (90.00% image compression), and a combination of three transform-based techniques – Discrete Fourier (DFT), Discrete Wavelet (DWT) and Discrete Cosine (DCT) (1:22.50). From a subjective visual quality perspective, the PCA compressed/reconstructed guava leaf images presented almost no loss of image detail. Finally, the CNN-RF model developed using PCA compressed/reconstructed guava leaf images outperformed the CNN-RF model developed using original guava leaf images by 0.10% accuracy increase, 0.10 F1-Score increase, 0.18 Phi Coefficient increase and 0.09 Fowlkes–Mallows increase.

Methods for processing and use of thermal neutron scattering data in OpenMC

OpenMC, an open source Monte Carlo particle transport code, relies on its own nuclear data format that is based on the HDF5 file format. The Python API within OpenMC includes an openmc.data module, which handles generation of thermal scattering HDF5 libraries starting from either ACE or ENDF files. When starting from ENDF files, NJOY is automatically executed to produce intermediate ACE files. In most cases, the resulting HDF5 data is equivalent to that stored in an ACE file. For incoherent elastic scattering, however, a novel sampling method is derived from the double-differential cross section and can be used to preserve the true continuous angular distribution. In this case, the characteristic bound cross section and Debye–Waller integral are taken directly from an ENDF file. Testing on the H in ZrH evaluation from ENDF/B-VIII.0 has demonstrated how the new sampling method matches the true distribution whereas the traditional treatment based on discrete cosines can leaves significant gaps in the angular distribution.

A high-performance two-dimensional transform architecture of variable block sizes for the VVC standard.

The versatile video coding standard H.266/VVC release has been accompanied with various new contributions to improve the coding efficiency beyond the high-efficiency video coding (HEVC), particularly in the transformation process. The adaptive multiple transform (AMT) is one of the new tools that was introduced in the transform module. It involves five transform types from the discrete cosine transform/discrete sine transform families with larger block sizes. The DCT-II has a fast computing algorithm, while the DST-VII relies on a complex matrix multiplication. This has led to an additional computational complexity. The approximation of the DST-VII can be used for the transform optimization. At the hardware level, this method can provide a gain in power consumption, logic resources use and speed. In this paper, a unifed two-dimensional transform architecture that enables exact and approximate DST-VII computation of sizes 8times 8, 8times 16, 8times 32, 16times 8, 16times 16, 16times 32, 32times 8, 32times 16 and 32times 32 is proposed. The exact transform computation can be processed using either multipliers or the MCM algorithm, while the approximate transform computation is based on additions and bit-shifting operations. All the designs are implemented under the Arria 10 FPGA device. The synthesis results show that the proposed design implementing the approximate transform matrices is the most efficient method with only 4% of area consumption. It reduces the logic utilization by more than 65% compared to the multipliers-based exact transform design, while about 53% of hardware cost saving is obtained when compared to the MCM-based computation. Furthermore, the approximate-based 2D transform architecture can operate at 78 MHz allowing a real-time coding for 2K and 4K videos at 100 and 25 frames/s, respectively.

Implementation of Multidigit Multiplication Basing on Discrete Cosine and Sine Transforms

