Introduction - Introduction to Data Compression - page 5

Data obtained from satellites often are processed later to obtain different numerical indi-
cators of vegetation, deforestation, and so on. If the reconstructed data are not identical to
the original data, processing may result in “enhancement” of the differences. It may not be
possible to go back and obtain the same data over again. Therefore, it is not advisable to allow
for any differences to appear in the compression process.
There are many situations that require compression where we want the reconstruction to
be identical to the original. There are also a number of situations in which it is possible to
relax this requirement in order to get more compression. In these situations, we look to lossy
compression techniques.

1.1.2 Lossy Compression

Lossy compression techniques involve some loss of information, and data that have been
compressed using lossy techniques generally cannot be recovered or reconstructed exactly. In
return for accepting this distortion in the reconstruction, we can generally obtain much higher
compression ratios than is possible with lossless compression.
In many applications, this lack of exact reconstruction is not a problem. For example,
when storing or transmitting speech, the exact value of each sample of speech is not necessary.
Depending on the quality required of the reconstructed speech, varying amounts of loss of
information about the value of each sample can be tolerated. If the quality of the reconstructed
speech is to be similar to that heard on the telephone, a significant loss of information can be
tolerated. However, if the reconstructed speech needs to be of the quality heard on a compact
disc, the amount of information loss that can be tolerated is much lower.
Similarly, when viewing a reconstruction of a video sequence, the fact that the reconstruc-
tion is different from the original is generally not important as long as the differences do not
result in annoying artifacts. Thus, video is generally compressed using lossy compression.
Once we have developed a data compression scheme, we need to be able to measure its
performance. Because of the number of different areas of application, different terms have
been developed to describe and measure the performance.

1.1.3 Measures of Performance

A compression algorithm can be evaluated in a number of different ways. We could measure
the relative complexity of the algorithm, the memory required to implement the algorithm,
how fast the algorithm performs on a given machine, the amount of compression, and how
closely the reconstruction resembles the original. In this topic we will mainly be concerned
with the last two criteria. Let us take each one in turn.
A very logical way of measuring how well a compression algorithm compresses a given
set of data is to look at the ratio of the number of bits required to represent the data before
compression to the number of bits required to represent the data after compression. This ratio is
called the compression ratio . Suppose storing an image made up of a square array of 256

256
pixels requires 65,536 bytes. The image is compressed and the compressed version requires
16,384 bytes. We would say that the compression ratio is 4:1. We can also represent the
compression ratio by expressing the reduction in the amount of data required as a percentage

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