Implementation of Hadamard Matrices for Image Processing

Chapter
Part of the Intelligent Systems Reference Library book series (ISRL, volume 73)

Abstract

The image quality influences the accuracy of obtained results. In the chapter, the application of the strip-method for noise-immune storage and transmission of images is analyzed. At the same time, before transmitting the matrix transformation of an original image has to be done, when the image fragments are mixed up and superimposed each other. The transformed image is transmitted over a communication channel, where it is distorted with a pulse noise, the latter being, for example, a possible reason for a complete loss of separate image fragments. After the signal transmission to the receiving end, an inverse transformation is performed. During this transformation, the reconstruction of the image takes place. If it is possible to provide a uniform distribution of the pulse noise over the whole area, which the image occupies without any changes of its energy, then a noticeable decrease of noise amplitude will take place and an acceptable quality of all fragments of the image are reconstructed. The tasks of the chapter are the consideration the versions of the two-sided strip-transformation of images and the choice of optimal transformation matrices. A great attention has been paid to the implementation of Hadamard matrices and matrices close to them such as Hadamard-Mersenne, Hadamard-Fermat, and Hadamard-Euler matrices.

Keywords

Image quality Strip-method Image transmission Matrix transformations Pulse noise Inverse transformation Hadamard matrix Two-levels M-matrix Three-levels M-matrix Multi-levels M-matrices 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.St. Petersburg State University of Aerocosmic InstrumentationSt. PetersburgRussian Federation
  2. 2.D.I. Mendeleyev Research Institute for MetrologySt. PetersburgRussian Federation

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