Introduction. The emergence of new parallel computing systems such as multi-core processors, clusters, distributed systems, due to the solution of various applications in different spheres. Among such problems are the calculation of systems of linear algebraic equations with the number of unknown 33-35 million, the calculation of nuclear reactor shells, modeling of physical and chemical processes, aerodynamics, hydrodynamics, information security, and so on. This greatly expands the use of multidigit arithmetic, due to the fact that ignoring rounding errors leads to the fact that sometimes computer solutions are obtained that do not correspond to the physical content. Multidigit multiplication operation is an integral part of the exponentiation by module operation, the speed of which determines the speed of asymmetric cryptographic software and hardware complexes. This paper presents algorithms for implementing the multiplication operation of two N-digit numbers based on discrete cosine and sine transforms (DCT and DST) by separating the calculation for the real and imaginary parts of the DFT. Calculation of DCT and DST at the expense of additional bit shifts, additions and subtractions reduces the algorithm complexity to linear complexity by the number of integer multiplication operations. The purpose of the article is to reduce the number of multiplication operations to speed up the execution time of the multiplication operation of two N-bit numbers based on discrete transforms. Reduce the number of complex multiplication operations. Reduce the overall computational complexity and find a modification in which the calculation steps will correspond to DCT, DSP, IDCT and IDST. Use the coefficients to take into account the rounding errors to exclude multiplication operations on calculating DCT, DST, IDCT and IDST. Results. The relationship between DCT, DST and DFT of a real signal is considered, which allows to separate calculations for real and imaginary parts of DFT of real signals. The computational complexity is reduced almost twice at the expense of use of DFT properties of real signals. It is shown that after optimization steps of the algorithm calculation correspond to DCT, DST, IDCT and IDST. Using additional coefficients, which allow to take into account rounding errors at each step so that all calculations use integers. An analysis of the choice of word length in the calculation is given. For each algorithm, examples of calculation are given. Tables of dependence of the minimum lengths of the coefficients on the length of the multidigit number and the length of the digit (in bits) are given. Conclusions. Multiplication algorithms of two N-digit numbers based on discrete cosine and sine transforms (DCT and DST) are presented in this paper. Separating the calculation for the real and imaginary parts of the DFT allows to reduce the number of multiplication operations by 33%. The use of additional coefficients and calculation of DCT, DST, IDCT, IDST at the expense of bit shifts, additions and subtractions reduces the complexity of the multiplication algorithm of two N-digit numbers to linear complexity by the number of simple integer multiplication operations. Based on comparative analysis, it is shown that the proposed method of multiplication based on DCT and DST using integers begins to exceed the Karatsuba method by the number of 32-bit multiplication operations when multiplying numbers, starting with a length of 4096 bits. Keywords: multidigit multiplication, multidigit arithmetic, asymmetric cryptography, discrete cosine transform, discrete sine transform, discrete Fourier transform, fast algorithm for Fourier calculation.

Modified algorithms for signal nonlinear trend detection

There is a problem of nonlinear (abrupt) signal trend detection in many digital signals processing practical applications. In particular, in the field of biomedical signals processing, the actual task is the elimination of abrupt signal baseline distortions caused by the patient's movements. For processing such signals containing edges and other discontinues, linear filtering based on discrete Fourier or cosine transforms leads to significant smoothing of a signal. Median type algorithms related to nonlinear stable (robust) filters are successfully applied for filtering such signals, in particular, high efficiency is provided by median hybrid filters with finite impulse response (FIR). The article considers simple algorithms of the class of FIR-median hybrid filters used for signal nonlinear trend detection. It is proposed to modify these algorithms by replacing the operation of finding the median of the data in the sliding filter window with the calculation of their myriad, as well as adding weights (number of duplications) to certain window elements. Statistical estimates of filter efficiency according to the mean square error (MSE) criterion for test signals like “step” and “ramp” edges, and triangular peak and parabola have been obtained. The high efficiency of the investigated nonlinear filters for the listed test signals types and the improvements achieved as a result of the proposed filter modifications are shown based on the analysis of the filter output signals and statistical estimates of their quality. Some examples of processing biomedical signals of electroencephalograms which illustrate good quality of noise suppression and signal abrupt changes preservation, and motion artifacts removal without large signal distortions are given.

Discrete cosine and sine transforms generalized to honeycomb lattice II. Zigzag boundaries

The discrete cosine and sine transforms are generalized to a triangular fragment of the honeycomb lattice with zigzag boundaries. The zigzag honeycomb point sets are constructed by subtracting the weight lattice from the refined root lattice points of the crystallographic root system A2. The two-variable (anti)symmetric orbit functions of the Weyl group of A2, discretized simultaneously on the triangular fragments of the root and weight lattices, induce a novel parametric family of zigzag extended Weyl and Hartley orbit functions. As specific linear combinations of the original orbit functions, the zigzag extended orbit functions retain the Neumann and Dirichlet boundary conditions. Three types of discrete complex Fourier–Weyl transforms and real-valued Hartley–Weyl transforms are detailed. The corresponding unitary transform matrices and interpolating behavior of the discrete transforms are exemplified.

