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Decimation
 
Decimation is the reduction of data at the digitized signal. Fewer samples are used to represent the signal. Decimation can be realized by decimation in frequency or decimation in time.
The opposite process is called interpolation, more samples are added.
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Further Reading:
  Basics:
The Scientist and Engineer's Guide to Digital Signal Processing
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Filtering
 
Filtering deletes components of the signal, high or low frequencies, band-pass, analog or digital. Whatever pattern or algorithms can be defined for data decimation.
Low pass filtering attenuates high frequency data and passes low frequency data. The reconstructed image will look a little blurrier, but nearly similar to the original image. The blurring is caused by the fact that the high spatial frequencies are lost, which contain information about edges in the image.
High pass filtering attenuates low frequencies and passes high frequencies. Most of the objects and contrast of the original image are lost in the reconstructed image, but the edges are clearly visible because high frequency data has been preserved.
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Further Reading:
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MR Image Reconstruction from Raw Data
   by dukemil.egr.duke.edu    
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The Scientist and Engineer's Guide to Digital Signal Processing
   by www.dspguide.com    
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