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Universal schemes for denoising disc...

Sivaramakrishnan, Kamakshi.

Universal schemes for denoising discrete-time continuous-amplitude signals.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Universal schemes for denoising discrete-time continuous-amplitude signals.
Author:	Sivaramakrishnan, Kamakshi.
Description:	180 p.
Notes:	Adviser: Tsachy Weissman.
Notes:	Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1227.
Contained By:	Dissertation Abstracts International69-02B.
Subject:	Statistics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3302872
ISBN:	9780549489153

Universal schemes for denoising discrete-time continuous-amplitude signals.
Sivaramakrishnan, Kamakshi.

Universal schemes for denoising discrete-time continuous-amplitude signals. - 180 p.

Adviser: Tsachy Weissman.

Thesis (Ph.D.)--Stanford University, 2008.

Noise removal (denoising) algorithms have been studied extensively in the statistical signal processing literature due to the significant impact of novel solutions to this problem in both engineering and scientific problems. Most techniques in the literature, so far, have been developed under specific assumptions on the statistics of the noise and the underlying 'clean' data. The optimality of these algorithms, however, is guaranteed only as far as model assumptions hold, which is not necessarily the case in many practical problems. In light of this, there is a need to develop denoising techniques that are provably optimal under general noise settings and statistics of the underlying clean data. In this thesis we discuss a universal, sequential denoising scheme which, based on the statistics of the noisy observations, estimates the underlying clean data in a manner that minimizes a user-specified loss function. This scheme compares with a genie-aided scheme that makes its decisions knowing the true distribution of the underlying clean sequence. We show that, with increasing block lengths of the noisy data, the performance of our scheme (probabilistically) approaches the performance of the genie-aided scheme at an exponential rate. Using this fact, we establish the universality of the proposed sequential scheme in the sense of asymptotically achieving the performance of the genie-aided scheme. These optimality results are established both in the semi-stochastic (where the underlying clean sequence is an unknown deterministic sequence and the only source of randomness is in the noise) and the fully stochastic setting (where the underlying clean source is stochastic as well, but at least stationary). We discuss the computational complexity of this sequential scheme and demonstrate its practicality and performance with encouraging experimental results.

ISBN: 9780549489153Subjects--Topical Terms:

182057
Statistics.

Universal schemes for denoising discrete-time continuous-amplitude signals.
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245 1 0 $a Universal schemes for denoising discrete-time continuous-amplitude signals.
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500 $a Adviser: Tsachy Weissman.
500 $a Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1227.
502 $a Thesis (Ph.D.)--Stanford University, 2008.
520 $a Noise removal (denoising) algorithms have been studied extensively in the statistical signal processing literature due to the significant impact of novel solutions to this problem in both engineering and scientific problems. Most techniques in the literature, so far, have been developed under specific assumptions on the statistics of the noise and the underlying 'clean' data. The optimality of these algorithms, however, is guaranteed only as far as model assumptions hold, which is not necessarily the case in many practical problems. In light of this, there is a need to develop denoising techniques that are provably optimal under general noise settings and statistics of the underlying clean data. In this thesis we discuss a universal, sequential denoising scheme which, based on the statistics of the noisy observations, estimates the underlying clean data in a manner that minimizes a user-specified loss function. This scheme compares with a genie-aided scheme that makes its decisions knowing the true distribution of the underlying clean sequence. We show that, with increasing block lengths of the noisy data, the performance of our scheme (probabilistically) approaches the performance of the genie-aided scheme at an exponential rate. Using this fact, we establish the universality of the proposed sequential scheme in the sense of asymptotically achieving the performance of the genie-aided scheme. These optimality results are established both in the semi-stochastic (where the underlying clean sequence is an unknown deterministic sequence and the only source of randomness is in the noise) and the fully stochastic setting (where the underlying clean source is stochastic as well, but at least stationary). We discuss the computational complexity of this sequential scheme and demonstrate its practicality and performance with encouraging experimental results.
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