American Institute of Mathematical Sciences

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August  2007, 1(3): 557-575. doi: 10.3934/ipi.2007.1.557

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, United States
2. 

Department of Mathematics, University of Kentucky, Lexington, KY 40515, United States

Received  February 2007 Revised  April 2007 Published  July 2007

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.
Keywords: Markov gradient descent, quanta set, total variation, Quantization, quantum, segmentation, photometric., maximum likelihood, geometric.
Mathematics Subject Classification: Primary: 94A08; Secondary: 68U10, 49N4.
Citation: Jianhong (Jackie) Shen, Sung Ha Kang. Quantum TV and applications in image processing. Inverse Problems and Imaging, 2007, 1 (3) : 557-575. doi: 10.3934/ipi.2007.1.557
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