# DCT Algorithm

## Top PDF DCT Algorithm: ### Embedding and Extracting Digital Watermark Based on DCT Algorithm

The principle of digital watermark is the method of adding digital watermark in the frequency domain. The digital watermark hides the watermark in digi- tal media, such as image, voice, video, etc., so as to realize the functions of copyright protection, and identity recognition. DCT for Discrete Cosine Transform is used to transform the image pixel value and the frequency do- main coefficient matrix to realize the embedding and extracting of the blind watermark in the paper. After success, the image is attacked by white noise and Gaussian low-pass filtering. The result shows that the watermark signal embedded based on the DCT algorithm is relatively robust, and can effective- ly resist some attack methods that use signal distortion to destroy the water- mark, and has good robustness and imperceptibility. ### Design of a JPEG Compressor with an Efficient and Reconfigurable DCT Algorithm

The discrete cosine transform (DCT) is popularly used in image and video compression. Since the DCT is computationally intensive, several algorithms have been proposed in the literature to compute it efficiently –. Recently, significant work has been done to derive approximate of 8-point DCT for reducing the computational complexity –. The main objective of the approximation algorithms is to get rid of multiplications which consume most of the power and computation- time, and to obtain meaningful estimation of DCT as well. Haweel  has proposed the signed DCT (SDCT) for 8 8 blocks where the basis vector elements are replaced by their sign, i.e, 1. Bouguezel-Ahmad-Swamy (BAS) have proposed a series of methods. They have provided a good estimation of the DCT by replacing the basis vector elements by 0, 1/2, 1 . In the same vein, Bayer and Cintra ,  have proposed two transforms derived from 0 and 1 as elements of transform kernel, and have shown that their methods perform better than the method in , particularly for low- and high-compression ratio scenarios. ### Image In painting and Compression Using DCT Algorithm

JPEG is an abbreviation for ''Joint Photographic Experts Group'' . For its standard coding method the Discrete Cosine Transform (DCT) is utilized. The authors in  first confirmed that DCT in a general sense is the same to the KLH (Karhunen–loeve–hotelling) alter that performs a de-correlation course In light of the fact that each coefficient can be dealt separately without losing compression proficiency, de-correlation is essential for compression. Basically, the nxn 2-D version of DCT disintegrates a nxn block of an image into a set, each with a specific spatial frequency. Because of this, we can reduce the information not visible to the human eyes. The redundancies existing, are of the following types, 1.Coding Redundancy: Present when a smaller amount than optimal code words are used. 2.Interpixel Redundancy: results from correlations between the pixels of an picture 3.Psychovisual Redundancy: is due to data that is ignored by the human visual system (i.e. visually non essential information). ### Video Compression Using Hybrid DWT-DCT Algorithm

The Hybrid DWT-DCT transform exploits the properties of both the DWT and DCT techniques and provides a better compression. The input frame obtained from the video is first converted into 32*32 blocks. Each block is then transformed individually. The 32*32 block is converted into 16*16 after one level dwt and discarding all the coefficients except the LL (i.e. LH, HH, and HL). The second level of the 2 dimensional DWT is applied on the retained LL coefficients. And this yields an 8*8 block after discarding all the LH, HH, HL coefficients and preserving only LL. The DCT is applied on this block. After the transformation by DCT, quantization is applied on the DCT coefficients which rounds off the high frequency components to zero . The reconstruction can be performed by the reverse process i.e. first the inverse quantization is done and then the IDCT is performed which yields an 8*8 block. The first level IDWT gives a16*16 blocks and the second level of IDWT gives the 32*32 block. This process is applied for the entire image. ### Enlightenment capacity for Powerful Face Recognition mechanism Using DCT algorithm

The simulation results showed that the proposed algorithm performs better with the total transmission energy metric than the maximum number of hops metric. The proposed algorithm provides energy efficient path for data transmission and maximizes the lifetime of entire network.As the performance of the proposed algorithm is analyzed between two metrics in future with some modifications in design considerations the performance of the proposed algorithm can be compared with other energy efficient algorithm. We have used very small network of 5 nodes, as number of nodes increases the complexity will increase. We can increase the number of nodes and analyze the performance. ### Encrypted Domain DCT Based on Homomorphic Cryptosystems

