An example of application of Hebbian learning rule to image compression

The proliferation of multi-media tools in computer communication networks has increased the demand for techniques to improve the efficiency of transmission and storage of image; so a large variety of algorithm for image compression has been realized.
The basic idea behind a class of image compression algorithms is to exploit the fact that nearby pixels in images are often highly correlate. A given image is therefore divided into several blocks of pixels, and each block (treated as vector) is linearly transformed into a vector whose component are mutually uncorrelated. These components are then independently quantized for transmission or storage. The reconstruction of the original image is obtained by using an inverse linear transform operation on the quantized coefficient vector. The optimal transform in which the average mean-squared reconstruction error is minimized is called Principal Component Analysis (or Karhunen-Loeve transform).

Image compression process consists of two phases:

  1. The image is used to train the network;
  2. With the trained network the image is compressed;
1. The network has mxn input neurons fully connected with k output neurons. The image to be compressed is divided into blocks of pixels with size mxn. The image is scanned from left to right and top to bottom, and these vectors are consecutively presented to the input units of the network.


2. The image is compressed by multiplying each block represented as a N-dimensional vector by each of the M weight vectors obtained after training to generate M coefficients for coding the block. Assuming that each block consists of pxp pixels, the coefficients for the block bn,m starting at position (n*p+1,m*p+1) in the image I are given by:


This values are a compressed representation of the original image.
To reconstruct the image from the yi this rule is used:

where k is the number of the output neurons.

This is an example of image compression: the first is the original image, the second is the same image compressed and then reconstructed.


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