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Image Compression by Graph Signal Processing

Sabbaqi, Mohammad | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 52430 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Babaiezadeh, Masoud
  7. Abstract:
  8. Image compression is a noteworthy problem in image processing field. Transform coding provides a scheme to confront the image compression problem. The discrete cosine transform (DCT) is used in the majority of image compression standards by transform coding. The DCT can efficiently represent smooth signals, but it becomes inefficient when the image contains arbitrary-shaped discontinuities. As an example, piecewise-smooth images (i.e., an image that contains multiple smooth areas separated with arbitrary-shaped boundaries), which are widely used in 3-dimensional image representation, cannot well represent by the DCT. Therefore, replacing the DCT with an adaptive transform can improve image compression performance. By the advent of graph signal processing, brand-new methods and tools are provided for structural-aware signal processing. Graph Fourier transform is one of these tools, and it can capture the structure of the image as an adaptive transform, to design a proper image representation for image compression. One of the main drawbacks of graph-based image compression techniques lies in the cost required to represent the graph, which may outweigh the gain provided by the graph Fourier transform. Hence, we took the graph-based transform learning method as the basis of our works in this thesis. Initially, we proposed a fast and scalable algorithm for solving the optimization problem in graph-based transform learning method to overcome one of its disadvantages.Then, to find similar structures in the image patches, we proposed an algorithm for multiple graph learning problem, called K-graphs. Moreover, we proposed an algorithm to design a low representation cost graph, corresponding to a graph Fourier transform. Finally, by applying this algorithm and K-graphs algorithm together, we proposed an image compression method. For the sake of using similar structures in an image, this algorithm has much better performance than the graph-based transform learning method
  9. Keywords:
  10. Image Compression ; Graph Signal Processing ; Graph Fourier Transform ; Graph Learning ; Multiple Graph Learning

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