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Discrete Universal Denoising: An Extension for Noisy Sequence Correction

The L-DUDE method offers denoising for discrete sequences with unknown clean distribution. It excels in correcting noisy sequences and is compared with the Original DUDE method. Applications include time-varying Markov chains, piece-wise stationary sequences, and images.

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Discrete Universal Denoising: An Extension for Noisy Sequence Correction

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  1. L-DUDE: An extension of the Discrete Universal Denoiser Manuel Gomez-Rodriguez BorjaPeleato-Inarrea

  2. Discrete Universal Denoising • The problem consists on denoising a discrete sequence that uses a finite alphabet. • Unlike in traditional approaches, the distribution of the clean sequence is unknown. • Information: • Noise distribution • Clean sequence is stationary (has SOME structure)

  3. Original DUDE CLEAN: YOU ARE SWEATING IN THAT SWEATER WHILE EATING MELTING CRAB NOISY: YOU ARE SWEATIRG IN THAT SWEHTER WHILE EATING MELTING CRAP CORRECTED YOU ARE SWEATING IN THAT SWEATER WHILE EATING MELTING CRAP

  4. L-DUDE • CLEAN: 1010101010101020202020202020202020202 • NOISY: 1010501010101060202020202020702020202 • DUDE: 2020202020202020202020202020202020202 • L-DUDE: 1010101010101010202020202020202020202

  5. Applications • Several scenarios have been considered: • Time-varying Markov Chains • Piece-wise stationary sequences • Stationary sequences • Images • Performance of L-DUDE and DUDE are compared.

  6. Time-varying Markov Chains Binary Markov source with one time-varying parameter passed through a BSC. Ternary Markov source with 5 time-varying parameters passed through a 5-ary symmetric channel

  7. Time-varying Markov Chains Binary Markov source with one time-varying parameter passed through a BSC. Ternary Markov source with 5 time-varying parameters passed through a 5-ary symmetric channel

  8. Piece-wise stationary sequence • Sequence drawn from a set of 5-state Markov Chains. There are unknown switching times.

  9. Stationary sequences

  10. Images Noisy image L-DUDE DUDE

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