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Mathematics in Image Processing: (IAS/Park City Mathematics Series)

Mathematics in Image Processing: (IAS/Park City Mathematics Series)


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About the Book

The theme of the 2010 PCMI Summer School was Mathematics in Image Processing in a broad sense, including mathematical theory, analysis, computation algorithms and applications. In image processing, information needs to be processed, extracted and analysed from visual content, such as photographs or videos. These demands include standard tasks such as compression and denoising, as well as high-level understanding and analysis, such as recognition and classification. Centred on the theme of mathematics in image processing, the summer school covered quite a wide spectrum of topics in this field. The summer school is particularly timely and exciting due to the very recent advances and developments in the mathematical theory and computational methods for sparse representation.

This volume collects three self-contained lecture series. The topics are multi-resolution based wavelet frames and applications to image processing, sparse and redundant representation modelling of images and simulation of elasticity, biomechanics, and virtual surgery. Recent advances in image processing, compressed sensing and sparse representation are discussed.

Table of Contents:

  • Preface
  • Hongkai Zhao: Introduction
  • Bin Dong and Zuowei Shen: MRA-Based Wavelet Frames and Applications
  • Introduction
  • Lecture 1. Multiresolution analysis
  • Lecture 2. MRA-based tight wavelet frames
  • Lecture 3. Pseudo-splines and tight frames
  • Lecture 4. Frame based image restorations
  • Lecture 5. Other applications of frames
  • Bibliography
  • Michael Elad: Five Lectures on Sparse and Redundant Representations Modelling of Images
  • Preface
  • Lecture 1. Introduction to sparse approximations - algorithms
  • Lecture 2. Introduction to sparse approximations - theory
  • Lecture 3. Sparse and redundant representation modelling
  • Lecture 4. First steps in image processing
  • Lecture 5. Image processing - more practice
  • Bibliography
  • J. M. Teran, J. L. Hellrung, Jr. and J. Hegemann: Simulation of Elasticity, Biomechanics, and Virtual Surgery
  • Introduction
  • Real-time computing
  • Lecture 1. Introduction to continuum mechanics and elasticity
  • Lecture 2. Numerical solutions of the equations of elasticity
  • Lecture 3. Supplemental material
  • Bibliography


About the Author :
Hongkai Zhao, University of California, Irvine, CA, USA.

Review :
...the book gives nice and concise overviews on wavelet-frame based image processing, spare and redundant representation models and simulation of elastic materials and can be recommended to students and lecturers." - DMV


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Product Details
  • ISBN-13: 9780821898413
  • Publisher: American Mathematical Society
  • Publisher Imprint: American Mathematical Society
  • Language: English
  • Series Title: IAS/Park City Mathematics Series
  • ISBN-10: 0821898418
  • Publisher Date: 30 Jul 2013
  • Binding: Hardback
  • No of Pages: 245
  • Weight: 670 gr


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