2D Discrete Cosine Transform Research Articles

A High-Performance Method Based on Features Fusion of EEG Brain Signal and MRI-Imaging Data for Epilepsy Classification

Abstract A 1-dimensional (1D) and 2-dimensional (2D) biomedical signal analysis based on the Discrete Cosine Transform (DCT) feature extraction method was performed to diagnose epilepsy disorders with high accuracy. For this purpose, Electroencephalogram (EEG) data were used for 1D signal analysis and Magnetic Resonance Imaging (MRI) data were used for 2D signal analysis. The feature vectors were obtained by applying 1D DCT together with statistical methods such as mean, variance, standard deviation, kurtosis, and skewness for EEG data and by applying 2D DCT together with the statistical method of mean for MRI data. The most useful features were selected by applying Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Forward Selection and Backward Selection methods to the obtained feature vectors. Using EEG stand-alone features, MRI stand-alone features and EEG-MRI fused features, the classification of healthy and epileptic subjects was performed in the form of two clusters. The result of epilepsy classification in this work is 96% success of 1D EEG data by using the features selected by the PCA method, 94% success of 2D MRI data using the selected features by applying the Forward Method, 100% classification accuracy of 1D EEG and 2D MRI datasets by LDA method using the obtained fused features . The article shows that the fused features of EEG-MRI can be used very effectively for the diagnosis of epilepsy.

FECAM: Frequency enhanced channel attention mechanism for time series forecasting

Time series forecasting (TSF) is a challenging problem in various real-world scenarios, such as industry, energy, weather, traffic, economics, and earthquake warning. TSF demands the model to have a high prediction accuracy. Despite the promising performance of deep learning-based methods in TSF tasks, mainstream forecasting models may sometimes produce results that deviate from the actual ground truth. Our analysis suggests that this may be attributed to the models’ limited ability to capture the frequency information that is abundantly present in real-world datasets. Currently, the Fourier Transform (FT) is the most widely used method for extracting frequency information, but it has some issues that lead to poor model performance, such as high-frequency noise caused by the Gibbs phenomenon and computational overhead of the inverse transformation in the FT-IFT process. To address these issues, we propose a novel frequency enhanced channel attention mechanism (FECAM) that models frequency interdependencies between channels based on Discrete Cosine Transform (DCT), which inherently mitigates the high-frequency noise caused by problematic periodicity during Fourier Transform. This approach improves the model’s capability to extract frequency features and resolves computational overhead concerns that arise from inverse transformations. Our contributions are threefold: (1) We propose a novel frequency enhanced channel attention mechanism that models frequency interdependencies between channels based on DCT, which improves the model’s capability to extract frequency features and resolves computational overhead concerns that arise from inverse transformations; (2) We theoretically prove that our method mitigates the Gibbs phenomenon, which introduces high frequency noise during Fourier Transform. We demonstrate that the result of 1D GAP linearly varies with the lowest frequency component of 1D DCT; (3) We demonstrate the generalization ability of the proposed method FECAM by embedding it into other networks, resulting in significant performance improvements when compared to the original model, with only a minor increase in parameters. Furthermore, we conduct extensive experiments on six different real-world TSF datasets to validate the effectiveness of our proposed model and compare it with several existing state-of-the-art models. Our findings indicate that the FECAM model is superior to these models in terms of accuracy, making it a promising solution for TSF in diverse real-world scenarios. Our codes and data are available at https://github.com/Zero-coder/FECAM.

A Novel ASIC Implementation of Two-Dimensional Image Compression Using Improved B.G. Lee Algorithm

A 2D Discrete Cosine Transform and Inverse Discrete Cosine Transform using the B.G. Lee algorithm, incorporating a signed error-tolerant adder for additions, and a signed low-power fixed-point multiplier to perform multiplications are proposed and designed in this research. A novel Application Specific Integrated Circuit hardware implementation is used for the 2D DCT/IDCT computation of each 8 × 8 image block by optimizing the input data using the concepts of pipelining. An enhanced speed in processing and optimized arithmetic computations was observed due to the eight-stage pipeline architecture. The 2D DCT/IDCT of each 8 × 8 image segment can be quickly processed in 34 clock cycles with a substantially reduced level of circuit complexity. The B.G. Lee algorithm has been implemented using signed error-tolerant adders, signed fixed-point multipliers, and shifters, reducing computational complexity, power, and area. The Cadence Genus tool synthesized the proposed architecture with gpdk-90 nm and gpdk-45 nm technology libraries. The proposed method showed a significant reduction of 31.01%, 12.17%, and 21.11% in power, area, and PDP in comparison to the existing image compression architectures. An improved PSNR of the reconstructed image was also achieved compared to existing designs.

