A new fast algorithm for computing prime-Length DCT through cyclic convolutions

The cyclic convolution algorithms of chapter 6 are efficient for special small block lengths, but as the size of the block length increases, other methods are required. First as discussed in chapter 6, these algorithms keep the number of required multiplications small, but can require many additions. Also, each size requires a different algorithm. There is no uniform structure that can be repeatedly called upon. In this chapter, a technique similar to the Good-Thomas PFA will be developed to decompose a large size cyclic convolution into several small size cyclic convolutions which in turn can be evaluated using the Winograd cyclic convolution algorithm. These ideas were introduced by Agarwal and Cooley [1] in 1977. As in the Good-Thomas PFA, the CRT is used to define an indexing of data. This indexing changes a one-dimensional cyclic convolution into a two-dimensional cyclic convolution. We will see how to compute a two-dimensional cyclic convolution by ‘nesting’ a fast algorithm for one-dimensional cyclic convolution inside another fast algorithm for one-dimensional cyclic convolution. There are several two-dimensional cyclic convolution algorithms which although important will not be discussed. These can be found in [2].KeywordsDiscrete Fourier TransformFast AlgorithmPermutation MatrixCirculant MatrixConvolution TheoremThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This paper presents new fast full search motion estimation (ME) algorithms using discrete cosine transform (DCT) coefficients as a gradient magnitude. The proposed algorithms use intra DCT coefficients to arrange the matching scan order. The proposed algorithm 1 uses some of DCT coefficients based on the relationship between gradient magnitude and DCT coefficients, and the proposed algorithm 2 uses all of DCT alternating current (AC) coefficients in order to predict the fluctuation of a block. The proposed algorithms significantly reduce the computational complexity of the conventional algorithm while maintaining the visual quality of video.

This paper proposes a high performance and low cost inverse discrete cosine transform (IDCT) processor for high definition Television (HDTV) applications by using cyclic convolution and hardwired multipliers. By properly arranging the input sequence, we formulate the one-dimensional (1-D) IDCT into cyclic convolution that is regular and suitable for VLSI implementation. The hardwired multiplier that implements multiplication with IDCT coefficients are first scaled and optimized by using the common sub-expression techniques. Based on these techniques, the data-path in the proposed two-dimensional (2-D) IDCT design costs 7504 gates plus 1024 bits of memory with 100 M pixels/sec throughput according to the cost estimation based on the cell library of COMPASS 0.6 μm SPDM CMOS technology. Also, we have verified that the precision analysis of the proposed 2-D 8 × 8 IDCT meets the demands of IEEE Std. 1180-1990. Due to the good performance in the computing speed as well as the hardware cost, the proposed design is compact and suitable for HDTV applications. This design methodology can be applied to forward DCT as well as other transforms like discrete sine transform (DST), discrete Fourier transform (DFT), and discrete Hartley transform (DHT).

With the wide use of various image altering tools, digital image manipulation becomes very convenient and easy, which makes the detection of image originality and authenticity significant. Among various image tampering detection tools, double JPEG image compression detector, which is not sensitive to specific image tampering operation, has received large attention. In this paper, we propose an improved double JPEG compression detection method based on noise-free DCT (Discrete Cosine Transform) coefficients mixture histogram model. Specifically, we first extract the block-wise DCT coefficients histogram and eliminate the quantization noise which introduced by rounding and truncation operations. Then, for each DCT frequency, a posterior probability can be obtained by solving the DCT coefficients mixture histogram with a simplified model. Finally, the probabilities from all the DCT frequencies are accumulated to give the posterior probability of a DCT block being authentic or tampered. Extensive experimental results in both quantitative and qualitative terms prove the superiority of our proposed method when compared with the state-of-the-art methods.

Blocking artifacts exist in images and video sequences compressed to low bit rates using block discrete cosine transform (DCT) compression standards. In order to reduce blocking artifacts, a novel DCT domain technique is presented in this paper. Firstly, a new FIR Wiener filter which exploits the dependence of neighboring DCT coefficients based on the linear minimum mean-square-error (LMMSE) criterion is proposed. Then we apply the new FIR Wiener filter twice in a dual adaptive filtering structure to restore each quantized DCT coefficient. In addition, an efficient parameter estimation method is proposed for the designed filter. Experimental results show that the performance of the proposed method is comparable to the state-of-the-art methods but has low computational complexity.

In this paper, a new block matching criterion is proposed for motion estimation in video coding. The new criterion is based on a comparison between the discrete cosine transform (DCT) coefficients of two blocks to be matched. Since the spectrum of DCT statistically concentrates on the neighborhood of the dc component and the number of non-zero coefficients is quite small, only few coefficients need to be considered when matching blocks according to the new criterion. Almost in all the video coding standards, DCT is a necessary step for spatial redundancy reduction. Thus the generated DCT coefficients can be utilized in the new criterion. However, there are still some blocks whose DCT coefficients are not available. Several algorithms of calculating DCT coefficients of these blocks are given. When this new criterion is combined with the logarithm search, promising results are produced.

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.

It is already known that a curve estimated via the discrete cosine transform (DCT) always passes through all the measured points without using imaginary numbers in the DCT coefficients, unlike the discrete Fourier transform. Moreover, owing to its character, the DCT can be used instead of the nonlinear least-squares method to express various theoretical curves. Because the DCT is a kind of Fourier transform, there is a possibility that the DCT could be employed to draw electron density distribution maps of crystals. If so, the probability that the DCT could be used to investigate the internal structure of materials by analysing the theoretical curves would increase. This article reports an attempt to draw the electron density distribution maps of the Mg3BN3 low-pressure phase [Mg3BN3(L)] by using the DCT in order to confirm the utility of the DCT for analysing the internal structure of materials. It is found that the DCT can provide mirror-symmetric electron density distribution projection maps and a modified DCT can be used to calculate whole standard electron density distribution projection maps for the surface plane of the unit cell. Moreover, a real crystal structure that has a centre of symmetry can be determined by the DCT by transforming a 1/4 part of the mirror-symmetric electron density distribution projection map.

