Quantum TV and applications in image processing

Jianhong (Jackie) Shen; Sung Ha Kang

doi:10.3934/ipi.2007.1.557

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2007, Volume 1, Issue 3: 557-575. Doi: 10.3934/ipi.2007.1.557

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Quantum TV and applications in image processing

Jianhong (Jackie) Shen^1, and
Sung Ha Kang^2,

1.
School of Mathematics, University of Minnesota, Minneapolis, MN 55455
2.
Department of Mathematics, University of Kentucky, Lexington, KY 40515

Received: January 31, 2007

Revised: March 31, 2007

Published: July 2007

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Abstract

Closely inspired by the total variation (TV) model of Rudin, Osher and Fatemi [Physica D, 60:259-268,1992], we propose the quantized or quantum TV model (either with a preassigned quanta set $Q$ or without), and study the associated mathematical properties and computational algorithms. An algorithm based on stochastic or Markovian gradient descent is proposed to handle the discrete programming nature of the quantum TV model, which further leads to a two-step iterative algorithm for the computationally more challenging free quantum TV model. We also demonstrate several major applications of the proposed models and algorithms in bar code scanning, image quantization, and image segmentation.

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Mathematics Subject Classification: Primary: 94A08; Secondary: 68U10, 49N45.

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