A novel triple-image encryption and hiding algorithm based on chaos, compressive sensing and 3D DCT

In this paper, a novel triple-image encryption and hiding algorithm is proposed by combining a 2D chaotic system, compressive sensing (CS) and the 3D discrete cosine transform (DCT). First, three grayscale plain images are sparsely represented by the 2D discrete wavelet transform (DWT). The resulting sparse matrices are scrambled twice through index sort scrambling and 3D zigzag scrambling. Then, the measurement matrix generated by the 2D chaotic system is used to compress the scrambled matrices. Finally, the compressed matrices are embedded into a color carrier image using the 3D DCT to obtain a visually meaningful cipher image. It is worth mentioning that most of the existing meaningful encryption algorithms encrypt and embed single images, which cannot meet the requirements of the era of big data. However, in our scheme, three grayscale images are simultaneously encrypted and embedded into a single color carrier image, which, when compared with existing algorithms, greatly improves the encryption efficiency. Moreover, simulation experiments and contrastive analyses show that the proposed visual encryption scheme has excellent visual security, robustness, decryption quality and running efficiency.

3D DCT Based Image Compression Method for the Medical Endoscopic Application.

This paper proposes a novel 3D discrete cosine transform (DCT) based image compression method for medical endoscopic applications. Due to the high correlation among color components of wireless capsule endoscopy (WCE) images, the original 2D Bayer data pattern is reconstructed into a new 3D data pattern, and 3D DCT is adopted to compress the 3D data for high compression ratio and high quality. For the low computational complexity of 3D-DCT, an optimized 4-point DCT butterfly structure without multiplication operation is proposed. Due to the unique characteristics of the 3D data pattern, the quantization and zigzag scan are ameliorated. To further improve the visual quality of decompressed images, a frequency-domain filter is proposed to eliminate the blocking artifacts adaptively. Experiments show that our method attains an average compression ratio (CR) of 22.94:1 with the peak signal to noise ratio (PSNR) of 40.73 dB, which outperforms state-of-the-art methods.

Area-Time Efficient Two-Dimensional Reconfigurable Integer DCT Architecture for HEVC

In this paper, we present area-time efficient reconfigurable architectures for the implementation of the integer discrete cosine transform (DCT), which supports all the transform lengths to be used in High Efficiency Video Coding (HEVC). We propose three 1D reconfigurable architectures that can be configured for the computation of the DCT of any of the prescribed lengths such as 4, 8, 16, and 32. It is shown that matrix multiplication schemes involving fewer adders can be used to derive parallel architectures for 1D integer DCT of different lengths. A novel transposition buffer is designed to be used for the proposed 2D DCT architecture, which offers double the throughput without increasing the size of the transposition buffer. We determine the optimal pipeline locations in the proposed design through the precise estimation of propagation delays and the critical path so that the area-delay-product is optimized and all the output samples are obtained in the same cycle in spite of the recursive nature of the structure. Implementation results show that the proposed 2D integer DCT architectures provide significantly higher throughput per unit area than the existing designs for HEVC.

Real-Time Full-Chip Thermal Tracking: A Post-Silicon, Machine Learning Perspective

This article presents a novel approach to real-time tracking of full-chip heatmaps for off-the-shelf microprocessors based on machine-learning. The proposed post-silicon approach, named RealMaps, only uses the existing temperature sensors and workload-independent utilization information. RealMaps does not require any knowledge of the proprietary design or manufacturing process-specific details of the chip. Consequently, the methods presented in this work can be implemented by either the original chip manufacturer or a third party alike. The approach involves offline acquisition of spatial heatmaps using a thermal imaging setup. To build the dynamic thermal model, a temporal-aware long-short-term-memory neutral network is trained with system-level features as inputs. 2D discrete cosine transformation (DCT) is performed on the heatmaps so that they can be expressed with just a few dominant DCT coefficients. This allows the model to be built to estimate just the dominant spatial features of the heatmaps, rather than the entire heatmap images, making it significantly more efficient. Experimental results from two commercial chips show that RealMaps can estimate the full-chip heatmaps with 0.9C and 1.2C root-mean-square-error respectively and take only 0.4ms for each inference. Compared to the state of the art pre-silicon approach, RealMaps shows similar accuracy, but with much less computational cost.

