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Light emitting diode (LED)-backlit liquid crystal displays (LCDs) hold the promise of improving image quality while reducing the energy consumption with signal-dependent local dimming. However, most existing local dimming algorithms are mostly motivated by simple implementation, and they often lack concern for visual quality. To fully realize the potential of LED-backlit LCDs and reduce the artifacts that often occur in current systems, we propose a novel local dimming technique that can achieve the theoretical highest fidelity of intensity reproduction in either l1 or l2 metrics. Both the exact and fast approximate versions of the optimal local dimming algorithm are proposed. Simulation results demonstrate superior performances of the proposed algorithm in terms of visual quality and power consumption.