Block and Sliding-Block Lossy Compression via MCMC
We propose an approach to lossy compression of finite-alphabet sources that utilizes Markov chain Monte Carlo (MCMC) and simulated annealing methods. The idea is to define an energy function over the space of reconstruction sequences. The energy of a candidate reconstruction sequence is defined such...
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| Published in | IEEE transactions on communications Vol. 60; no. 8; pp. 2187 - 2198 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.08.2012
Institute of Electrical and Electronics Engineers |
| Subjects | |
| Online Access | Get full text |
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| Abstract | We propose an approach to lossy compression of finite-alphabet sources that utilizes Markov chain Monte Carlo (MCMC) and simulated annealing methods. The idea is to define an energy function over the space of reconstruction sequences. The energy of a candidate reconstruction sequence is defined such that it incorporates its distortion relative to the source sequence, its compressibility, and the point sought on the rate-distortion curve. The proposed algorithm samples from the Boltzmann distribution associated with this energy function using the "heat-bath" algorithm. The complexity of each iteration is independent of the sequence length and is only linearly dependent on a certain context parameter, which grows sub-logarithmically with the sequence length. We show that the proposed algorithm achieves optimum rate-distortion performance in the limits of large number of iterations, and sequence length, when employed on any stationary ergodic source. Inspired by the proposed block-coding algorithm, we also propose an algorithm for constructing sliding-block (SB) codes using similar ideas. |
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| AbstractList | We propose an approach to lossy compression of finite-alphabet sources that utilizes Markov chain Monte Carlo (MCMC) and simulated annealing methods. The idea is to define an energy function over the space of reconstruction sequences. The energy of a candidate reconstruction sequence is defined such that it incorporates its distortion relative to the source sequence, its compressibility, and the point sought on the rate-distortion curve. The proposed algorithm samples from the Boltzmann distribution associated with this energy function using the "heat-bath" algorithm. The complexity of each iteration is independent of the sequence length and is only linearly dependent on a certain context parameter, which grows sub-logarithmically with the sequence length. We show that the proposed algorithm achieves optimum rate-distortion performance in the limits of large number of iterations, and sequence length, when employed on any stationary ergodic source. Inspired by the proposed block-coding algorithm, we also propose an algorithm for constructing sliding-block (SB) codes using similar ideas. |
| Author | Jalali, Shirin Weissman, Tsachy |
| Author_xml | – sequence: 1 givenname: Shirin surname: Jalali fullname: Jalali, Shirin organization: Center for Mathematics of Information at California Institute of Technology – sequence: 2 givenname: Tsachy surname: Weissman fullname: Weissman, Tsachy organization: Department of Electrical Engineering at Stanford University |
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| Keywords | Alphabet Lossy compression Performance evaluation Block code Energy function Rate distortion theory Ergodicity Iterative method Gibbs sampling Gibbs sampler MCMC algorithm Coding universal lossy compression Markov chain Monte Carlo Simulated annealing Rate-distortion coding |
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| SubjectTerms | Applied sciences Coding, codes Compression algorithms Encoding Entropy Exact sciences and technology Gibbs sampler Information, signal and communications theory Markov chain Monte Carlo Markov processes Rate-distortion Rate-distortion coding Signal and communications theory Simulated annealing Telecommunications and information theory universal lossy compression Vectors |
| Title | Block and Sliding-Block Lossy Compression via MCMC |
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