Key-Frame Detection and Video Retrieval Based on DC Coefficient-Based Cosine Orthogonality and Multivariate Statistical Tests

This paper presents a method, which is developed based on the Discrete Cosine (DC) coefficient and multivariate parametric statistical tests, such as tests for equality of mean vectors and the covariance matrices. Background scenes and forefront objects are separated from the key-frame, and the salient features, such as colour and Gabor texture, are extracted from the background and forefront components. The extracted features are formulated as a feature vector. The feature vector is compared to that of the feature vector database, based on the statistical tests. First, the feature vectors are compared with respect to covariance. If the feature vector of the key-frame and the feature vector of the feature vector database pass the test, then the test for equality of mean vector is performed; otherwise, the testing process is stopped. If the feature vectors pass both tests, then it is inferred that the query key-frame represents the target video in the video database. Otherwise, it is concluded that the query key-frame not representing the video; and the proposed system takes the next feature vector for matching. The proposed method results in an average retrieval rate of 97.232%, 96.540%, and 96.641% for CC_WEB, UCF101, and our newly constructed database, respectively. Further, the mAP scores computed for each video datasets, which resulted in 0.807, 0.812, and 0.814 for CC_WEB, UCF101, and our newly constructed database, respectively. The output results obtained by the proposed method are comparable to the existing methods.

A fast and high frame rate adaptive beamforming using DCT‐based RF‐line recovery in line‐by‐line ultrasound imaging

AbstractUltrasound imaging is an important modality used in medical imaging. One of the significant stages in the ultrasound imaging is the beamforming process. This article proposes a new technique for reducing the overall computational time of adaptive linear ultrasound imaging. The method uses the discrete cosine transform‐based reconstruction for missing data imputation. The novelty of the paper is that we do not need to beam‐form the total scan lines, so the time of image construction can be saved significantly. In other words, a fraction of the total scan lines is selected for beamforming and the others are assumed to have values as Not‐a‐Number (NaN). The proposed reconstruction technique tries to assign appropriate values to the NaN ones. We applied the proposed method to the simulated and experimental radio frequency (RF) datasets for resolution and contrast evaluation. Results showed that the proposed technique is near to the minimum variance (MV) method in terms of resolution and contrast, and has less computational time for image formation compared to the MV. As some quantitative examples in some experiments we have formed only 50% and 33% of the total lines and reconstructed the rest, then we have been able to increase the frame rate twice and three times, respectively, which can be very useful in many applications, especially in echocardiography imaging. In addition, since the execution time of the reconstruction algorithm is not very significant, we were also able to increase the speed by two and three times while achieving an error of less than 10% compared to the case of using all image lines.

Anti-forensic approach for JPEG compressed images with enhanced image quality and forensic undetectability

Most of the detectors employed in digital image forensics are based on JPEG compression. To determine the capability of these forensic detectors, proficient anti-forensic techniques that challenge and help in the upgradation of forensic techniques are required. This paper proposes an anti-forensic technique based on the shifted block Discrete Fractional Cosine Transform (DFrCT) approach. Afterwards, Total variation (TV) -based deblocking operation is used in order to remove the compression blocking artifacts. Due to the shifted block approach, the proposed method performs histogram smoothing without adding any dithering signal, which means that it is capable of applying dithering by itself. Further, to remove blocking artifacts which are left during the JPEG compression TV-based deblocking is used. The DFrCT approach provides an additional fractional parameter to improve the accuracy of the proposed approach. The proposed scheme is evaluated based on the UCID dataset images by considering the scalar based and machine learning-based forensic detectors. It is observed from the experimental results that the proposed approach provides improved performance in terms of PSNR, SSIM, and forensic undetectability when compared to existing techniques. The analysis performed in this paper challenges the security and robustness of JPEG compression forensic techniques.