1.1. Our Contributions. Solutions to the above issues will be provided in this paper, whose rest is organized as follows. In Section 2 a brief review of homomorphic cryptosystems, with particular attention to the Paillier scheme, is given. In order to properly represent the pixel values, the DCT coe ﬃ cients and the transformed values in the encrypted domain, a convenient s.p.e.d. signal model is proposed in Section 3. Such a model allows us to define in Section 4 both an s.p.e.d. DCT and an s.p.e.d. fast DCT and to extend them to the 2D case. The proposed representation permits also to avoid the use of interactive protocols, by letting the magnitude of the intermediate results propagates to the end of the processing chain. A solution to the problem of encrypting each pixel separately is proposed in Section 5. A block-based s.p.e.d. DCT, relying on a suitable composite representation of the encrypted pixels, permits the parallel application of the s.p.e.d. DCT algorithm to diﬀerent image blocks, thus lowering both the bandwidth usage and the computational burden. In Section 6 we consider the ### Review on Digital Watermarking Images

The methodology for digital water marking of images is proposed in . “Digital watermarking in the work presented was considered particularly on a satellite image by making use of the DCT algorithm after JPEG compression. By anticipating which coefficients will be modified by the succeeding transforms, it is possible to produce a watermarking method with good capacity, moderate robustness, and low visual impact. This method holds particularly true in the case of compression techniques, were the compression algorithms are well known. Additional work can be done as an enhancement of the single watermark to embed more than one watermark in a satellite image. The communication networks allows the widespread distribution of multimedia data in various ways because of its rapid growth. Since digital productions can be easily duplicated, encouraging illegal distribution of electronic documents and unauthorized cloning are issues that have to be resolved. This paper demonstrates a technique for digital watermarking using the Discrete Cosine Transform (DCT) Domain and for the purpose of authentication it introduces the use of pseudo random noise in watermarking to hide information. The underlying system is based on Code Division multiple Access (CDMA) is a form of spread spectrum communication. The main objectives are development of a watermark embedding strategy and the analysis of the results. A compression technique was considered as an image attack to perform the implemented approach. The proposed technique provided a robust watermark extraction and has been successfully tested on a simple satellite image”. In this methodology of digital water marking of images is proposed in . “This technique deals with medical image watermarking, we aimed at using the Error Correcting Code and the DCT space. On other side, to improve the message integrity and the ECC to increase the security ### Scaled Discrete Cosine Transform (DCT) using AAN Algorithm on FPGA

Discrete cosine transform (DCT's) are the most widely used transforms in the signal processing of digital image, video data, especially in the coding for compression algorithms. In video coding application applications, a two- dimensional DCT on small input sizes eight x eight is used. A digital unit called DCT soft core developed to perform the Discrete Cosine Transform (DCT). It performs two dimensional eight x eight point DCT for the period of 64 clock cycles in pipelined trending mode. Pipelined mode reduces the number of clock cycles required. To minimize the amount of calculations, the Arai, Agui, and Nakajama 8-point DCT algorithm is used. ### Design and Implementation of CORDIC-based 8-point 1D DCT

One such simple and hardware-efficient algorithm is CORDIC, an acronym for Coordinate Rotation Digital Computer, proposed by Jack E Volder . CORDIC uses only Shift-and Add arithmetic with table Look-Up to implement different functions. By making slight adjustments to the initial conditions and the LUT values, it can be used to efficiently implement Trigonometric, Hyperbolic, Exponential functions, Coordinate Transformations etc. using the same hardware. Since it uses only shift-add arithmetic, VLSI implementation of such an algorithm is easily achievable. DCT algorithm has diverse applications and is widely used for Image compression. Implementing DCT using CORDIC algorithm reduces the number of computations during processing, increases the accuracy of reconstruction of the image, and reduces the chip area of implementation of a processor built for this purpose. This reduces the overall power consumption. ### A Novel Video Encryption Technique for Real Time applications

Abstract- Various video encryption techniques are purposed to encrypt the videos and used for obtaining highly encrypted videos. In this paper, a method for encryption in video is taken place by using the Huffmann encryption algorithm. Instead of using the text or the images, the video encoding is taken place here. The video is converted into number of frames, which in turn converted to blocks used for encryption. The division of video resulted in images in turn this image is followed by encryption. The block cipher algorithm is used for converting frames to blocks. The DCT algorithm is used, because of its simplicity, efficient working syntax. ### A Digital Image Watermarking Algorithm Based on DWT DCT and SVD

spatial domain approaches, the watermark is embedded directly to the pixel locations , . Embedding the watermark in the spatial domain is the direct method. It has various advantages like less computational cost, high capacity, more perceptual quality but less robust and it mainly suits for authentication applications. In transform domain approaches, a mathematical transform is applied to the original image to embed watermark into the transform coefficients, then apply inverse transform to get the embedded image. It has more robust, less control of perceptual quality and mainly suits for copyright application. The most frequent used methods are discrete cosine transform (DCT) domain , , discrete wavelet transform (DWT) domain , singular value decomposition (SVD) domain . They now come into more widespread used as they always have good robustness to common image processing. ### Analysis on Domain based Method for Image Enhancement