DVCast: denoising and variable dct for analog visual communications

Recently, analog visual transmission has attracted considerable attention owing to its graceful performance degradation for various wireless channels. In this study, we propose a novel analog visual communications system, named DVCast, in which an image denoising algorithm is used to fully utilize spatial correlation; moreover, the variable block size Discrete Cosine Transform (DCT) is used to preserve more correlation information in an image. Obviously, there is a tradeoff between system performance and computing complexity. Therefore, to improve the real-time performance of the proposed system, implementation of Block Matching with 3D filtering (BM3D) and DCT by Graphics Processing Units (GPUs) is introduced. According to DCT block size, i.e., 8×8, 16×16, and 32×32, the schemes DVCast8, DVCast16, and DVCast32, respectively, are designed and implemented. Simulations show that DVCast with larger block size achieves better gain and visual quality than reference schemes. Moreover, it requires less computing time. DVCast32 outperforms conventional digital schemes by approximately 3.51 ​dB and achieves a 1.12 ​dB gain over state-of-the-art reference schemes. Furthermore, the analysis shows that DVCast can reduce overhead by at least 75%.

Quality controlled ECG data compression based on 2D discrete cosine coefficient filtering and iterative JPEG2000 encoding

This paper presents a quality controlled reconstruction of ECG signal by the formulation of 2D Discrete Cosine Transform (DCT) coefficient and iterative JPEG2000 encoding scheme for Electrocardiogram (ECG) data compression. It employs variable blockwise (L = 32 to 2048 samples) DCT to exploit inter and intra-beat correlation inherent in ECG. The Regula-Falsi method is applied to obtain the optimal threshold for the DCT coefficients, which are stacked row-wise in order to form a 2D DCT coefficient array for the correlation analysis. Afterwards, window-based filtering is applied to retain the significant DCT coefficients with varying window size (ws). Differential pulse code modulation based quantization scheme is then applied to 2D DCT coefficients array in order to make it conformal to JPEG2000 encoding. Finally, iterative JPEG2000 encoding is utilized for achieving the overall predefined reconstruction error. The experimentations were performed on all the 48 records of Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) arrhythmia database. The proposed method provides compression ratio = 39.48 & 40.18; percentage root mean square difference = 2.02 & 2.06 and the quality score = 19.45 & 19.56 at ws = 50% & 20% respectively for L = 256. The proposed technique results were also validated on all records of four standard ECG databases including i) MIT-BIH Normal sinus rhythm ii) CU ventricular tachyarrhythmia iii) CSE and iv) PTB Database. Further, a comparative analysis between the proposed method and some recent existing works was also performed. The results clearly demonstrate the superiority of proposed method.

Improved Low-Power Cost-Effective DCT Implementation Based on Markov Random Field and Stochastic Logic

Discrete Cosine Transform (DCT) is a commonly used building block for image and video compression. In this article, we present a Markov Random Field (MRF)-based design for DCT implementation because MRF logic gates outperform standard non-MRF units by achieving high noise immunity for applications to logic-based computing systems in deep sub-micron condition. Furthermore, it is found that stochastic logic, a low-cost form of number representation, can also efficiently simplify computations. By combining these two techniques, we present an improved DCT hardware circuit. The example eight-point one-dimensional DCT (1D DCT) system is simulated using 65 nm CMOS technology. Simulation results show that the proposed MRF design can achieve 13% higher noise immunity and 47% area saving, compared with the typical stochastic 1D DCT using classical Master-and-Slave architecture. While achieving the same error rate of 0.21, power consumption is reduced by 52%.

High compressive ghost imaging method based on discrete cosine transform using weight coefficient matching

ABSTRACTGhost imaging can capture a scene without directly catching sight of the target, but in the case of high compression ratio, high-quality imaging is challenging at present. Here a ghost imaging method using weight coefficient matching based on discrete cosine transform (DCT) is proposed, in which the high-quality target images can be retrieved by obtaining the larger weight value in one-dimensional (1D) DCT spectrum. In the case of low sampling, the proposed method can not only acquire the spectral coefficients with large weight, but also put them in the correct position; eventually it can obtain the desired image by inverse discrete cosine transform of the spectrum. At the same sampling ratio, both simulation results and optical experiments show that the reconstructed image quality of the proposed method exhibits better performance. In addition, even the sampling ratio is as low as about 3%, the outline of the target image can still be roughly recognized.

