One-dimensional Discrete Cosine Transform Research Articles

Secure Electronic Commerce Transactions Using Pythagorean Triple-based Cryptography and Audio Steganography

The rapidly increasing utilization of Information Technology (IT) in electronic commerce and other aspects of human existence has led to a rise in worries about the privacy and safe-ty/security of those involved. Due to the alarmingly high frequency with which data or user privacy breaches occur today, conducting online transactions can represent a major threat to buyers (and even business owners') privacy. Existing solutions to these security issues are still vulnerable to classic phishing scams. As a result, the construction of a robust and effi-cient audio steganography system for secure electronic commerce transactions is presented in this work. The developed system first encrypts sensitive financial data using the Pythagorean Triple-based Cryptographic (PTC) algorithm, then compresses the resulting cipher-text using the Lempel Ziv Welch (LZW) and Huffman's Compression Algorithms, and finally embeds the compressed file (using one-dimensional Discrete Cosine Transform (DCT)) in a suitable audio-file cover to produce an output (stego file) that is indistinguishable from the cover file. This output can then be exchanged between communicating entities across open networks. The new system has a little or no alteration in its outputs, as evidenced by the Signal-to-Noise Ratio (SNR), in the experimental results gotten.

Development and Implementation of a Video Watermarking Method Based on DCT Transform

This paper presents a new color video watermarking technique based on the one-dimensional Discrete Cosine Transform (DCT). This approach uses a differential embedding technique to insert the bits of the watermark into the video frames so that the extraction process is blind and straightforward. To further ensure the security of the method, the binary image watermark is scrambled using Arnold transform before embedded into the video segment. Also, a color space transformation from Red, Green and Blue (RGB) to YUV is performed in order to deal with the color nature of the video segments. The proposed approach exhibits good robustness against a wide range of attacks such as video compression, cropping, Gaussian filtering, and noise adding. Finally, we propose an implementation of the video watermarking technique using the Raspberry Pi 3 platform. Nearly the same remarks may be made as in the simulation resultsconcerning the robustness against video compression attacks

Spectral and Energy Efficient Fast-OFDM With Index Modulation for Optical Wireless Systems

This letter introduces fast-orthogonal frequency-division multiplexing (FOFDM) with index modulation (IM) based on discrete cosine transform (DCT) for optical wireless systems. For intensity-modulation and direct detection, the proposed approach realizes a real-valued intensity waveform by employing real-valued one-dimensional modulation formats and DCT; and brings about non-negativity via direct current bias. We shall establish that it attains up to 64% higher spectral efficiency (SE) with low order alphabets than conventional IM based approach on discrete Fourier transform and provides better flexibility to address energy efficiency/SE trade-off.

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.

Geometrically robust video hashing based on ST-PCT for video copy detection

Copy videos flooding in the network infringe the video copyright and heavy the storage pressure on the video services server, which raises a huge demand for video copy detection techniques that can accurately and quickly detect the copies of video from huge video database. This paper aims to generate a video hash which has not only high discrimination but also robustness against geometrical and spatial-temporal transformations. First, we propose Spatial-Temporal Polar Cosine Transform (ST-PCT), which considers a video as a three-dimensional matrix and performs two-dimensional Polar Cosine Transforms (PCT) after performing a one-dimensional Discrete Cosine Transform (DCT) on video. This transformation can extract features of the spatial-temporal domain and has geometric invariance. Then, based on ST-PCT, we propose a geometrically robust video hashing method for video copy detection. The video features generated by ST-PCT are compressed and quantified to a compact binary hash code. Experimental results show that compared with the state-of-the-art methods, the proposed method has better robustness, higher accuracy, and faster calculation speed.

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.