Artificial neural network applications for data compression in video data transfer protocols

The article describes the current state of data transfer protocols and methods of image and video compression through the use of artificial neural networks, namely convolutional multilayer networks and deep structured learning. Based on recent publications, a comparative analysis of the performance of classical compression methods and methods based on neural networks was performed. The most effective are those compression methods which are based on decorrelation transforms, namely discrete cosine (JPEG standard) and wavelet (JPEG-2000 standard) transforms. The transform coefficients have a well-understood physical content of spatial frequencies and can be further quantized for a more optimal representation of components that are less important for human perception. The HEVC standard guarantees a more efficient image compression scheme that further takes advantage of the similarity of adjacent blocks and uses interpolation (intracoding). Based on the HEVC standard, the BPG (better portable graphics) format was developed to be used on the Internet as an alternative to JPEG, which is much more efficient than other standards. An overview of the current state of open standards, provided in the article, gives an explanation of what properties of neural networks can be applied to image compression. There are two approaches towards the compression using neural networks: in case of the first approach neural network is used as a part of an existing algorithm (hybrid coding), and in case of the second approach the neural network gives a concise representation of the data (compression network). The final conclusions were made as regards to the application of these algorithms in H.265 protocol (HEVC) and the possibility of creating a new protocol which is completely based on the neural network. Protocols using neural network show better results during image compression, but are currently hard to be subjected to standardization in order to obtain the expected result in case of different network architects. We may expect and predict an increase in the need for video transmission in the future, which will bump into the imitating nature of classical approaches. At the same time, the development of specialized processors for parallel data processing and implementation of neural networks is currently underway. These two factors indicate that neural networks must be embedded into the industrial data standards.

Bacterial Foraging Optimization of Speech Coder for Software Defined Radio Application

The paper presents integration of Discrete Wavelet Cosine Transform technique and Bacterial Foraging Algorithm (BFO) for the development and optimization of speech coder. It is depicted how by filtering the limited number of high energy components of transformed coefficients with parallel programming can maintain the speech signal quality in coding over wide range of bit rates. The performance of existing and proposed speech coding techniqueattributes such as compression ratio, coding delay, computational complexity and quality of reconstructed speech is examined for multiple bit rates and compared with other existing speech coding techniques in Matlab environment. The result showsimprovement in performancewith respect to all attributes at the cost of increase in complexity.

An Efficient Image Steganography Approach over Wireless Communication System

This paper presents a robust color image steganography approach for image communication over wireless communication systems. The objective of this approach is to hide three color images in one color cover image to increase the capacity of hiding as most previously published steganography approaches suffer from a capacity problem. Moreover, the investigation of wireless communication of steganography images is presented in this paper to study the sensitivity of extraction of hidden images to the channel degradation effects, which is not studied appropriately in the literature. The proposed approach depends on the Discrete Cosine and Discrete Wavelet transform. The cover image is first transformed to luminance and chrominance components for embedding the images to be hidden. The secret images are encrypted by chaotic Baker map, which is a good representative of the family of permutation-based algorithms, which tolerate the channel degradations better. The investigated wireless communication system is the Orthogonal Frequency Division Multiplexing system with channel equalization. The simulation results reveal the success of the proposed work for robust image communication.

An asymmetric and optimized encryption method to protect the confidentiality of 3D mesh model

3D models are widely used in computer graphics, design and manufacture engineering, art animation and entertainment. With the universal of acquisition equipment and sensors, a huge number of 3D models are generated, which are becoming the major source of engineering data. How to preserve the privacy of the 3D models is a challenge issue. In this paper, an asymmetric and optimized encryption method is presented to protect the 3D mesh models. Firstly, we propose an asymmetric encryption method for 3D mesh models to overcome the drawbacks of traditional symmetric encryption. The primary benefit is that our approach can enhance the security of the key. Secondly, we extend the typically asymmetric encryption algorithm from integer domain to float domain. In our method, we present a normalization function to map the float DC (Discrete Cosine) coefficients to integer domain. Thirdly, considering that the shape error and encryption/decryption computation cost are contradictory in the normalization mapping, we formulate the contradiction as a multi-objective optimization problem. And then, we propose a multi-objective solution to find an optimized mapping range for encryption/decryption efficiently. Furthermore, benefiting from the proposed asymmetric encryption framework, we continue to put forward a method to check the integrity of the encrypted 3D mesh model, in which the digest is encrypted twice to generate digital signature more safely. The proposed method has been tested on 3D mesh models from Stanford university and other sources to demonstrate the effect of the proposed encryption method and optimization mechanism.