Hardware Efficient Architecture for 2D DCT and IDCT Using Taylor-Series Expansion of Trigonometric Functions

This paper presents a hardware architecture for 8 x 8 2D Discrete Cosine Transform (DCT) and Inverse DCT (IDCT) using Taylor-series expansion of trigonometric functions. The processing of DCT/IDCT is modified to eliminate the need for: 1) partitioning the input image into fixed-size blocks and 2) use of transpose buffer for storing intermediate results, achieving low clock cycle time compared to existing techniques. The values obtained from Taylor-series are approximated by fixed-point numbers that reduce the hardware complexity at the cost of acceptable loss in quality of the output image. Based on the fixed-point approach, 18-bit, 24-bit, and 32-bit DCT and IDCT architectures are proposed. This DCT architecture considers the implementation of all 64 coefficients and hence, it is named as DCT64. An important observation about 2D DCT is that most of the compaction energy is concentrated on the low-frequency DCT coefficients which are sufficient to reconstruct the original image. Taking this point into consideration, three DCT architectures, namely, DCT15, DCT10, and DCT6 with 15, 10, and 6 coefficients are designed which are compared with the DCT64. The percentage improvement in the area and performance utilization is obtained for DCT15, DCT10, and DCT6 against DCT64. A gradual increase in the percentage is observed from DCT15 through DCT6 with a marginal decline in the quality of the output image at each step which can be seen from the measured PSNR and SSIM values. Regarding IDCT, the proposed architecture achieved a low percentage of area utilization and similar performance to that of the DCT. The field-programmable gate array (FPGA) implementation of the proposed DCT architecture operates at a higher frequency, achieving lower values of dynamic power, slice reg, slice LUTs metrics that outperforms the processing capabilities of existing Algebraic Integer (AI) and fixed-point implementations.

Reserved Discrete Cosine Transform Coefficients Effects on Image Compression

Discrete Cosine Transform (DCT) is a special case of Discrete Fourier Transform (DFT) in which the sine component has been eliminated leaving only the cosine terms. DCT packing the energy into few numbers of transformed coefficients associated with low frequencies, the high frequency coefficients are discarded and replaced by zero coefficients. These coefficients may be discarded with little loss in energy and that will not effect that much on the image quality since the human eye doesn’t sense the high frequency components. The discarding process provides a trade-off between compression ratio and peak signal to noise ratio. Simulation programs were written using MATLAB with three images each of them of size (256×256) with 256 grayscale levels. Each line of these images is divided into blocks and each block is considered as a row vector of 128 pixels. 1D DCT is applied to convert each vector of pixels into a vector of 128 transformed coefficients. When the number of retained useful low frequency coefficient is 30% and less, the reconstructed images shows a noticeable degradation at all, in spite of increasing compression ratio. Two performance measurements have been employed, namely the objective and subjective.

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.

Robust Template-Based Watermarking for DIBR 3D Images

Several depth image-based rendering (DIBR) watermarking methods have been proposed, but they have various drawbacks, such as non-blindness, low imperceptibility and vulnerability to signal or geometric distortion. This paper proposes a template-based DIBR watermarking method that overcomes the drawbacks of previous methods. The proposed method exploits two properties to resist DIBR attacks: the pixel is only moved horizontally by DIBR, and the smaller block is not distorted by DIBR. The one-dimensional (1D) discrete cosine transform (DCT) and curvelet domains are adopted to utilize these two properties. A template is inserted in the curvelet domain to restore the synchronization error caused by geometric distortion. A watermark is inserted in the 1D DCT domain to insert and detect a message from the DIBR image. Experimental results of the proposed method show high imperceptibility and robustness to various attacks, such as signal and geometric distortions. The proposed method is also robust to DIBR distortion and DIBR configuration adjustment, such as depth image preprocessing and baseline distance adjustment.