An Improved Neigh Shrink in Hybrid Wavelet Transform for Image Compression

Rapid progress in mobile communication, demands high-speed multimedia data processing. This has lead the compression technology to speed up the process by reducing the size of data without disturbing image quality. This paper attempts to develop the quality of compression by using improved neigh shrink in hybrid wavelet algorithm to compress an image. After wavelet decomposition, one-dimensional Discrete Cosine Transform is applied to decorrelate approximate coefficients and stored as T-matrix. The detail coefficients are thresholded using ‘improved neigh shrink' and Eliminate Zero and Store Data algorithm are applied to eliminate redundancy and stored as reduced array. The compressed approximate and detailed coefficients are encoded by arithmetic coding. The simulated results show that proposed algorithm has significant improvement in image quality in terms of PSNR and SSIM when compared with existed wavelet-based compression methods including JPEG 2000 at high compression rate. Keywords: Discrete Wavelet Transform (DWT), T-matrix coding, improved Neigh Shrink, EZSD.

DCT and DST Based Image Compression for 3D Reconstruction

This paper introduces a new method for 2D image compression whose quality is demonstrated through accurate 3D reconstruction using structured light techniques and 3D reconstruction from multiple viewpoints. The method is based on two discrete transforms: (1) A one-dimensional Discrete Cosine Transform (DCT) is applied to each row of the image. (2) The output from the previous step is transformed again by a one-dimensional Discrete Sine Transform (DST), which is applied to each column of data generating new sets of high-frequency components followed by quantization of the higher frequencies. The output is then divided into two parts where the low-frequency components are compressed by arithmetic coding and the high frequency ones by an efficient minimization encoding algorithm. At decompression stage, a binary search algorithm is used to recover the original high frequency components. The technique is demonstrated by compressing 2D images up to 99% compression ratio. The decompressed images, which include images with structured light patterns for 3D reconstruction and from multiple viewpoints, are of high perceptual quality yielding accurate 3D reconstruction. Perceptual assessment and objective quality of compression are compared with JPEG and JPEG2000 through 2D and 3D RMSE. Results show that the proposed compression method is superior to both JPEG and JPEG2000 concerning 3D reconstruction, and with equivalent perceptual quality to JPEG2000.

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.

Area and Power Efficient VLSI Architecture for Two Dimensional 16-point Modified Gate Diffusion Input Discrete Cosine Transform

The two-dimensional (2D) Discrete Cosine Transform (DCT) is used widely in image and video processing systems. The perception of human visualization permits us to design approximate rather than exact DCT. In this paper, we propose a digital implementation of 16-point approximate 2D DCT architecture based on one-dimensional (1D) DCT and Modified Gate Diffusion Input (MGDI) technique. The 8-point 1D Approximate DCT architecture requires only 12 additions for realization in digital VLSI. Additions can be performed using the proposed 8 transistor (8T) MGDI Full Adder which reduces 2 transistors than the existing 10 transistor (10T) MGDI Full Adder. The Approximate MGDI 2D DCT using 8T MGDI Full adders is simulated in Tanner SPICE for 0.18㎛ CMOS process technology at 100MHZ.The simulation result shows that 13.9% of area and 15.08 % of power is reduced in the 8-point approximate 2D DCT, 10.63 % of area and 15.48% of power is reduced in case of 16-point approximate 2D DCT using 8 Transistor MGDI Full Adder than 10 Transistor MGDI Full Adder. The proposed architecture enhances results in terms of hardware complexity, regularity and modularity with a little compromise in accuracy.

CHEBINT

We present the fast approximation of multivariate functions based on Chebyshev series for two types of Chebyshev lattices and show how a fast Fourier transform (FFT) based discrete cosine transform (DCT) can be used to reduce the complexity of this operation. Approximating multivariate functions using rank-1 Chebyshev lattices can be seen as a one-dimensional DCT while a full-rank Chebyshev lattice leads to a multivariate DCT. We also present a MATLAB/Octave toolbox which uses this fast algorithms to approximate functions on a axis aligned hyper-rectangle. Given a certain accuracy of this approximation, interpolation of the original function can be achieved by evaluating the approximation while the definite integral over the domain can be estimated based on this Chebyshev approximation. We conclude with an example for both operations and actual timings of the two methods presented.

