Non-differentiable constrained signal restoration by subgradient level methods.
Item
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Title
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Non-differentiable constrained signal restoration by subgradient level methods.
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Identifier
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AAI9986354
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identifier
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9986354
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Creator
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Luo, Jian.
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Contributor
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Adviser: Patrick L. Combettes
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Date
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2000
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Language
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English
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Publisher
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City University of New York.
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Subject
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Engineering, Electronics and Electrical
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Abstract
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The classical signal restoration problem is to estimate the original form of a signal from a degraded observation and some a priori information. Mathematically, a wide range of digital signal restoration problems can be formulated as minimizing a convex objective over a convex set representing the constraints derived from a priori knowledge and the observed signal. The goal of this dissertation is to develop numerical algorithms to solve this type of problems with nondifferentiable objectives. Such objectives arise for instance in constrained minimax, total variation, or L1 norm problems. They have become popular in recent years due to their ability to capture certain features of signals such as sharp edges. However, the problem of developing reliable numerical schemes to solve the resulting constrained nondifferentiable optimization problems has received little attention. In the algorithms proposed in this dissertation, the potentially complex constraint set is disintegrated into an intersection of simpler sets defined by convex inequalities. At each iteration, the update is obtained through a combination of subgradient projections onto the individual constraint sets and a subgradient projection onto adaptively refined approximations to the unknown optimal level set of the objective. Various algorithms based on this variable target feasibility principle are developed and their convergence is established. The implementation of the algorithms is also discussed. Several numerical applications to signal and image restoration/denoising are demonstrated, with special emphasis on the total variation approach.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