Enhanced Median Flow Tracker Based on Photometric Correction for Videos with Abrupt Changing Illumination

Object tracking is a fundamental task in video surveillance, human-computer interaction and activity analysis. One of the common challenges in visual object tracking is illumination variation. A large number of methods for tracking have been proposed over the recent years, and median flow tracker is one of them which can handle various challenges. Median flow tracker is designed to track an object using Lucas-Kanade optical flow method which is sensitive to illumination variation, hence fails when sudden illumination changes occur between the frames. In this paper, we propose an enhanced median flow tracker to achieve an illumination invariance to abruptly varying lighting conditions. In this approach, illumination variation is compensated by modifying the Discrete Cosine Transform (DCT) coefficients of an image in the logarithmic domain. The illumination variations are mainly reflected in the low-frequency coefficients of an image. Therefore, a fixed number of DCT coefficients are ignored. Moreover, the Discrete Cosine (DC) coefficient is maintained almost constant all through the video based on entropy difference to minimize the sudden variations of lighting impacts. In addition, each video frame is enhanced by employing pixel transformation technique that improves the contrast of dull images based on probability distribution of pixels. The proposed scheme can effectively handle the gradual and abrupt changes in the illumination of the object. The experiments are conducted on fast-changing illumination videos, and results show that the proposed method improves median flow tracker with outperforming accuracy compared to the state-of-the-art trackers

A vehicle detection scheme based on two-dimensional HOG features in the DFT and DCT domains

Histogram of oriented gradients (HOG) are often used as features for object detection in images, since they are robust to changes in illumination and environmental conditions. However, these features are not invariant to changes in the resolution of input images. A 2D representation of these features, referred to as 2DHOG features, has been used since it preserves the relations among the neighboring pixels or cells. In this paper, a new vehicle detection scheme using transform-domain 2DHOG features is proposed. The method is based on extracting the 2DHOG features from the input image and applying to it 2D discrete Fourier or cosine transform. This is followed by a truncation process through which only the low frequency coefficients, referred to as the transform-domain 2DHOG (TD2DHOG) features, are retained. It is shown that the TD2DHOG features obtained from an image at the original resolution and a downsampled version from the same image are approximately the same within a multiplicative factor. This property is then utilized in our scheme for the detection of vehicles of various resolutions using a single classifier rather than multiple resolution-specific classifiers. Experimental results show that the use of the single classifier in the proposed detection scheme reduces drastically the training and storage cost over the use of a classifier pyramid, yet providing a detection accuracy similar to that obtained using TD2DHOG features with a classifier pyramid. Furthermore, the proposed method provides a detection accuracy that is similar or even better than that provided by the state-of-the-art techniques.

Hardware Design and Implementation of Adaptive Multiple Transforms for the Versatile Video Coding Standard

Versatile video coding is the next generation video coding standard expected by the end of 2020. Several new contributions have been proposed to enhance the coding efficiency beyond the high efficiency video coding standard. One of these tools is the adaptive multiple transform (AMT) as a new approach of the transform core design. The AMT involves five discrete cosine transform/discrete sine transform types with larger and more flexible partitioning block sizes. However, the AMT coding efficiency comes with the cost of higher computational complexity, especially at the encoder side. In this paper, a efficient pipelined hardware implementation of the AMT including the five types of sizes $4\times 4$ , $8\times 8$ , $16\times 16$ and $32\times 32$ is proposed. The architecture design takes advantage of the internal software/hardware resources of the target field-programmable gate array device such as library of parametrized modules core intellectual properties and digital signal processing blocks. The proposed 1-D 32-point AMT design allows to process 4K video at 44 frames/s. A unified 2-D implementation of the 4, 8, 16, and 32-point AMT design is also presented.The implementation takes into account all the asymmetric 2-D block size combinations from 4 to 32. The 2-D architecture design is able to sustain 2K video coding at 50 frames/s with an operational frequency up to 147 MHz.