Zero‐quantised discrete cosine transform coefficients prediction technique for intra‐frame video encoding

One promising solution to reduce the computational complexity of discrete cosine transform (DCT) is to identify the redundant computations and to get rid of them. In this study, the authors present a new method to predict zero-quantised DCT coefficients for efficient implementation of intra-frame video encoding by identifying such redundant computations. Traditional methods use the Gaussian statistical model of residual pixels to predict all-zero or partial-zero blocks. The proposed method is based on two key ideas. At first, the bounds of DCT coefficients are derived from the intermediate signals of the Loeffler DCT algorithm instead of calculating the sum of absolute difference (SAD) of residual pixels. The sufficiency conditions are then suitably chosen to predict the zero-quantised coefficients to reduce the arithmetic complexity without degrading the video quality. Simulation results are found to validate the analytical model and show that the proposed prediction eliminates more redundant computations than the existing methods. Moreover, the authors have derived a pipelined VLSI architecture of the proposed prediction scheme which offers a saving of more than 63 and 91% of multiplications of the second stage of one-dimensional DCT for high and low bit-rate intra-video encoding, respectively.

Discrete cosine transform-analysis-based deblocking algorithm for block-transform compressed images

We propose a discrete cosine transform (DCT) analysis-based adaptive deblocking algorithm to reduce the block discontinuities. First we analyze the properties of the one-dimensional DCT coefficients. Based on this analysis, we utilize two adjacent vectors to classify the vector-containing block boundary into three models. For each model, we apply different filters according to the local properties. Comprehensive experiments indicate that the proposed method outperforms a large number of deblocking methods in the literature in terms of the evaluation of peak signal-to-noise ratio, perceptual quality, and computational complexity.

Low-power and high-quality Cordic-based Loeffler DCT for signal processing

A computationally efficient and high-quality preserving discrete cosine transform (DCT) architecture is presented. It is obtained by optimising the Loeffler DCT based on the coordinate rotation digital computer (Cordic) algorithm. The computational complexity is reduced significantly from 11 multiply and 29 add operations (Loeffler DCT) to 38 add and 16 shift operations (i.e. similar to the complexity of the binDCT) without losing quality. After synthesising with TSMC 0.13-mum technology library, Synopsys PrimePower was used to estimate the power consumption at gate-level. The experimental results show that the proposed 8-point one-dimensional DCT architecture only consumes 19% of the area and about 16% of the power of the original Loeffler DCT. Moreover, it also retains the good transformation quality of the original Loeffler DCT. In this regard, the proposed Cordic-based Loeffler DCT is very suitable for low-power and high-quality encoder/decoders (codecs) used in battery-based systems.

Inverse discrete cosine transform architecture exploiting sparseness and symmetry properties

In this paper, a novel architecture for two-dimensional (2-D) inverse discrete cosine transform (IDCT) is implemented using 90-nm CMOS technology. By exploiting the sparseness property of a 2-D discrete cosine transform (DCT) coefficient matrix and the even and odd symmetry properties of the basis vectors of the one-dimensional (I-D) DCT, the proposed architecture reduces computational complexity and increases a throughput rate effectively. First, we derive a recursion equation from the definition of the 2-D IDCT algorithm and use it to design an efficient 2-D IDCT architecture. The proposed architecture consisting of processing elements is suitable for very-large-scale-integration implementation due to its highly regular and scalable structure for 2-D N /spl times/ N IDCT computations. Based on the derived recursion equation, we show how data How for the outer products scaled by only nonzero 2-D DCT coefficients performs 2-D IDCT naturally with low complexities of the controller and the interconnection. The proposed architecture based on the recursion equation provides optimum balance in both hardware complexity and throughput rate when compared with other 2-D IDCT architectures.

Condensed recursive structures for computing multidimensional DCT/IDCT with arbitrary length

In this paper, efficient recursive structures for computing arbitrary length M-dimensional (M-D) discrete cosine transform (DCT) and its inverse DCT (IDCT) are proposed. The M-D DCT and IDCT are first converted into condensed one-dimensional (1-D) DCT and discrete sine transform (DST) with a regular preprocessing procedure. The recursive filters for condensed 1-D DCT/DST are then derived by using Chebyshev polynomials to compute M-D DCT/IDCT without data transposition. The proposed structures require fewer recursive loops than traditional 1-D recursive structures, which are realized in M passes and (M-1) data transposition by the so-called row-column approach. With advantages of fewer recursive loops and no transposition memory, the proposed structures attain more accurate results and less power consumption than traditional row-column structures. The proposed recursive M-D DCT/IDCT structures are suitable for very large-scale integration implementation due to regular and modular features.

