Essay on Lossy compression

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ABSTRACT The requirement that no information be lost in the compression process puts a limit on the amount of compression we can obtain. The lowest number of bits per sample is the entropy of the source. This is a quantity over which we generally have no control. In many applications this requirement of no loss is excessive. For example, there is high frequency information in an image which cannot be perceived by the human visual system. It makes no sense to preserve this information for images that are destined for human consumption. In short, there are numerous applications in which the preservation of all information present in the source output is not necessary. For these applications we relax the requirement that the…show more content…
We pay for this decrease in distortion in several different ways. The first is through an increase in the complexity of the encoder. The scalar quantizer has a very simple encoder. In the case of the two-dimensional quan- -1.0 , -2.0 , -3.0 , -4.0 we need to block the input samples into “vectors” and then compare them against all the possible quantizer output values. For three bits per sample and two dimensions this translates to 64 possible compares. However, for the same number of bits and a block size, or vector dimension, of 10, the number of quantizer outputs would be 1,073,741,824! As it generally requires a large block size to get the full advantage of a vector quantizer, this means that the rate at which a vector quantizer (VQ) operates (i.e., bits per sample) is usually quite low. B. Predictive Coding If we have a sequence with sample values that vary slowly as in the signal shown in Fig. 11, knowledge of the previous samples gives us a lot of information about the current sample. This knowledge can be used in a number of different ways. One of the earliest attempts at exploiting this redundancy was in the development of differential pulse code modulation (DPCM) C. Transform Coding Transform coding consists of three steps. The data to be compressed is divided into blocks, and the data in each block is transformed to a set of coefficients. The transform is
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