First, an image is separated into illumination and reflectance components. Next, the illumination component is manipulated adaptively for image dynamics by using a content measure. The content measure using the energy distribution of the DCT coefficients is defined directly in each DCT block of an image. Then, the reflectance component is altered by a multi-scale α-rooting method for enhancing image details based on human visual perception. The expected advantages of the proposed scheme are: the algorithm processes fast because it operates directly on the compressed domain; It improves details in dark area and in bright area without any iteration over previous approaches; The algorithm does not affect the compressibility of the original image; and the proposed IE algorithm can be applied to any DCT-based image compression standard, such as JPEG, MPEG, and H.26X without any significant modification. In order to handle the enhancement of an image, the proposed algorithm employed a basic concept of Retinex theory and defined spectral control values according to the frequency bands of the image. Block dependent enhancement value based on the characteristics of image content was applied to DC and AC coefficient areas differently for image dynamics and details, respectively. ### A New DCT based Channel Estimation Algorithm for OFDM Systems

The performances of the existing and proposed methods are investigated through MATLAB simulation. An OFDMA system with N =64 subcarriers is considered. The guard interval is 24. A 4-path channel model is used. The symbols are modulated by 16QAM.The delay of the antenna is delay=(0, 1.5, 2.5, 3.5, 4.5)µs. Fig.1 shows the least squares estimation using linear and cubic spline interpolation methods. Fig.2 shows the estimated channel using conventional DCT based channel estimation. Using the estimated channel the data transmitted is extracted and the number of points at which the estimated data differed from the original transmitted data for 10000 iterations is calculated and the result is shown in table1. From table 1it can see that cubic spline interpolation method is better than the liner interpolation method and hence cubic spline interpolation method is used in further calculations. From table1 it can also been seen that when the DCT based method is used a better result obtained. Fig.3 shows the estimated channel using the improved DFT based method and table 2 shows the number of points at which the estimated data differ from the original transmitted data for 10000 iterations for the improved DFT based method. From table 2, it can see that as the leakage path increases the result of improved DFT based method becomes better. Fig.4 shows the estimated channel using the new DCT based method and corresponding result is shown in table3 which shows that for the same leakage path the new DCT based method is better than the improved DFT based method. Also it can be seen that as the leakage path number increases the performance of the new DCT based method gets improved. So proper l leak should be selected in order to ### A DCT-based Local Feature Extraction Algorithm For Palm-print Recognition

In the proposed method, instead of taking the DCT coefficients of the entire image, the DCT coefficients obtained form each module of an image are considered to form a feature vector. However, if all of these coefficients were used, it would definitely result in a feature vector with a very large dimension. One advantage of working in the DCT domain is that, because of its energy compaction property, a few DCT coefficients with higher magnitudes would be sufficient to represent a portion of an image. Hence, in view of reducing the feature dimension, we propose to utilize the magnitudes corresponding to the dominant DCT coefficients as spectral features. The 2D- DCT coefficient corresponding to the maximum magnitude is treated as the dominant coefficient (D1) and the corresponding 2D-frequencies are termed as the dominant frequencies. Considering the magnitudes of the 2D-DCT coefficients in descending order, magnitude values other than the dominant one may also be treated as possible candidates for desired features. In accordance with their magnitude values, these dominant magnitudes are termed as second-dominant (D2), third-dominant (D3), and so on. If the magnitude variations along all the segments for the case of different dominant magnitudes remain similar, it would be very difficult to select one of those dominant magnitudes as a desired feature. In order to demonstrate the characteristics of the dominant magnitudes in different modules, sample palm-print images of two different persons are shown in Fig. 9. In Fig. 10, four dominant magnitudes (D1, D2, D3, and D4) obtained from all the modules of the sample palm-print image of Person 1 appeared in Fig. 9(a) are shown. In this figure, the sample palm-print image is divided into 30 segments. It is found that different dominant magnitudes obtained from the spatial modules exhibit completely different characteristics. However, the magnitude value for the first dominant (D1) is found reasonably higher than other dominant magnitudes. An analogous behavior is obtained for Person 2 of Fig. 9(b). It is evident from Fig. 10 that D1 is the most significant among all the dominant magnitudes and thus, it is sufficient to consider only D1 as a desired feature, which also offers an advantage of reduced feature dimension. Computing D1 in each segment of the palm-print image, the proposed feature vector is obtained. For a palm-print image of dimension N × N with M number of segments (with ### Orthogonal Approximation of DCT in Video Compressing Using Generalized Algorithm ### A Hardware Efficient Robust Digital Image Watermarking Algorithm Using Integer DCT