DESIGN AND IMPLEMENTATION OF A VHDL PROCESSOR FOR DCT BASED IMAGE COMPRESSION

This paper describes the design and implementation of a VHDL processor meant for performing 2D-Discrete Cosine Transform (DCT) to use in image compression applications. The design flow starts from the system specification to implementation on silicon and the entire process is carried out using an advanced workstation based design environment for digital signal processing. The software allows the bit-true analysis to ensure that the designed VLSI processor satisfies the required specifications. The bit-true analysis is performed on all levels of abstraction (behavior, VHDL etc.). The motivation behind the work is smaller size chip area, faster processing, reducing the cost of the chip

A two-stage algorithm for the early detection of zero-quantized discrete cosine transform coefficients in High Efficiency Video Coding

For High Efficiency Video Coding (HEVC) using block-based prediction, the discrete cosine transform (DCT), and quantization, a large number of DCT coefficients in a transform block (TB) are commonly found to be quantized to zero. A two-dimensional transform in HEVC is usually implemented by first applying a butterfly-based one-dimensional (1D) DCT to each row of the residual block, followed by a 1D DCT to each column. Accordingly, we propose a two-stage method for the early detection of zero-quantized DCT coefficients in this paper. In the first stage, a distribution-based method, which uses the sum of absolute differences as the threshold criterion and compares it to threshold values obtained for all columns, is employed to detect zero-quantized columns in the pixel domain prior to conducting the actual DCT. After conducting the 1D row DCT, the second detection stage, which uses the intermediate matrix resulting from the row transform as the input, is applied in the transform domain only to those columns predicted to contain non-zero coefficients. As an orthogonal transform, the 1D row DCT has a tendency to pack a large fraction of the signal energy into a relatively few coefficients. Therefore, the second stage of our algorithm is more effective than methods that conduct detection in the pixel domain, particularly for TBs greater than 8×8. Experimental results demonstrate that an HEVC encoder with our proposed two-stage algorithm can dramatically reduce unnecessary 1D row and column DCT operations compared with a standard encoder and therefore exhibits applicability to practical HEVC encoder implementation.

Low-Complexity Multidimensional DCT Approximations for High-Order Tensor Data Decorrelation.

In this paper, we introduce low-complexity multidimensional discrete cosine transform (DCT) approximations. 3D DCT approximations are formalized in terms of high-order tensor theory. The formulation is extended to higher dimensions with arbitrary lengths. Several multiplierless 8×8 ×8 approximate methods are proposed and the computational complexity is discussed for the general multidimensional case. The proposed methods complexity cost was assessed, presenting considerably lower arithmetic operations when compared with the exact 3D DCT. The proposed approximations were embedded into 3D DCT-based video coding scheme and a modified quantization step was introduced. The simulation results showed that the approximate 3D DCT coding methods offer almost identical output visual quality when compared with exact 3D DCT scheme. The proposed 3D approximations were also employed as a tool for visual tracking. The approximate 3D DCT-based proposed system performs similarly to the original exact 3D DCT-based method. In general, the suggested methods showed competitive performance at a considerably lower computational cost.

Comparison of Discrete Cosine Transforms (DCT), Discrete Fourier Transforms (DFT), and Discrete Wavelet Transforms (DWT) in Digital Image Watermarking

Digital Image Watermarking is used recently to secure the image by embedding another digital image. It is typically used to identify ownership of the copyright of the signal. Frequency domain transformation methods used widely in Digital Image Compression and Digital Image Watermarking. They reduce the weakness of classics digital image watermarking such as Least Significant Bit (LSB) methods which is more noise-tolerant. Popular transformation method used are Two Dimensional Discrete Cosine Transform (2D DCT), Two Dimensional Discrete Fourier Transforms (2D DFT), and Two Dimensional Discrete Wavelet Transform (2D DWT). This paper will show the comparison result of those three transformation method. The experiments are comparison analysis of image watermark quality using Peak Signal to Noise Ratio (PSNR), color converting, image resizing, image optical scanning and the noise-tolerant of the image watermarked by giving Gaussian noise.

A Fast DCT Algorithm for Watermarking in Digital Signal Processor

Discrete cosine transform (DCT) has been an international standard in Joint Photographic Experts Group (JPEG) format to reduce the blocking effect in digital image compression. This paper proposes a fast discrete cosine transform (FDCT) algorithm that utilizes the energy compactness and matrix sparseness properties in frequency domain to achieve higher computation performance. For a JPEG image of8×8block size in spatial domain, the algorithm decomposes the two-dimensional (2D) DCT into one pair of one-dimensional (1D) DCTs with transform computation in only 24 multiplications. The 2D spatial data is a linear combination of the base image obtained by the outer product of the column and row vectors of cosine functions so that inverse DCT is as efficient. Implementation of the FDCT algorithm shows that embedding a watermark image of 32 × 32 block pixel size in a 256 × 256 digital image can be completed in only 0.24 seconds and the extraction of watermark by inverse transform is within 0.21 seconds. The proposed FDCT algorithm is shown more efficient than many previous works in computation.