This book teaches the fundamentals and mathematical formulas of reversible transformations (or transforms) that are used in many source coding and signal processing systems. These mathematical transforms are often necessary or crucial toward reduction of data storage and transmission rate requirements. The author emphasizes the wavelet transform as it is the preferred transform for practical application in many coding and signal processing systems. The book also covers the tap (coefficient) values for some of those filters that satisfy the perfect reconstruction property. Examples of the use of filter-based and matrix-based transforms are also provided. This self-contained work contains insight gained through research and practice, which makes it a valuable reference and tutorial for readers interested in the subject of mathematical transforms.
This book:
- Teaches the fundamentals and mathematical formulas of reversible transformations, as well as their applications
- Highlights the wavelet transformation, which is the preferred transform for many practical applications
- Contains insight gained through research and practice, making it a valuable resource those interested in the topic
Introduction.- The Optimal Karhunen-Loeve Transform.- Suboptimal Transforms.- Lapped Orthogonal Transform.- Transforms via Filter Banks.- Two-Dimensional Transforms for Images.- Subband Transforms.- Concluding Remarks.- Problems.
William A. Pearlman, Ph.D., is the Founder, President, and Chief Scientific Officer of PrimaComp, Inc. He is also Professor Emeritus in the Electrical, Computer, and Systems Engineering Department at Rensselaer Polytechnic Institute. He is best known as co-inventor of two celebrated image compression algorithms, Set Partitioning in Hierarchical Trees (SPIHT) and Set Partitioning Embedded Block (SPECK) coding. Dr. Pearlman obtained his B.S. and M.S. degrees at MIT and his Ph.D. at Stanford University. He has authored or co-authored more than 250 publications in the fields of image and video compression, information theory, communications theory, and digital signal processing. He is lead author of the textbook, Digital Signal Compression: Principles and Practice, with co-author Amir Said, published by Cambridge University Press. He is also a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and a Fellow of the SPIE- The InternationalSociety for Optical Engineering.
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