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Squeezing through the pipe: digital compression
Published in Jonathan Higgins, Satellite Newsgathering, 2012
In general, adjacent pixels within an image tend to be similar and this can be exploited to eliminate redundancy. There are a number of mathematical analyses of a signal that can be made to determine the redundancy, but the one most commonly used in video compression is the discrete cosine transform (DCT). DCT is a specific implementation of a mathematical process called a Fourier transform, in which a signal is represented as a sum of a number of different frequency sinusoidal waves. The discrete cosine transform expresses an image block as a weighted sum of ‘basis functions’ that represent various horizontal and vertical spatial frequencies.
Multimedia Data Compression
Published in Sreeparna Banerjee, Elements of Multimedia, 2019
A finite sequence of data points can be expressed in terms of a sum of cosine functions oscillating at different frequencies using DCT. DCT is essentially a Fourier-related transform using only real numbers. The DCTs are equivalent to DFTs of roughly double the length, operating on data with even symmetry. Since computations are on real numbers only, DCT is advantageous over DFT where computations are performed on complex numbers. The 2D DCT is defined as: b(u,v)=2NC(u)C(v)∑x=0N−1∑y=0M−1a(x,y)cos{πu(2x+1)2N}cos{πv(2y+1)2M}
Digital Video Transmission
Published in Goff Hill, The Cable and Telecommunications Professionals' Reference, 2012
The Discrete Cosine Transform (DCT) separates the image into parts (or spectral subbands) of differing importance with respect to the image's visual quality. The DCT is similar to the discrete Fourier transform: It transforms a signal or image from the spatial domain to the frequency domain. With an input image, A, the coefficients for the output image, B, are B(k1,k2)=∑i=0N1−1∑j=0N2−14⋅A(i,j)cos[π⋅k12⋅N1⋅(2⋅i+1)]⋅cos[π⋅k22⋅N2⋅(2⋅j+1)]
An unsupervised heterogeneous change detection method based on image translation network and post-processing algorithm
Published in International Journal of Digital Earth, 2022
Decheng Wang, Feng Zhao, Hui Yi, Yinan Li, Xiangning Chen
DCT is a special form of Discrete Fourier Transform (DFT) (Oktem and Ponomarenko 2007). If in the Fourier series expansion, the function to be expanded is a real even function, then only the cosine term is included in the Fourier series, and thus the DCT transform can be obtained. After DCT, the binary change map forms the DCT coefficient map. The upper left corner represents the low-frequency part. The farther away from the upper left corner, the higher the frequency. The position where the more prominent value component appears represents the frequency distribution of the image. A patch proportional to the image size is used to intercept the low-frequency part of the DCT coefficients to filter out high-frequency noise. For the size of the image patch, a series of reference values are set. According to experiments, it is found that the smaller the size of the selected image patch, the more pronounced the noise removal, but the more the loss in the details of the changed image. The larger the selected image patch, the more details of the changed image are retained, but the noise removal effect is poor. Therefore, the image patch size has become an important factor in the quality of the generated change map.
Secured steganographic scheme for highly compressed color image using weighted matrix through DCT
Published in International Journal of Computers and Applications, 2021
Partha Chowdhuri, Biswapati Jana, Debasis Giri
DCT converts a digital signal into frequency domain. The one-dimensional DCT is used for processing one-dimensional signals such as speech whereas 2D DCT is useful for image and video processing. In DCT, most significant information of a digital image is represented by low-frequency coefficients. This property is known as energy compaction. Because of its strong energy compaction property, it is used for lossy data compression used in JPEG images. This energy compaction feature of DCT separates and removes high-frequency insignificant components from images. The two-dimensional forward transform formula of DCT is given below: where and The inverse DCT transformation formula is given below:
An efficient design of CORDIC in Quantum-dot cellular automata technology
Published in International Journal of Electronics, 2019
Ismail Gassoumi, Lamjed Touil, Bouraoui Ouni, Abdellatif Mtibaa
On the other hand, the Coordinate Rotation Digital Computer (CORDIC) (Volder, 1959, 2000) is a well-known algorithm using simple adders and shifters to evaluate various elementary functions. It has been widely applied in digital signal processing applications (especially in image/video processing) including Direct Digital Frequency Synthesizers (DDS), digital filter, linear system, matrix solver and Fast Fourier Transform (FFT) (Doukhnitch & Ozen, 2011; Ercegovac & Lang, 1990; Huang & Xiao, 2013; Hu & Chern, 1990; Park & Yu, 2012; Sun, Ruan, Heyne, & Goetze, 2007; Vaidyanathan, 1985; Yu & Swartzlander, 2002). Image processing algorithms like image rotation and Hough transform have been implemented using CORDIC. The CORDIC can also be used for computation of Discrete Cosine Transform (DCT). It provides an energy efficient method for computation of DCT which can be used in JPEG image compression. CORDIC algorithm plays an important role for these applications. In this area, due to the explosive growth of multimedia applications, the demand for low-power implementations of complex signal processing algorithms are tremendously increasing. In addition, designers need to estimate, rapidly and accurately, both power consumption and area occupation of complex applications. QCA technology has been emerged as an attractive solution for designers to address this challenge at the nanoscale level.