Fundamentals of digital image processing
Fundamentals of digital image processing
Digital image processing
Two-dimensional signal and image processing
Two-dimensional signal and image processing
SIAM Review
A Course in Digital Signal Processing
A Course in Digital Signal Processing
Image and Video Compression Standards: Algorithms and Architectures
Image and Video Compression Standards: Algorithms and Architectures
IEEE Computer Graphics and Applications
Algorithms for Manipulating Compressed Images
IEEE Computer Graphics and Applications
IEEE Transactions on Computers
Symmetric convolution and the discrete sine and cosine transforms
IEEE Transactions on Signal Processing
Manipulation and compositing of MC-DCT compressed video
IEEE Journal on Selected Areas in Communications
Fast DCT domain filtering using the DCT and the DST
IEEE Transactions on Image Processing
Comments on “Fast algorithms and implementation of 2-D discrete cosine transform”
IEEE Transactions on Circuits and Systems for Video Technology
DCT convolution and its application in compressed domain
IEEE Transactions on Circuits and Systems for Video Technology
Hybrid fractal image coding with quadtree-based progressive structure
Journal of Visual Communication and Image Representation
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Discrete trigonometric transforms, such as the discrete cosine transform (DCT) and the discrete sine transform (DST), have been extensively used in signal processing for transform-based coding. The even type-II DCT, used in image and video coding, became specially popular to decorrelate the pixel data and minimize the spatial redundancy. Albeit this DCT tends to be the most often used, it integrates a broader family of transforms composed of eight DCTs and eight DSTs. However, even though most applications require little knowledge more than the actual DCT definition and its inverse, it is often widely regarded that the implementation of more complex operations on transformed data sequences (transcoding) requires a more in-depth knowledge about its precise definitions and formal mathematical properties. One of such relations is the multiplication-convolution property, often required to implement more specific and complex manipulations. Considering that such information is still spread into several documents and manuscripts, the main purpose of this article is to provide a broad set of practical and useful information in a single and self-contained source, embracing a wide range of definitions and properties related to the DCT and DST families, with a special emphasis on its application to image and video processing.