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Some Applications of Singular Values Decomposition in Image Processing

Ghobadi Ghadikalaei, Vahideh | 2009

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 39421 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahdavi Amiri, Nezamoddin
  7. Abstract:
  8. The field of digital image processing refers to processing digital images by means of a digital computer. One of the principal applications used in digital image processing is image compression. Image compression is the problem of reducing the amount of data required to represent a digital image. The basis of the reduction process is the removal of redundant data. One of the other principal applications of image processing is noise reduction (filtering) of images corrupted with additive noise. Filtering techniques are oriented toward modeling the degradation and applying the inverse process in order to recover the original image. Image watermarking is another application of image processing. A digital watermark is a sequence of information that is inserted invisibly in another image (host image) so that it can be extracted at later times for the evidence of rightful ownership. Any real valued matrix can be decomposed uniquely as, where and are orthogonal matrices and is a diagonal matrix. The diagonal elements of can be arranged in a descending order and are called the singular values of . An image is just an matrix, where entry is interpreted as the brightness of pixel . Then we can decompose image into its singular values decomposition representation, and it is possible to represent many image processing operations in terms of linear algebra. In this thesis, we describe some methods of using singular values decomposition in image compression, image restoration and image watermarking. We implement described methods in Matlab R2006a, and then show the results on some images
  9. Keywords:
  10. Image Processing ; Singular Value Decomposition (SVD) ; Image Compression ; Image Watermarking ; Noise Reduction

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