Abstract
Closely inspired by the total variation (TV) model of Rudin, Osher and Fatemi [<em>Physica D</em>, 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 <em> free</em> 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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