For testing the algorithm, images of Lena, Baboon, Cameraman and Peppers are used. Fig. 6 shows the host images and fig. 7 shows the watermark images. In order to verify the performance of the proposed watermarking algorithm, PSNR, MSE and NC values are calculated and are reported in table I. The value of PSNR is satisfactorily good (above 40 dB) in all cases which implies the validity of the proposed algorithm. NC is excellent (equal to 1 in every case) that shows the successful retrieval of the watermark image without distortion. The original host image is taken to be of 512x512 in size and the watermark is a binary image of size 128x128 and the value of N=8. For testing the robustness of the algorithm, following attacks are considered: Blurring (5 degrees), 3x3 Median filtering, 50% Resizing and Gaussian noise (0.001). The proposed architecture is designed using VHDL and simulated in XILINX ISE 9.1. Spartan 3 family device is used for synthesis. The FPGA used is XCS200-4-FT256. The synthesis report and device utilization for the proposed architecture using XCS200 FPGA is given in table III and IV. The architecture designed using FPGA is suitable for real time applications because it provides less delay in computation which results in higher speed. Maximum combinational path delay in watermark embedding unit is 39.085ns and in watermark retrieval unit is 48.123ns. The results of simulation and synthesis done in XILINX ISE 9.1 for XCS200 FPGA clearly indicates that the architecture for the proposed image watermarking algorithm is area efficient and has high speed of operation. For three adder/subtractor circuits, six multiplexer units and two 8-bit comparators used in the embedding unit, only 24 slices and 42 LUTs are used. One in-built 18x18 multiplier is used. In retrieval unit, 17 slices and 30 LUTs are used. These ### A Proposed Approach to Hide Image on Video Using DCT and ID3 Algorithm of Data Mining

Image or Signal being transformed by DCT is converted to m×m block most probably it is 8×8 block only. The Steganography can be performed on image by breaking the image into 8×8 blocks of pixels. The DCT is applied to each block from left to right and top to bottom. Then through Quantization table, each block is compressed to scale the DCT Coefficients and message is embedded on it. And then to extract the image again inverse DCT is performed. ### Efficient Hybrid DCT-Domain Algorithm for Video Spatial Downscaling

A highly eﬃcient video downscaling algorithm for any arbitrary integer scaling factor performed in a hybrid pixel transform do- main is proposed. This algorithm receives the encoded DCT coeﬃcient blocks of the input video sequence and eﬃciently computes the DCT coeﬃcients of the scaled video stream. The involved steps are properly tailored so that all operations are performed using the encoding standard block structure, independently of the adopted scaling factor. As a result, the proposed algorithm oﬀers a significant optimization of the computational cost without compromising the output video quality, by taking into account the scaling mechanism and by restricting the involved operations in order to avoid useless computations. In order to meet any system needs, an optional and possible combination of the presented algorithm with high-order AC frequency DCT coeﬃcients discarding techniques is also proposed, providing a flexible and often required complexity scalability feature and giving rise to an adaptable tradeoﬀ between the involved scalable computational cost and the resulting video quality and bit rate. Experimental results have shown that the proposed algorithm provides significant advantages over the usual DCT decimation approaches, both in terms of the involved computational cost, the output video quality, and the resulting bit rate. Such advantages are even more significant for scaling factors other than integer powers of 2 and may lead to quite high PSNR gains. ### Design and Implementation of Modified Butterworth Filter for Watermarking

Watermarking can resolve the stealing problem of intellectual properties. The main objective of this paper was to design and implement Modified Butterworth filter for improvement of image quality in watermarking. Two performance parameters (PSNR & MSE) were used for analyzing the proposed approach. The experimental analysis was carried out by implementing Basic DCT algorithm, DCT algorithm with existing Butterworth filter and DCT algorithm with Modified Butterworth filter for five different file formats of original image and watermark image The experimental results show that the PSNR value is highest and the MSE value is lowest for png file format in comparison to other file ### DCT/IDCT Implementation with Loeffler Algorithm

In this paper, a novel 8-point DCT/IDCT processor is implemented using Loeffler factorization. This paper also describes how to avoid floating point arithmetic for implementation of DCT/IDCT. Minimum 11 multiplications are used for implantation. In future, the work can extended to the N bit variable input signals. The implemented design can be used as a basic block for further computation. The pipelined architecture can also be added to DCT and IDCT. The proposed processor can be integrated with other components which can be used as a stand-alone processor for many applications.