Fast algorithms for multidimensional DCT-to-DCT computation between a block and its associated subblocks

In this paper, we first propose an efficient algorithm for computing one-dimensional (1-D) discrete cosine transform (DCT) for a signal block, given its two adjacent subblocks in the DCT domain and then introduce several algorithms for the fast computation of multidimensional (m-D) DCT with size N/sub 1//spl times/N/sub 2//spl times/.../spl times/N/sub m/ given 2/sup m/ subblocks of DCT coefficients with size N/sub 1//2/spl times/N/sub 2//2/spl times/.../spl times/N/sub m//2, where N/sub i/(i=1,2,...,m) are powers of 2. Obviously, the row-column method, which employs the most efficient algorithms along each dimension, reduces the computational complexity considerably, compared with the traditional method, which employs only the one-dimensional (1-D) fast DCT and inverse DCT (IDCT) algorithms. However, when m/spl ges/2, the traditional method, which employs the most efficient multidimensional DCT/IDCT algorithms, has lower computational complexity than the row-column method. Besides, we propose a direct method by dividing the data into 2/sup m/ parts for independent fast computation, in which only two steps of r-dimensional (r=1,2,...,m) IDCT and additional multiplications and additions are required. If all the dimensional sizes are the same, the number of multiplications required for the direct method is only (2/sup m/-1)/m2/sup m-1/ times of that required for the row-column method, and if N/spl ges/2/sup 2m-1/, the computational efficiency of the direct method is surely superior to that of the traditional method, which employs the most efficient multidimensional DCT/IDCT algorithms.

A memory-efficient realization of cyclic convolution and its application to discrete cosine transform

This paper presents a memory-efficient approach to realize the cyclic convolution and its application to the discrete cosine transform (DCT). We adopt the way of distributed arithmetic (DA) computation, exploit the symmetry property of DCT coefficients to merge the elements in the matrix of DCT kernel, separate the kernel to be two perfect cyclic forms, and partition the content of ROM into groups to facilitate an efficient realization of a one-dimensional (1-D) N-point DCT kernel using (N-1)/2 adders or subtractors, one small ROM module, a barrel shifter, and ((N-1)/2)+1 accumulators. The proposed memory-efficient design technique is characterized by rearranging the content of the ROM using the conventional DA approach into several groups such that all the elements in a group can be accessed simultaneously in accumulating all the DCT outputs for increasing the ROM utilization. Considering an example using 16-bit coefficients, the proposed design can save more than 57% of the delay-area product, as compare with the existing DA-based designs in the case of the 1-D seven-point DCT. Finally, a 1-D DCT chip was implemented to illustrate the efficiency associated with the proposed approach.

Two-dimensional DCT∕IDCT architecture

A fully parallel architecture for the computation of a two-dimensional (2-D) discrete cosine transform (DCT), based on row-column decomposition is presented. It uses the same one-dimensional (1-D) DCT unit for the row and column computations and (N2+N) registers to perform the transposition. It possesses features of regularity and modularity, and is thus well suited for VLSI implementation. It can be used for the computation of either the forward or the inverse 2-D DCT. Each 1-D DCT unit uses N fully parallel vector inner product (VIP) units. The design of the VIP units is based on a systematic design methodology using radix-2n arithmetic, which allows partitioning of the elements of each vector into small groups. Array multipliers without the final adder are used to produce the different partial product terms. This allows a more efficient use of 4:2 compressors for the accumulation of the products in the intermediate stages and reduces the number of accumulators from N to one. Using this procedure, the 2-D DCT architecture requires less than N2 multipliers (in terms of area occupied) and only 2N adders. It can compute a N×N-point DCT at a rate of one complete transform per N cycles after an appropriate initial delay.