Integer Discrete Cosine Transform (DCT) reduces hardware complexity by eliminating floating point multiplication. Multiplier less multiple constant multiplication (MCM) is used to further optimize integer multiplication by replacing it with shifters and adders. As N-point DCT takes 25% of hardware complexity in high efficiency video coding (HEVC), further optimizing DCT in terms speed and power remains critical. Lately, an alternate real-valued DCT coefficients were proposed which reduced the amount of scaling used in Integer DCT coefficients. It achieved the low dynamic range, high speed and low power at same degree of approximation for DCT coefficients. In this paper, an effort is made to further approximate real-valued DCT coefficients of N-point DCT so that critical path due to MCM is reduced. Proposed approximate real-valued DCT coefficients has relatively good PSNR with optimized hardware compared to existing real-valued DCT coefficients. FPGA implementation of 1D-DCT architecture for 32-point DCT with approximate real-valued coefficients shows the reduction of 35% and 24% in area-delay product and power respectively.

This paper presents an efficient image cipher based on applying the chaotic Baker Map (BM) in the Discrete Cosine Transform (DCT). The encryption module of the proposed DCT-based BM image cipher employs a DCT on the original plain-image then, the DCT coefficients of the plain-image are shuffled with the BM. Finally, the inverse DCT is applied to the shuffled plain-image DCT coefficients to obtain the final cipher-image. The decryption module of the proposed DCT-based BM image cipher employs a DCT on the input cipher-image then, the DCT coefficients of the cipher-image are inversely shuffled with the BM. Finally, the inverse DCT is applied to the inversely shuffled cipher-image DCT coefficients to obtain the original plain-image. A set of experimental tests are performed to test the validity of the proposed DCT-based BM image cipher and the performed tests demonstrated the superiority of the proposed DCT-based BM image cipher in terms of statistical, differential, sensitivity and noise immunity.

Most of hybrid motion compensated video coding standards uses a well known discrete cosine transform (DCT) at the encoder to remove redundancy from video random processes. Due to the huge number of computations required to compute the DCT, reduction of its complexity is essential to speed up video processing. To optimize the computation of the DCT, we take into account the fact that the output of the DCT has often small values. The goal is not to compute DCT coefficients that will be quantized towards zero. This method of computing only a subset of DCT coefficients is commonly referred as pruning. In this paper we propose a method to perform the pruning of the two-dimensional (2-D) DCT based on the algorithm proposed in E. Feig and S. Winograd (1992) for any number of low-frequency components.

-With developing of computer networks and digital techniques, the electronic image are easily created, edited, reproduced and distributed. Unfortunately, illegal copy and malicious tamper are also facilitated. At present, fragile watermark is researched greatly to authenticate the veracity and integrity of electronic contents. In this paper, a chaotic watermarking scheme for authentication of popular JPEG images is proposed. The quantized DCT ( Discrete Cosine Transform ) coefficients after entropy decoding are mapped to the initial values of the chaotic system, then the generated watermark information by chaotic iteration is embedded into JPEG compressed domain. Thanks to the high sensitivity on initial values of the chaotic mapping, the very accurate localization is realized for the malicious tampers to JPEG images. Because we directly modify the DCT coefficients after quantization for embedding the watermark, the proposed method can prevent the invalidation of tamper detection by JPEG re-quantization. Furthermore, because the proposed scheme avoids a large of computation on full decoding and re-encoding process, the low complexity and a high extracting speed are obtained. Simulation results show the proposed scheme can directly localize the tampers happened on the watermarked JPEG images. Furthermore, the ability of tamper localization is very sensitivity. So the proposed scheme is very fit for the integrity authentication of the electronic image in Internet.

Proposed is an efficient face recognition algorithm using the discrete cosine transform DCT Technique for reducing dimensionality and image parameterization. These DCT coefficients are examined by a MLP (Multi-Layer Perceptron) and radial basis function RBF neural networks. Their purpose is to present a face recognition system that is a combination of discrete cosine transform (DCT) algorithm with a MLP and RBF neural networks. Neural networks have been widely applied in pattern recognition for the reason that neural-networks-based classifiers can incorporate both statistical and structural information and achieve better performance than the simple minimum distance classifiers. The authors demonstrate experimentally that when DCT coefficients are fed into a back propagation neural network for classification, a high recognition rate can be achieved by using a very small proportion of transform coefficients. Comparison with other statistical methods like Principal component Analysis (PCA) and Linear Discriminant Analysis (LDA) is presented. Their face recognition system is tested on the computer vision science research projects and the ORL database.

Statistical Computation of Discrete Cosine Transform in Video Encoders

At recently, the most of the digital images are stored and transferred in their compressed format using discrete cosine transform (DCT)-based compression technique. DCT is one of the most important data compression technique due to the efforts from Joint Photographic Experts Group(JPEG). Blind steganalysis means how to detect the presence of the messages that are hidden using different types of steganography algorithms and has the ability to detect new unknown steganography algorithms. This paper presents blind steganalysis technique that can reliably detect the existence of messages hidden in JPEG files. In order to save the computation and memory cost, it is desirable to have image processing operations implemented directly in the DCT domain. The proposed method is based on extracting features directly from DCT domain through the analysis of differences between DCT coefficients before and after cropping. The extracted features are prepared as input to Support Vector Machine (SVM) to classify the image as stego (image that contain secret message) or clean (image that does not contain secret message). The experiments performed show that the proposed method yields better classification accuracy compared with other related works.