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Chapter 5:
Rate-Distortion Theory and Lossy Compression
The performance bound on the encoding rate of an information source, as defined by the source entropy, pertains only to the lossless encoding of the data. In many practical situations, a certain degree of irreversible image degradation can be tolerated. This level of degradation is usually controlled by the user by adjusting a set of parameters, e.g., quantization intervals. A relevant question is: What is the minimum bit rate required to encode a source while keeping the resulting degradation below a certain level? This fundamental question is addressed by a branch of information theory known as rate-distortion theory [22]. Rate-distortion theory establishes theoretical performance bounds for lossy data compression according to a fidelity criterion. For a broad class of distortion measures and source models, the theory provides a rate-distortion function R(D) that has the following properties: - For any given level of distortion D, it is possible to find a coding scheme with rate arbitrarily close to R(D) and average distortion arbitrarily close to D. - It is impossible to find a code that achieves reproduction with distortion D (or better) at a rate below R(D).
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