TY - JOUR
T1 - The Discrete Cosine Transform and Its Impact on Visual Compression
T2 - Fifty Years From Its Invention [Perspectives]
AU - Wang, Yao
AU - Mukherjee, Debargha
N1 - Publisher Copyright:
© 1991-2012 IEEE.
PY - 2023/9/1
Y1 - 2023/9/1
N2 - Compression is essential for efficient storage and transmission of signals. One powerful method for compression is through the application of orthogonal transforms, which convert a group of N data samples into a group of N transform coefficients. In transform coding, the N samples are first transformed, and then the coefficients are individually quantized and entropy coded into binary bits. The transform serves two purposes: one is to compact the energy of the original N samples into coefficients with increasingly smaller variances so that removing smaller coefficients have negligible reconstruction errors, and another is to decorrelate the original samples so that the coefficients can be quantized and entropy coded individually without losing compression performance. The Karhunen-Loève transform (KLT) is an optimal transform for a source signal with a stationary covariance matrix in the sense that it completely decorrelates the original samples, and that it maximizes energy compaction (i.e., it requires the fewest number of coefficients to reach a target reconstruction error). However, the KLT is signal dependent and cannot be computed with a fast algorithm.
AB - Compression is essential for efficient storage and transmission of signals. One powerful method for compression is through the application of orthogonal transforms, which convert a group of N data samples into a group of N transform coefficients. In transform coding, the N samples are first transformed, and then the coefficients are individually quantized and entropy coded into binary bits. The transform serves two purposes: one is to compact the energy of the original N samples into coefficients with increasingly smaller variances so that removing smaller coefficients have negligible reconstruction errors, and another is to decorrelate the original samples so that the coefficients can be quantized and entropy coded individually without losing compression performance. The Karhunen-Loève transform (KLT) is an optimal transform for a source signal with a stationary covariance matrix in the sense that it completely decorrelates the original samples, and that it maximizes energy compaction (i.e., it requires the fewest number of coefficients to reach a target reconstruction error). However, the KLT is signal dependent and cannot be computed with a fast algorithm.
UR - http://www.scopus.com/inward/record.url?scp=85172243919&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85172243919&partnerID=8YFLogxK
U2 - 10.1109/MSP.2023.3282775
DO - 10.1109/MSP.2023.3282775
M3 - Article
AN - SCOPUS:85172243919
SN - 1053-5888
VL - 40
SP - 14
EP - 17
JO - IEEE Signal Processing Magazine
JF - IEEE Signal Processing Magazine
IS - 6
ER -